Quantile Connectedness Between Carbon Emission Allowances and Commodity Futures Markets: Evidence from China

Abstract

Carbon pricing is central to China’s low-carbon transition, and its effectiveness is tied to the carbon market’s links with commodities. This paper examines state-dependent return connectedness between China’s national carbon emission allowance (CEA) market and 20 representative commodity futures. Using daily data from July 2021 to February 2026, we combined quantile vector autoregression (QVAR) connectedness, the Baruník–Křehlík frequency decomposition, and wavelet-based coherence and quantile-based correlation methods to characterize return transmission across market states and frequencies. We obtained four findings. First, total connectedness is almost identical at the lower and upper tails (around 92%) and far higher than at the median (around 59%)—tail symmetry with median heterogeneity—and is dominated by the short-term band. Second, the CEA is largely decoupled from the commodity system under normal conditions and is drawn in only at the tails as a net receiver. Third, the two tails exhibit distinct event contexts, with downside episodes associated with external financial shocks and upside episodes associated with domestic policy expectations. Fourth, the CEA tends to precede high-emission commodities at long horizons. These results suggest that institutional and policy factors continue to play an important role in shaping CEA price dynamics, with implications for carbon market regulation and cross-market hedging.

1. Introduction

Climate change has become one of the major systemic challenges confronting the global economy, and carbon pricing has emerged as the principal market-based instrument for steering economies toward a low-carbon transition. More than 130 economies have now announced carbon neutrality or net zero pledges, and emissions trading mechanisms have spread from the European Union to China, the world’s largest emitter. As the carbon price is increasingly incorporated into firms’ production and investment decisions, it ceases to be an isolated environmental variable and becomes a financial price whose fluctuations can propagate across the broader commodity complex.

China launched its national carbon emission allowance (CEA) market in July 2021, consolidating a decade of regional pilots into a unified nationwide trading system that is now the world’s largest by covered emissions. The market has since entered a phase of rapid institutional change: the sectoral expansion reform proposed for public consultation in September 2024 and first implemented in March 2025 extends coverage from the power sector to steel, cement, and electrolytic aluminium. Because allowances are allocated and tightened through administrative aggregate control mechanisms, the CEA price is shaped by policy trajectories no less than by market fundamentals, giving it behavioral characteristics distinct from those of the more mature EU ETS. As the cornerstone of China’s dual-carbon goals—carbon peaking before 2030 and neutrality before 2060—the carbon market can steer the low-carbon transition only insofar as its price signal reaches the high-emission real economy; understanding its connectedness with commodity markets is therefore essential both for the effectiveness of carbon pricing and for managing transition-related financial risk.

Several economic channels link the CEA market to commodity futures. First, through a carbon cost channel, allowance prices enter directly into the marginal production costs of energy-intensive producers of steel, non-ferrous metals, and chemicals, so that carbon price shocks are transmitted to the pricing of the corresponding commodities. Second, through an energy price channel, the carbon and fossil energy markets respond jointly to common demand and macroeconomic conditions, generating co-movement between the CEA and energy-linked commodities. Third, through a supply chain cost transmission channel, allowance cost shocks propagate downstream along industrial production chains. Fourth, through a policy expectation channel, expectations of allowance tightening or market expansion move the CEA price and, via investors’ position adjustments, spill over to related commodities, consistent with evidence linking investor sentiment and news-driven shifts to observable asset-price movements [1].

A growing body of evidence documents these linkages, yet their scope remains incomplete. Studies of the carbon–energy–metal nexus consistently find significant and time-varying connectedness among these markets that strengthens during crises [2]; recent work on China further confirms that risk transmission between the carbon market and commodities is both frequency- and state-dependent [3], and exhibits extreme risk spillovers that intensify around climate and policy events [4]. Evidence from the national market also indicates that the CEA mainly acts as a net receiver of shocks from energy-intensive industries, occupying a relatively passive position in the risk transmission network [5]. However, existing studies either focus on commodity sectors and aggregate indices, or—although broader in coverage—rely on correlation-based methods and are largely based on pilot period data; a systematic characterization within a unified quantile–frequency–time framework, targeting the national market and a broad cross-section of individual futures, is still lacking.

Three gaps follow. First, systematic evidence on the unified national CEA market that covers a broad cross-section of individual commodity futures remains relatively limited: existing studies are either based on regional pilot data predating 2021 or focus on commodity sectors and aggregate indices, lacking heterogeneous characterization at the level of individual futures. Second, an integrated analysis that simultaneously captures state (quantile) heterogeneity, frequency heterogeneity, and localized time–frequency dependence within a single framework is still lacking; accordingly, the asymmetry between downside and upside extremes, and the change in asset roles between the short and long run, are difficult to identify systematically. Third, and more fundamentally, although recent evidence already points to the relatively passive, less-mature role of China’s national carbon market [5], this evidence is largely based on aggregate indicators and conventional connectedness frameworks; whether the national CEA behaves more like a financialized mature asset or a policy-driven institutional market therefore remains insufficiently understood.

To address these gaps, this paper examines the return connectedness between the CEA and 20 representative Chinese commodity futures from July 2021 to February 2026, combining four methods, each corresponding to a distinct dimension under a clear problem-to-tool mapping. To characterize connectedness that varies with the market state (quantile), we estimate a quantile vector autoregression (QVAR) and measure connectedness separately at the lower tail, the median, and the upper tail; to distinguish short- from long-run transmission, we follow Baruník and Křehlík [6] and decompose connectedness across frequency bands; to localize co-movement and lead–lag structure jointly in time and frequency, we apply wavelet coherence (WTC); and to characterize frequency-specific dependence that varies across quantiles, we employ wavelet quantile correlation (WQC).

This integrated chain is more informative than any single tool: mean-based connectedness would miss state (quantile) heterogeneity, a purely time-domain analysis would obscure the short- versus long-run sign changes, and a single-scale method could not reveal the localized, quantile-varying co-movements uncovered at the wavelet stage. The four tools are therefore complementary rather than redundant. Throughout, the QVAR–frequency connectedness analysis constitutes the core of the empirical design and addresses the three research questions directly, whereas the wavelet coherence and wavelet quantile correlation analyses provide complementary, corroborating evidence on the localized time–frequency and quantile structure of these linkages; the analysis is therefore organized around the empirical questions rather than around the methods.

Our results reveal a highly state-dependent system. Total connectedness is almost identical at the two extremes—around 92% at both the 5% and 95% quantiles—yet substantially lower at the median, around 59%, so that the system is symmetric in magnitude across the tails but markedly heterogeneous between normal and extreme states. Under normal conditions, connectedness is dominated by the short-term (one-to-five-day) band, whereas persistent external shocks are accompanied by episodes in which the long-term band overtakes the short-term band.

The CEA occupies a distinctive position. At the median, it is largely decoupled from the commodity system, with negligible connectedness in either direction; at both tails it turns into a net receiver. The event contexts associated with the two tails are themselves asymmetric: downside tail episodes coincide with external financial shocks (e.g., the March 2023 Silicon Valley Bank and Credit Suisse turmoil), whereas upside tail episodes align with domestic policy expectations surrounding the market-expansion reform. Wavelet analysis further shows that, over long horizons (about 64–256 days), the CEA tends to precede high-emission commodities such as aluminium, zinc, and coking coal and moves almost synchronously with crude oil, and that its positive co-movement with commodities is most concentrated at the median quantiles of the long-frequency band.

To make the empirical objectives explicit, the analysis is organized around three research questions:

RQ1: Is the connectedness between the CEA and commodity futures markets significantly stronger under extreme (tail) market states than under normal (median) conditions?

RQ2: What is the net directional role of the CEA within the system, and does this role differ between normal and tail states?

RQ3: How does the frequency dimension—short- versus long-run horizons—shape the transmission of risk between the CEA and commodity markets?

This paper makes three contributions, each addressing one of the gaps above. First, relative to existing studies that mostly examine China’s carbon–commodity relationship using sector indices or pilot period data (e.g., [3,7]), this paper targets the national carbon market (including the expansion period) and systematically characterizes its return connectedness with 20 individual commodity futures spanning six sectors, providing more granular and more timely evidence. Second, this paper uncovers the upside/downside tail asymmetry and the short- versus long-run differences in directional connectedness that single-method designs are less able to reveal, supplemented by evidence on the CEA’s long-horizon lead–lag co-movement with high-emission commodities and its frequency–quantile-specific dependence; these features have rarely been examined together in prior work. Third, the findings deepen the understanding of a more fundamental question—whether the national carbon market behaves as a financialized mature asset or a policy-driven institutional market. Building on prior evidence of the carbon market’s passive role [5], the individual-futures evidence indicates that, at the current stage, CEA price formation is still primarily shaped by institutional and policy factors rather than driven by market-based financial forces, thereby providing a basis for risk regulation and hedging under the ongoing market expansion.

The remainder of the paper is organized as follows. Section 2 reviews the related literature; Section 3 introduces the methodology and data; Section 4 reports and discusses the empirical results; and Section 5 concludes.

2. Literature Review

This study draws on three strands of literature: the interaction between carbon and commodity markets; research on dynamic spillovers and frequency- and tail-dependent connectedness; and the methodological evolution of connectedness measurement. We review each in turn and indicate where the present study extends it.

Research on carbon–commodity linkages has progressed from bivariate carbon–energy analyses to system-level connectedness. Internationally, energy fundamentals are regarded as important determinants of the EU ETS carbon price [8], and significant asymmetric spillovers exist between the carbon and energy markets [9]; studies also consistently find that the carbon, energy, and metal markets are integrated, with linkages that strengthen during crises and evolve over time [2]. For China, the evidence points to frequency- and state-dependent transmission between the carbon market and commodities [3], as well as extreme risk spillovers that intensify around climate and policy events [4]. A recurrent finding is that the national carbon market, as a latecomer, absorbs more shocks than it transmits to energy-intensive industries, occupying a relatively passive position in the system [5]. Closest to this paper, Qi et al. [3] use the Baruník–Křehlík frequency connectedness and the Baruník–Kley cross-quantile coherency methods to examine the time–frequency and quantile dependence of China’s carbon–commodity relationship based on sector indices over the pilot period (2013–2022); Zhao and Yang [7] employ a copula-CoVaR approach to characterize asymmetric tail spillovers between the carbon market and broad commodity sectors; and Wu and Huang [10] focus on the quantile–frequency connectedness of carbon–energy–metal markets. However, these studies are either based on pilot period data and sector indices or do not introduce wavelet time–frequency–quantile tools (WTC/WQC), and have not been applied to the national CEA market and individual commodity futures; thus, their state dependence, frequency-dependent sign changes, and time–frequency–quantile co-movement therefore remain to be systematically characterized.

A parallel strand studies how risk propagates across financial and commodity markets, emphasizing that connectedness is neither constant nor symmetric. Spillovers rise sharply during systemic episodes and reconfigure the network of transmitters and receivers [11]. Because mean-based measures cannot characterize tail behavior, recent work models connectedness across the entire return distribution, showing that linkages are typically stronger in extreme states than under normal conditions [12]. This amplification of connectedness in extreme states is consistent with broader macro-finance evidence that uncertainty shocks propagate across markets during periods of stress [13]. Another line of research combines the frequency domain with climate policy uncertainty, demonstrating that spillovers to commodity markets differ markedly between the short and long run [14]. However, tail dependence and frequency dependence are still mostly studied separately, and the joint question—whether upside and downside extremes are asymmetric and whether market roles reverse across frequencies—remains largely unresolved, particularly in the carbon–commodity setting.

The measurement of connectedness has developed along different problem dimensions, with each class of tool answering a different question rather than superseding the others. The generalized variance-decomposition framework of Diebold and Yilmaz [15,16] lays the time-domain foundation and characterizes connectedness at the conditional-mean level. Building on this, quantile connectedness [12,17] captures state-dependent, tail-sensitive transmission; the frequency decomposition of Baruník and Křehlík [6] distinguishes short- from long-run components; and wavelet methods describe dependence jointly in time and frequency—wavelet coherence localizes co-movement and lead–lag structure [18], and wavelet quantile correlation characterizes frequency-specific dependence that varies across quantiles [19,20]. These methods address distinct dimensions—state, frequency, and time–frequency localization—and are complementary rather than representing a linear progression. A few studies have begun to combine the quantile and frequency dimensions [21], but their integration with wavelet-based, quantile-varying co-movement analysis remains uncommon and has not been applied to China’s national carbon market.

Taken together, these strands motivate the present study. To our knowledge, relatively few prior studies have jointly, within a unified framework integrating quantile connectedness, frequency decomposition, and wavelet analysis, examined the return connectedness between China’s unified national CEA market and a broad cross-section of 20 commodity futures; this paper helps fill this gap.

3. Methodology and Data

3.1. Quantile Vector Autoregression (QVAR) Model

The conventional vector autoregression (VAR) model estimates inter-variable relationships within a conditional mean framework and cannot fully characterize tail dependence when return distributions exhibit heavy tails and asymmetry. The quantile vector autoregression (QVAR) model proposed by Ando et al. [12] extends the VAR framework to arbitrary quantile levels, enabling the analysis of spillover dynamics under different market states.

Let ${\mathrm{y}}_{\mathrm{t}}={\left({\mathrm{y}}_{1,\mathrm{t}},{\mathrm{y}}_{2,\mathrm{t}},\dots ,{\mathrm{y}}_{\mathrm{k},\mathrm{t}}\right)}^{\prime }$ denote a $\mathrm{k}$-dimensional return vector. The QVAR($\mathrm{p}$) model at quantile level $\mathrm{q}\in \left(\mathrm{0,1}\right)$ is given by:

$$Q_{{\mathrm{y}}_t}\left(q\mid {\mathcal{F}}_{t-1}\right)=\mathrm{\mu }\left(q\right)+{\displaystyle {\sum }_{j=1}^p}{\mathrm{\Phi }}_j\left(q\right)\hspace{0.17em}{\mathrm{y}}_{t-j}$$

(1)

where ${\mathrm{Q}}_{{\mathrm{y}}_{\mathrm{t}}}\left(\mathrm{q}\mid {\mathcal{F}}_{\mathrm{t}-1}\right)$ denotes the conditional $\mathrm{q}$-quantile vector of ${\mathrm{y}}_{\mathrm{t}}$ (given the information set ${\mathcal{F}}_{\mathrm{t}-1}$); $\mathrm{\mu }\left(\mathrm{q}\right)$ is the intercept vector at the corresponding quantile; and ${\mathrm{\Phi }}_{\mathrm{j}}\left(\mathrm{q}\right)$ is the k × k autoregressive coefficient matrix at the corresponding quantile. When q = 0.50, the QVAR reduces to the conditional-median VAR; when q takes tail quantiles, the model characterizes the dependence structure under extreme market conditions. This study selects q = 0.05, 0.50, and 0.95 as three representative quantiles, where 0.05 and 0.95 correspond to extreme bearish and bullish market conditions, respectively, and 0.50 corresponds to the normal market condition.

The QVAR parameters are estimated by applying quantile regression separately to each equation. For the i-th equation in the system, the following optimization problem is solved:

$${\widehat{\mathrm{\Phi }}}_i\left(q\right)=\mathrm{a}\mathrm{r}\mathrm{g}\underset{{\mathrm{\Phi }}_i}{\mathrm{m}\mathrm{i}\mathrm{n}}{\displaystyle {\sum }_{t=1}^T}{\rho }_q\left(y_{i,t}-{\mu }_i\left(q\right)-{\displaystyle {\sum }_{j=1}^p}{\mathrm{\Phi }}_{i,j}\left(q\right)\hspace{0.17em}{\mathrm{y}}_{t-j}\right)$$

(2)

where ${\mathrm{\rho }}_{\mathrm{q}}\left(\mathrm{u}\right)=\mathrm{u}\left(\mathrm{q}-1\left(\mathrm{u}<0\right)\right)$ is the quantile loss function. After estimation, the quantile regression residuals ${\widehat{\mathrm{u}}}_{\mathrm{t}}\left(\mathrm{q}\right)={\mathrm{y}}_{\mathrm{t}}-{\widehat{\mathrm{Q}}}_{{\mathrm{y}}_{\mathrm{t}}}\left(\mathrm{q}\mid {\mathcal{F}}_{\mathrm{t}-1}\right)$ are obtained, and $\widehat{\mathrm{\Sigma }}\left(\mathrm{q}\right)={\mathrm{T}}^{-1}{\displaystyle {\sum }_{\mathrm{t}=1}^{\mathrm{T}}}{\widehat{\mathrm{u}}}_{\mathrm{t}}\left(\mathrm{q}\right)\hspace{0.17em}{\widehat{\mathrm{u}}}_{\mathrm{t}}{\left(\mathrm{q}\right)}^{\prime }$ is constructed as the residual covariance matrix, which serves as the input for the subsequent generalized variance decomposition.

3.2. Generalized Forecast Error Variance Decomposition (GFEVD) and Connectedness Measures

Building on the QVAR estimation results, this study employs the generalized variance decomposition framework of Diebold and Yilmaz [15,16] to construct the connectedness measures. The framework adopts the GFEVD of Koop et al. [22] and Pesaran and Shin [23], and the resulting decomposition is invariant to variable ordering.

Following Chatziantoniou et al. [17], the QVAR system estimated at each quantile level is treated as a local linear VAR approximation under the corresponding market state, and the residual covariance matrix required for the GFEVD is constructed from the quantile regression residuals; the system is then inverted to obtain its VMA(∞) representation. At the H-step-ahead forecast horizon, the GFEVD from variable j to variable i is given by:

$${\tilde{\theta }}_{ij}^{\left(q\right)}\left(H\right)={\displaystyle \frac{{\sigma }_{jj}^{-1}\left(q\right){\displaystyle {\sum }_{h=0}^{H-1}}{\left({\mathrm{e}}_{i\prime }{\mathrm{\Psi }}_h\left(q\right)\hspace{0.17em}\Sigma \left(q\right)\hspace{0.17em}{\mathrm{e}}_j\right)}^2}{{\displaystyle {\sum }_{h=0}^{H-1}}{\mathrm{e}}_{i^{\prime }}{\mathrm{\Psi }}_h\left(q\right)\hspace{0.17em}\Sigma \left(q\right)\hspace{0.17em}{\mathrm{\Psi }}_{h^{\prime }}\left(q\right)\hspace{0.17em}{\mathrm{e}}_i}}$$

(3)

where Σ(q) is the residual covariance matrix, σ_jj(q) is its j-th diagonal element, e_i is the selection vector, and H is the forecast horizon. The row-normalized GFEVD is then:

$${\theta }_{ij}^{\left(q\right)}\left(H\right)={\displaystyle \frac{{\tilde{\theta }}_{ij}^{\left(q\right)}\left(H\right)}{{\displaystyle {\sum }_{j=1}^k}{\tilde{\theta }}_{ij}^{\left(q\right)}\left(H\right)}}\times 100$$

(4)

Each row of the normalized GFEVD therefore sums to 100. Here, θ_ij^(q)(H) represents, over a forecast horizon of H, the normalized contribution of variable j to the forecast error variance of variable i. Based on the normalized GFEVD, the following connectedness measures are defined:

The total connectedness index (TCI) measures the average intensity of spillover effects across all variables in the system, expressed as the average variance contribution across all i ≠ j pairs at forecast horizon H:

$$TC{I}^{\left(q\right)}\left(H\right)={\displaystyle \frac{1}{k}}{\displaystyle {\sum }_{\begin{array}{c}i,j=1\\ i\ne j\end{array}}^k}{\theta }_{ij}^{\left(q\right)}\left(H\right)$$

(5)

Directional connectedness characterizes the spillover relations between an individual variable and the others, and is decomposed into the spillovers received from all other variables (FROM) and the spillovers transmitted to all other variables (TO):

$$FRO{M}_i^{\left(q\right)}\left(H\right)={\displaystyle {\sum }_{\begin{array}{c}j=1\\ j\ne i\end{array}}^k}{\theta }_{ij}^{\left(q\right)}\left(H\right), T{O}_i^{\left(q\right)}\left(H\right)={\displaystyle {\sum }_{\begin{array}{c}j=1\\ j\ne i\end{array}}^k}{\theta }_{ji}^{\left(q\right)}\left(H\right)$$

(6)

The net total directional connectedness (NET) is defined as the difference between TO and FROM. A positive NET indicates that the variable is a net spillover transmitter in the system, whereas a negative value indicates a net receiver.

$$NE{T}_i^{\left(q\right)}\left(H\right)=T{O}_i^{\left(q\right)}\left(H\right)-FRO{M}_i^{\left(q\right)}\left(H\right)$$

(7)

The net pairwise directional connectedness (NPDC) measures the direction and magnitude of net spillovers between variable i and variable j; it is defined as the difference between the directional spillover from variable i to variable j and the reverse spillover:

$${NPDC}_{ij}^{\left(q\right)}\left(H\right)={\theta }_{ji}^{\left(q\right)}\left(H\right)-{\theta }_{ij}^{\left(q\right)}\left(H\right)$$

(8)

where NPDC_ij > 0 indicates that variable i is a net transmitter to variable j, NPDC_ij < 0 indicates that variable i is a net receiver from variable j, and its absolute value reflects the magnitude of the pairwise net spillover. The measure is antisymmetric, i.e., NPDC_ij = −NPDC_ji.

3.3. Baruník–Křehlík Frequency Decomposition

The Diebold–Yilmaz framework measures spillover effects in the time domain but cannot distinguish the contributions of different frequency bands. Baruník and Křehlík [6] extend the GFEVD into the frequency domain, allowing connectedness measures to be computed separately across distinct frequency bands and thereby identifying the relative importance of short-term shock transmission versus long-term structural spillovers.

Specifically, the Baruník–Křehlík (BK) approach applies a Fourier transform to the MA coefficient matrix ${\mathrm{\Psi }}_{\mathrm{h}}\left(\mathrm{q}\right)$ in the VMA(∞) representation to obtain the frequency response function. Building on this, the generalized causation spectrum decomposes the time-domain GFEVD into different frequency intervals, with the spectral density acting as a weight that captures each band’s contribution to overall connectedness. Let ${\tilde{\mathrm{\theta }}}_{\mathrm{i}\mathrm{j}}^{\left(\mathrm{q},\mathrm{d}\right)}\left(\mathrm{H}\right)$ denote the unnormalized frequency-domain variance decomposition share on the frequency band $\mathrm{d}=({\mathrm{\omega }}_{\mathrm{l}},{\mathrm{\omega }}_{\mathrm{u}}]$. The unnormalized total variance contribution decomposes exactly into the sum of the frequency-band shares:

$${\tilde{\theta }}_{ij}^{\left(q\right)}\left(H\right)={\sum }_d{\tilde{\theta }}_{ij}^{\left(q,d\right)}\left(H\right)$$

(9)

The share for each frequency band is normalized using the row sum of the total GFEVD as a common denominator:

$${\theta }_{ij}^{\left(q,d\right)}\left(H\right)={\displaystyle \frac{{\tilde{\theta }}_{ij}^{\left(q,d\right)}\left(H\right)}{{\displaystyle {\sum }_{j=1}^k}{\tilde{\theta }}_{ij}^{\left(q\right)}\left(H\right)}}\times 100$$

(10)

Because all bands share the same normalization denominator, additivity is preserved after normalization, i.e., ${\mathrm{\theta }}_{\mathrm{i}\mathrm{j}}^{\left(\mathrm{q}\right)}\left(\mathrm{H}\right)=\sum _{\mathrm{d}}{\mathrm{\theta }}_{\mathrm{i}\mathrm{j}}^{\left(\mathrm{q},\mathrm{d}\right)}\left(\mathrm{H}\right)$. The spectral density acts as a weight in the decomposition: even when connectedness within a given band is high, that band’s contribution to overall connectedness still depends on its share of total variance. Accordingly, the connectedness measure on the frequency band d is then defined as:

$$TC{I}^{\left(q,d\right)}\left(H\right)={\displaystyle \frac{1}{k}}{\displaystyle {\sum }_{\begin{array}{c}i,j=1\\ i\ne j\end{array}}^k}{\theta }_{ij}^{\left(q,d\right)}\left(H\right)$$

(11)

$\mathrm{N}\mathrm{E}\mathrm{T}$ and $\mathrm{N}\mathrm{P}\mathrm{D}\mathrm{C}$ admit analogous frequency-domain definitions. Because the BK frequency decomposition and the maximal overlap discrete wavelet transform (MODWT) correspond to different frequency representation systems, the BK framework is implemented using short-term (1–5 days) and long-term (above 5 days) frequency bands, whereas the WQC analysis adopts a MODWT-based multi-scale decomposition.

The baseline specification is selected as follows. The QVAR lag order is set to p = 1, which minimizes the Schwarz information criterion (SIC) among candidate orders from one to four. This parsimonious specification is also consistent with the weak serial dependence typically observed in daily financial returns and helps avoid over-parameterization in the twenty-one-variable system. Time-domain connectedness is computed at a forecast horizon of H = 20 trading days, the conventional choice in this literature [15,16], whereas the frequency decomposition (Baruník–Křehlík [6]) uses a longer horizon of 100 days, because reliable identification of persistent low-frequency connectedness requires a sufficiently long forecast horizon over which spectral variance shares can accumulate. Dynamic measures use a rolling window of w = 200 trading days, which balances the number of observations available to estimate the high-dimensional quantile system against the need to track time variation, in line with connectedness studies on daily financial data [11]. Following the frequency-partitioning convention in the connectedness literature [6], the short-term band covers one to five days (within-week transmission), whereas the long-term band captures horizons beyond five days. The three quantiles q = 0.05, 0.50, and 0.95 represent the lower-tail (downside stress), central (normal), and upper-tail (upside) states, a commonly adopted tail specification in the quantile connectedness literature [12,17]. The robustness section confirms that the main results are insensitive to shortening the window to w = 150 and the time-domain horizon to H = 10. Taken together, these checks indicate that the main conclusions are not driven by particular parameter choices.

The connectedness statistics are point estimates that do not, by themselves, convey sampling uncertainty (Diebold and Yilmaz [15,16]). To enable inference, we construct 95% confidence intervals by a moving block bootstrap following Greenwood-Nimmo et al. [24]: we draw B = 1000 resamples of the return matrix (block length of 20 trading days, resampled jointly across the 21 series to preserve serial and cross-sectional dependence), re-estimate the model on each resample, and report the 2.5th and 97.5th percentiles of each statistic. Tail symmetry is tested by bootstrapping the difference between the total connectedness indices at q = 0.05 and q = 0.95.

3.4. Wavelet Coherence (WTC)

To further characterize inter-market dependence along both the time and frequency dimensions, this study employs wavelet coherence to examine the co-movement patterns across markets, complemented by phase difference analysis of local lead–lag relations. Following Torrence and Compo [25], the cross-wavelet transform (XWT) of two time series a(t) and b(t) is defined as:

$$W_{ab}(u,s)=W_a(u,s)W_b^{\ast }(u,s)$$

(12)

where Wa(u,s) and Wb(u,s) denote the wavelet transforms of a(t) and b(t), respectively; u is the position index; s is the scale; and the superscript * denotes the complex conjugate. The cross-wavelet power spectrum reveals the distribution of common fluctuation energy in the time frequency domain, while the squared wavelet coherence coefficient captures the strength of local dependence between variables. Following Torrence and Webster [26], it is defined as:

$$R^2(u,s)={\displaystyle \frac{\mid M\left(M^{-1}{W}_{ab}\right(u,s\left)\right){\mid }^2}{M\left(M^{-1}{\left|W_a(u,s)\right|}^2\right)M\left(M^{-1}{\left|W_b(u,s)\right|}^2\right)}}$$

(13)

where $\mathrm{M}$ is the smoothing operator and ${\mathrm{R}}^2(\mathrm{u},\mathrm{s})$ takes values in [0, 1]: values close to 0 indicate weak dependence, while values close to 1 indicate strong dependence.

Following Grinsted et al. [18], a Monte Carlo simulation method based on an AR(1) red noise background spectrum is used to assess the statistical significance of the wavelet coherence coefficients, and the lead–lag relationship between the two series is characterized through the phase difference of the cross-wavelet transform.

3.5. Wavelet Quantile Correlation (WQC)

Kumar and Padakandla [20] build on the quantile correlation (QC) method of Li et al. [19] by introducing wavelet quantile correlation (WQC), which extends quantile correlation to the wavelet domain and characterizes the dependence structure between variables X and Y simultaneously along scale and quantile dimensions. Following Li et al. [19], Q_q,Y denotes the unconditional q-th quantile of Y, and Q_q,Y(X) denotes the q-th quantile of Y conditional on X.

The quantile covariance is defined as:

$${\mathrm{q}}_{{\mathrm{c}\mathrm{o}\mathrm{v}}_{\mathrm{q}}}(\mathrm{Y},\mathrm{X})=\mathrm{c}\mathrm{o}\mathrm{v}\left\{\mathrm{I}\left(\mathrm{Y}-{\mathrm{Q}}_{q,\mathrm{Y}}>0\right),\mathrm{X}\right\}=\mathrm{E}\left({\phi }_q\left(\mathrm{Y}-{\mathrm{Q}}_{q,\mathrm{Y}}\right)(\mathrm{X}-\mathrm{E}(\mathrm{X}\left)\right)\right.$$

(14)

where cov(·) denotes the covariance; I(·) is the indicator function; E(·) is the expectation operator; and q is the quantile level with 0 < q < 1.

The quantile loss function ${\phi }_q$ is defined as:

$${\phi }_q\left(\mathrm{w}\right)=q-\mathrm{I}(\mathrm{w}<0)$$

(15)

Li et al. [19] further define the quantile correlation as:

$${\mathrm{q}\mathrm{c}\mathrm{o}\mathrm{r}}_{\mathrm{q}}(\mathrm{Y},\mathrm{X})={\displaystyle \frac{{\mathrm{q}\mathrm{c}\mathrm{o}\mathrm{v}}_{\mathrm{q}}(\mathrm{Y},\mathrm{X})}{\sqrt{\left(\mathrm{v}\mathrm{a}\mathrm{r}\left({\phi }_q\left(\mathrm{Y}-{\mathrm{Q}}_{q,\mathrm{Y}}\right)\mathrm{v}\mathrm{a}\mathrm{r}\left(\mathrm{X}\right)\right)\right.}}}$$

(16)

Kumar and Padakandla [20] apply the maximal overlap discrete wavelet transform (MODWT) of Percival and Walden [27] to decompose the variables Xt and Yt. For the j-th level wavelet coefficients of Xt and Yt at each scale, the WQC is defined as:

$$WQ{C}_q\left(d_j\left[X\right],d_j\left[Y\right]\right)={\displaystyle \frac{q{\mathrm{c}\mathrm{o}\mathrm{v}}_q\left(d_j\left[Y\right],d_j\left[X\right]\right)}{\sqrt{\mathrm{v}\mathrm{a}\mathrm{r}\left({\phi }_q\left(d_j\left[Y\right]-Q_{q,d_j\left[Y\right]}\right)\right)\mathrm{v}\mathrm{a}\mathrm{r}\left(d_j\left[X\right]\right)}}}$$

(17)

where X and Y denote the two markets under consideration, respectively. The WQC takes values in [−1, 1] and characterizes market dependence simultaneously along the scale and quantile dimensions.

3.6. Data

This paper selects China’s carbon emission allowance market (CEA) together with 20 representative Chinese commodity futures to construct the sample (

Table 1. Variable description.

Category	Symbol	Name	Exchange
Carbon market	CEA	Carbon emission allowance	SEEE
Precious metals	AU	Gold	SHFE
	AG	Silver	SHFE
Non-ferrous metals	CU	Copper	SHFE
	AL	Aluminium	SHFE
	ZN	Zinc	SHFE
Ferrous metals	RB	Steel rebar	SHFE
	I	Iron ore	DCE
	J	Coke	DCE
	JM	Coking coal	DCE
Energy	SC	Crude oil	INE
	FU	Fuel oil	SHFE
Chemicals	TA	PTA (purified terephthalic acid)	ZCE
	MA	Methanol	ZCE
	EG	Ethylene glycol	DCE
	FG	Glass	ZCE
	SA	Soda ash	ZCE
Agriculture	M	Soybean meal	DCE
	P	Palm oil	DCE
	CF	Cotton	ZCE
	SR	White sugar	ZCE

Notes: Each series is the daily log return of the daily closing price (continuous main contract for the 20 commodity futures; national carbon allowance price for the CEA); all data are obtained from the Wind database. SHFE, Shanghai Futures Exchange; INE, Shanghai International Energy Exchange; DCE, Dalian Commodity Exchange; ZCE, Zhengzhou Commodity Exchange; SEEE, Shanghai Environment and Energy Exchange.

), with the sample period running from 19 July 2021 to 5 February 2026 and comprising 1106 daily observations. All data are sourced from the Wind database. The commodity sample includes the continuous main contract series of AU, AG, CU, AL, ZN, RB, I, J, JM, SC, FU, TA, MA, EG, FG, SA, M, P, CF, and SR, covering the major commodity sectors of metals, energy, chemicals, and agricultural products. These 20 contracts span the major commodity sectors traded in China—ferrous and non-ferrous metals, energy, chemicals, agriculture, and precious metals—and are among the most actively traded futures on Chinese exchanges, thereby ensuring both market liquidity and sectoral representativeness.

Data construction and calendar alignment. For every commodity, we use the continuous main contract (dominant contract) series, in which the dominant contract on each date is the contract with the largest trading volume and open interest, and the series rolls to the next contract once the latter’s open interest (and volume) overtakes that of the incumbent. Daily log returns are computed from the closing prices of these continuous series. Because the continuous series are not price-adjusted across contract changes, the return on a roll day can, in principle, incorporate the price gap between the outgoing and incoming dominant contracts; we address this directly in the robustness analysis below. The CEA market and the four futures exchanges (SHFE, INE, DCE, ZCE) follow the Chinese mainland trading calendar but differ on a small number of dates; we therefore align all series on their common trading days and discard dates on which any series does not trade, yielding a balanced panel of 1106 daily observations over the period from 19 July 2021 to 5 February 2026. To verify that the roll convention does not drive the results, we identify roll dates from large upward discontinuities in open interest (which mark the switch to a new dominant contract) and re-estimate the connectedness after setting the returns on these roll days to missing and linearly interpolating them; the main findings—tail symmetry with median heterogeneity and the CEA’s tail-state role as a net receiver—are unaffected (Appendix A 

Table A6. Robustness to the futures roll convention.

	Baseline	Roll-Cleaned
TCI (q = 0.05)	92.17	92.21
TCI (q = 0.50)	58.77	59.80
TCI (q = 0.95)	92.08	92.28
CEA NET (q = 0.05)	−13.96	−16.83
CEA NET (q = 0.50)	−0.74	−0.61
CEA NET (q = 0.95)	−10.65	−11.49

Notes: Baseline uses the continuous main-contract returns; in the roll-cleaned panel the return on each roll day (identified from open-interest discontinuities) is set to missing and linearly interpolated. TCI is the total connectedness index; CEA NET is the carbon allowance’s net total directional connectedness. The headline results are materially unchanged.

).

Following the existing connectedness literature, each market price series is converted to daily log returns:

r_i,t = 100 × (ln P_i,t − ln P_i,t−1)

(18)

where P_i,t denotes the closing price of market i at time t, and r_i,t denotes the corresponding daily log return. The sample period covers major events, including the Russia–Ukraine conflict, global financial market volatility, and the expansion of China’s carbon market, thereby providing a suitable setting for examining the return connectedness between the CEA and commodity futures markets under different market conditions.

4. Empirical Results

4.1. Basic Analysis

Table 2. Descriptive statistics.

	Mean	Variance	Skewness	Kurtosis	JB	ERS
AG	0.118	3.470	−0.773	15.356	7145.346 ***	−3.198 ***
AL	0.017	1.355	−0.947	8.339	1478.896 ***	−6.221 ***
AU	0.096	1.098	−2.158	40.385	65,265.344 ***	−5.277 ***
CF	−0.013	1.411	−0.225	11.384	3248.598 ***	−7.258 ***
CU	0.034	1.219	−0.032	7.824	1072.736 ***	−6.424 ***
EG	−0.031	2.414	−0.089	6.959	723.921 ***	−4.761 ***
FG	−0.094	5.304	0.085	6.657	617.472 ***	−10.402 ***
FU	0.009	5.366	−0.463	6.176	504.554 ***	−15.513 ***
I	−0.043	5.857	−0.866	8.237	1402.013 ***	−9.539 ***
J	−0.040	5.902	−0.297	5.010	202.311 ***	−10.610 ***
JM	−0.050	8.180	−0.463	7.226	862.428 ***	−14.632 ***
M	−0.027	2.228	−2.817	31.082	37,804.054 ***	−6.784 ***
MA	−0.017	2.669	−0.238	6.765	663.856 ***	−5.056 ***
P	0.010	3.596	−1.005	9.358	2049.138 ***	−10.624 ***
RB	−0.053	2.027	−0.586	6.285	560.695 ***	−14.566 ***
SA	−0.059	7.039	−1.183	14.533	6387.617 ***	−11.393 ***
SC	0.006	5.023	−0.389	6.391	557.877 ***	−8.717 ***
SR	−0.005	0.631	−0.125	9.548	1978.798 ***	−3.356 ***
TA	0.001	2.723	0.076	5.647	324.039 ***	−7.515 ***
ZN	0.007	1.623	−0.125	7.560	960.981 ***	−15.004 ***
CEA	0.039	3.329	0.263	9.606	2023.874 ***	−4.866 ***

Notes: *** denotes statistical significance at the 1% level. ERS refers to the Elliott–Rothenberg–Stock unit root test, while JB represents the Jarque–Bera goodness-of-fit test.

reports the descriptive statistics of the daily log-return series of the CEA and 20 representative commodity futures over the sample period. The mean daily return of every variable is close to zero, consistent with the typical features of high-frequency financial assets. In terms of variance, the ferrous-metal and chemical sectors exhibit the highest volatility—JM (8.180), SA (7.039), J (5.902), and I (5.857)—whereas the precious metal AU (1.098) and the agricultural product SR (0.631) show the lowest, indicating clear cross-sector heterogeneity in risk levels.

In terms of skewness, the 21 series generally display asymmetry: most are negatively skewed, with M (−2.817) and AU (−2.158) exhibiting the most pronounced left skew, implying a higher probability of large declines than of large gains. Notably, the CEA is positively skewed (0.263), exhibiting a tail distribution opposite to that of most commodity futures and preliminarily suggesting that its extreme-upside risk exceeds its downside risk, consistent with the view that allowance prices are shaped by policy trajectories and the allowance mechanism rather than by market fundamentals alone. All kurtosis values are significantly above the normal benchmark of 3, with AU (40.385) and M (31.082) being the most pronounced, indicating significant heavy tails in all series. The Jarque–Bera test uniformly rejects the null of normality at the 1% significance level, while the Elliott–Rothenberg–Stock unit-root test uniformly rejects the unit-root null, confirming that all log-return series are stationary. The joint features of non-normality, heavy tails, and stationarity provide direct justification for adopting a quantile-based nonlinear framework to examine return connectedness under extreme market states.

Figure 1 displays the time paths of the daily log returns of the CEA and 20 commodity futures over the sample period. All series exhibit pronounced volatility clustering, with marked synchronous fluctuations during several periods, preliminarily indicating non-negligible cross-market linkages among the 21 assets.

4.2. QVAR Connectedness Analysis

To keep the main text focused on the core findings, the three full static connectedness matrices (q = 0.05, 0.50, and 0.95) are reported in Appendix A (

Table A3. Static connectedness (q = 0.05).

Panel A. Overall Frequency
	AG	AL	AU	CF	CU	EG	FG	FU	I	J	JM	M	MA	P	RB	SA	SC	SR	TA	ZN	CEA	FROM
AG	8.14	5.28	6.02	4.35	5.65	4.44	4.07	4.65	4.44	4.46	4.48	3.55	4.72	4.45	4.54	4.06	4.71	4.47	4.63	5.11	3.79	91.86
AL	4.49	6.94	4.04	4.24	5.28	4.93	4.51	4.93	4.73	4.84	4.62	3.92	5.00	4.70	4.88	4.46	4.90	4.38	4.82	5.39	3.98	93.06
AU	6.67	5.11	9.31	4.20	5.50	4.32	3.97	4.76	4.20	4.37	4.23	3.67	4.57	4.34	4.28	3.88	4.70	4.66	4.59	4.82	3.86	90.69
CF	4.46	4.88	3.76	7.53	5.01	4.95	4.29	4.91	4.83	4.65	4.48	3.78	4.65	4.81	4.92	4.03	4.91	4.60	5.45	5.09	4.03	92.47
CU	5.10	5.53	4.40	4.43	7.48	4.77	4.33	4.81	4.71	4.69	4.44	3.40	4.69	4.71	4.94	4.31	4.70	4.20	4.93	5.73	3.68	92.52
EG	4.11	4.93	3.47	4.65	4.85	7.59	4.36	5.03	4.84	4.95	4.82	3.65	5.86	4.35	4.95	4.28	5.04	4.11	5.58	4.94	3.64	92.41
FG	4.09	4.82	3.51	4.29	4.64	4.72	7.98	4.44	5.06	5.21	5.10	3.90	5.12	3.97	5.36	5.68	4.29	4.36	4.68	4.80	3.98	92.02
FU	4.23	4.69	3.83	4.53	4.84	4.96	4.05	7.43	4.63	4.45	4.39	3.83	4.88	5.06	4.64	4.10	6.43	4.42	5.92	4.91	3.76	92.57
I	4.11	4.75	3.36	4.38	4.63	4.91	4.66	4.65	7.34	5.36	5.15	3.86	4.96	4.45	6.05	4.65	4.57	4.19	4.83	5.03	4.11	92.66
J	3.93	4.91	3.48	4.33	4.64	4.84	4.80	4.37	5.34	7.41	6.65	3.63	5.12	4.31	5.94	4.82	4.41	4.06	4.75	4.58	3.70	92.59
JM	4.15	4.86	3.64	4.31	4.48	4.87	4.78	4.42	5.21	6.63	7.39	3.55	5.23	4.09	5.72	4.86	4.42	4.15	4.80	4.77	3.66	92.61
M	4.14	4.63	3.71	4.66	4.32	4.64	4.57	4.95	4.64	4.52	4.47	9.54	4.42	4.77	4.62	4.27	4.84	4.76	4.69	4.58	4.26	90.46
MA	4.22	4.97	3.63	4.37	4.65	5.69	4.67	4.84	4.90	5.18	5.09	3.46	7.43	4.34	5.20	4.82	4.89	4.18	5.07	4.79	3.60	92.57
P	4.40	5.05	3.63	4.64	5.04	4.62	3.84	5.53	4.72	4.57	4.36	4.01	4.71	8.10	4.82	4.06	5.26	4.27	5.34	4.90	4.11	91.90
RB	4.02	4.99	3.34	4.43	4.83	4.79	4.85	4.46	5.94	5.89	5.60	3.55	5.13	4.39	7.37	4.88	4.23	3.96	4.81	4.85	3.67	92.63
SA	4.05	4.81	3.39	4.24	4.64	4.66	5.79	4.37	5.21	5.27	5.29	3.67	5.30	4.18	5.46	8.23	4.18	4.17	4.55	4.78	3.75	91.77
SC	4.32	4.68	3.78	4.55	4.72	5.06	3.91	6.61	4.48	4.49	4.40	3.92	4.98	4.91	4.40	3.84	7.59	4.56	6.08	4.78	3.94	92.41
SR	4.65	4.72	4.12	4.67	4.67	4.58	4.50	4.94	4.57	4.60	4.60	4.15	4.81	4.62	4.63	4.32	5.04	8.15	4.74	4.83	4.10	91.85
TA	4.18	4.83	3.64	4.82	4.88	5.38	4.22	5.77	4.76	4.69	4.67	3.57	5.01	4.79	4.83	4.11	5.81	4.20	7.28	4.77	3.79	92.72
ZN	4.65	5.56	3.81	4.51	5.76	4.88	4.36	4.90	4.94	4.74	4.58	3.59	4.84	4.55	4.95	4.35	4.72	4.16	4.81	7.48	3.84	92.52
CEA	4.33	4.86	3.88	4.48	4.39	4.57	4.33	4.83	4.81	4.75	4.51	4.13	4.76	4.73	4.72	4.19	4.81	4.61	4.79	4.74	8.78	91.22
TO	88.30	98.84	76.43	89.11	97.42	96.60	88.85	98.15	96.96	98.33	95.94	74.78	98.78	90.50	99.87	87.97	96.86	86.48	99.86	98.19	77.26	1935.49
NET	−3.56	5.78	−14.26	−3.36	4.90	4.19	−3.17	5.58	4.30	5.75	3.34	−15.68	6.21	−1.39	7.24	−3.80	4.45	−5.37	7.14	5.67	−13.96	TCI = 92.17
NPDC	6	16	2	5	14	13	6	14	11	16	10	0	17	8	19	5	12	3	18	14	1
Panel B. Short-term frequency (1–5 days)
AG	6.53	4.16	4.73	3.47	4.44	3.62	3.36	3.80	3.58	3.58	3.62	2.96	3.80	3.63	3.62	3.40	3.84	3.77	3.72	4.06	3.09	74.24
AL	4.14	6.32	3.76	3.90	4.84	4.64	4.26	4.69	4.42	4.50	4.31	3.74	4.69	4.41	4.48	4.20	4.65	4.17	4.48	4.97	3.73	86.99
AU	5.47	4.17	7.73	3.45	4.48	3.55	3.31	3.96	3.41	3.58	3.50	3.02	3.74	3.56	3.49	3.24	3.96	3.98	3.78	3.93	3.19	74.76
CF	3.05	3.36	2.56	5.41	3.38	3.49	3.00	3.45	3.28	3.26	3.14	2.74	3.27	3.33	3.40	2.83	3.47	3.24	3.78	3.49	2.84	64.38
CU	4.24	4.54	3.60	3.53	6.13	3.94	3.64	3.93	3.79	3.90	3.67	2.80	3.89	3.82	4.03	3.60	3.90	3.52	4.00	4.73	3.03	76.08
EG	3.24	3.84	2.75	3.60	3.74	6.01	3.49	4.00	3.81	3.98	3.87	2.96	4.60	3.40	3.92	3.44	4.00	3.30	4.40	3.89	2.89	73.13
FG	3.29	3.87	2.84	3.42	3.76	3.74	6.42	3.59	4.12	4.15	3.99	3.09	4.04	3.21	4.28	4.60	3.43	3.42	3.76	3.83	3.24	73.67
FU	3.14	3.40	2.79	3.27	3.54	3.69	2.98	5.59	3.33	3.21	3.19	2.88	3.59	3.75	3.33	2.92	4.92	3.24	4.38	3.61	2.79	67.94
I	3.75	4.33	3.04	3.99	4.16	4.51	4.24	4.24	6.48	4.83	4.69	3.60	4.49	4.05	5.47	4.15	4.23	3.87	4.36	4.60	3.79	84.38
J	3.36	4.19	3.01	3.70	3.96	4.09	4.16	3.75	4.56	6.32	5.73	3.21	4.33	3.78	5.05	4.17	3.82	3.56	4.04	3.83	3.21	79.49
JM	3.27	3.80	2.86	3.45	3.54	3.89	3.86	3.58	4.15	5.28	5.95	2.92	4.13	3.31	4.56	3.91	3.56	3.37	3.85	3.74	2.93	73.96
M	3.31	3.71	3.00	3.79	3.49	3.75	3.65	4.03	3.77	3.73	3.66	7.85	3.60	3.88	3.77	3.44	3.95	3.90	3.81	3.73	3.44	73.40
MA	3.64	4.20	3.11	3.69	3.93	4.77	4.02	4.13	4.17	4.40	4.35	2.95	6.28	3.69	4.40	4.16	4.16	3.63	4.28	4.05	3.04	78.74
P	3.51	4.12	2.85	3.61	4.02	3.72	3.08	4.53	3.72	3.70	3.56	3.22	3.85	6.62	3.92	3.27	4.37	3.49	4.34	3.96	3.37	74.21
RB	3.15	3.85	2.59	3.38	3.72	3.72	3.73	3.48	4.56	4.54	4.35	2.78	4.01	3.44	5.65	3.74	3.36	3.09	3.70	3.65	2.82	71.66
SA	3.27	3.90	2.70	3.46	3.84	3.83	4.76	3.59	4.34	4.26	4.28	2.94	4.35	3.42	4.44	6.78	3.44	3.31	3.74	3.94	3.03	74.86
SC	3.54	3.76	3.05	3.75	3.82	4.21	3.20	5.44	3.72	3.73	3.61	3.32	4.12	4.03	3.58	3.15	6.27	3.77	5.00	3.91	3.29	76.01
SR	3.59	3.65	3.22	3.66	3.62	3.59	3.52	3.92	3.59	3.57	3.56	3.28	3.74	3.58	3.61	3.43	3.92	6.55	3.76	3.74	3.18	71.73
TA	3.16	3.60	2.71	3.61	3.64	4.14	3.24	4.48	3.55	3.60	3.60	2.80	3.82	3.67	3.62	3.07	4.58	3.20	5.65	3.55	2.93	70.57
ZN	3.72	4.37	3.03	3.57	4.54	3.94	3.55	3.98	3.93	3.76	3.63	2.93	3.89	3.68	3.88	3.48	3.84	3.38	3.82	6.08	3.13	74.06
CEA	4.12	4.63	3.71	4.29	4.16	4.38	4.11	4.62	4.55	4.55	4.32	3.93	4.58	4.51	4.51	3.99	4.58	4.43	4.56	4.51	8.24	87.05
TO	71.95	79.45	61.92	72.60	78.62	79.20	73.17	81.17	78.35	80.09	78.64	62.07	80.57	74.15	81.36	72.17	79.97	71.63	81.55	79.72	62.95	1581.30
NET	−2.30	−7.54	−12.84	8.23	2.54	6.07	−0.50	13.23	−6.02	0.61	4.69	−11.33	1.83	−0.07	9.69	−2.69	3.96	−0.10	10.99	5.66	−24.11	TCI = 75.30
NPDC	4	3	1	17	12	16	9	20	5	9	14	3	10	10	18	6	13	6	19	15	0
Panel C. Long-term frequency (more than 5 days)
AG	1.61	1.12	1.28	0.88	1.21	0.82	0.71	0.85	0.86	0.88	0.86	0.59	0.91	0.82	0.92	0.66	0.88	0.69	0.91	1.05	0.70	17.62
AL	0.36	0.62	0.28	0.34	0.43	0.29	0.25	0.24	0.31	0.34	0.31	0.18	0.31	0.30	0.40	0.26	0.25	0.21	0.34	0.42	0.24	6.07
AU	1.20	0.94	1.58	0.75	1.03	0.77	0.66	0.80	0.79	0.79	0.73	0.64	0.83	0.78	0.79	0.64	0.74	0.68	0.81	0.89	0.67	15.94
CF	1.41	1.52	1.20	2.12	1.62	1.46	1.29	1.46	1.55	1.39	1.34	1.04	1.37	1.47	1.52	1.20	1.44	1.36	1.66	1.60	1.19	28.09
CU	0.86	0.99	0.81	0.90	1.36	0.83	0.70	0.88	0.93	0.79	0.77	0.60	0.81	0.89	0.91	0.71	0.80	0.68	0.94	1.01	0.65	16.44
EG	0.88	1.08	0.73	1.05	1.11	1.59	0.86	1.03	1.03	0.97	0.94	0.69	1.26	0.94	1.03	0.84	1.04	0.81	1.19	1.05	0.75	19.28
FG	0.80	0.95	0.67	0.87	0.88	0.99	1.56	0.84	0.94	1.07	1.11	0.80	1.07	0.76	1.09	1.08	0.86	0.95	0.92	0.97	0.75	18.35
FU	1.09	1.29	1.04	1.26	1.30	1.27	1.07	1.85	1.31	1.24	1.20	0.95	1.29	1.31	1.31	1.18	1.52	1.18	1.54	1.30	0.97	24.63
I	0.36	0.42	0.31	0.39	0.47	0.41	0.42	0.41	0.85	0.54	0.46	0.27	0.46	0.40	0.58	0.50	0.34	0.32	0.47	0.43	0.33	8.29
J	0.57	0.72	0.47	0.63	0.68	0.75	0.63	0.62	0.78	1.10	0.92	0.42	0.79	0.53	0.90	0.65	0.59	0.51	0.72	0.75	0.49	13.10
JM	0.89	1.06	0.78	0.87	0.94	0.98	0.91	0.84	1.06	1.36	1.45	0.63	1.10	0.78	1.16	0.94	0.86	0.78	0.96	1.03	0.73	18.65
M	0.83	0.91	0.70	0.87	0.83	0.88	0.92	0.92	0.87	0.79	0.82	1.70	0.82	0.89	0.85	0.83	0.89	0.86	0.89	0.85	0.81	17.06
MA	0.58	0.77	0.52	0.68	0.72	0.92	0.66	0.71	0.73	0.78	0.75	0.51	1.16	0.65	0.81	0.67	0.73	0.55	0.79	0.73	0.57	13.83
P	0.89	0.93	0.78	1.03	1.03	0.91	0.76	1.00	1.01	0.87	0.80	0.79	0.86	1.48	0.90	0.80	0.90	0.77	0.99	0.94	0.74	17.68
RB	0.87	1.14	0.75	1.04	1.12	1.07	1.12	0.98	1.38	1.35	1.26	0.77	1.12	0.95	1.72	1.14	0.88	0.88	1.11	1.19	0.85	20.97
SA	0.78	0.92	0.68	0.78	0.80	0.84	1.03	0.78	0.86	1.01	1.01	0.73	0.95	0.76	1.02	1.45	0.74	0.85	0.80	0.84	0.72	16.91
SC	0.79	0.92	0.73	0.80	0.89	0.85	0.71	1.17	0.76	0.76	0.79	0.60	0.86	0.87	0.81	0.69	1.32	0.78	1.07	0.88	0.65	16.40
SR	1.05	1.07	0.90	1.01	1.05	0.99	0.98	1.02	0.97	1.03	1.04	0.87	1.07	1.03	1.02	0.89	1.12	1.60	0.98	1.09	0.92	20.11
TA	1.02	1.23	0.93	1.21	1.24	1.23	0.98	1.29	1.21	1.09	1.07	0.77	1.19	1.13	1.21	1.04	1.22	1.01	1.63	1.22	0.87	22.16
ZN	0.94	1.19	0.78	0.94	1.22	0.94	0.81	0.93	1.01	0.98	0.95	0.66	0.95	0.87	1.07	0.88	0.88	0.78	0.98	1.41	0.71	18.46
CEA	0.21	0.22	0.18	0.19	0.23	0.20	0.21	0.21	0.25	0.20	0.19	0.20	0.18	0.22	0.21	0.21	0.22	0.18	0.24	0.23	0.54	4.17
TO	16.36	19.39	14.52	16.50	18.80	17.40	15.68	16.98	18.61	18.24	17.30	12.71	18.21	16.36	18.51	15.80	16.89	14.84	18.31	18.48	14.32	354.19
NET	−1.26	13.32	−1.42	−11.59	2.36	−1.88	−2.67	−7.65	10.32	5.14	−1.35	−4.34	4.38	−1.33	−2.45	−1.11	0.49	−5.27	−3.85	0.02	10.15	TCI = 16.87
NPDC	10	19	9	0	15	10	7	1	18	16	9	3	17	8	7	9	14	3	3	12	20

Notes: Each panel reports the static (full-sample) connectedness. The ij-th entry is the share of the H-step-ahead forecast-error variance of market i explained by innovations to market j. FROM and TO denote the total directional connectedness received from and transmitted to all other markets; NET = TO − FROM, with a positive (negative) value indicating a net transmitter (receiver); NPDC is the net pairwise directional connectedness; and TCI is the total connectedness index. Panels A, B, and C correspond to the overall, short-term (1–5 days), and long-term (more than 5 days) frequency bands, respectively.

,

Table A4. Static connectedness (q = 0.50).

Panel A. Overall Frequency
	AG	AL	AU	CF	CU	EG	FG	FU	I	J	JM	M	MA	P	RB	SA	SC	SR	TA	ZN	CEA	FROM
AG	46.25	4.66	17.06	1.36	10.27	1.27	0.57	1.78	0.84	0.94	0.86	0.26	1.36	1.55	1.10	0.69	1.55	1.26	1.96	4.39	0.01	53.75
AL	3.32	30.59	1.66	2.17	11.30	4.07	1.67	2.58	2.61	3.96	3.45	0.58	4.49	2.96	4.98	2.39	2.30	0.76	3.69	10.39	0.08	69.41
AU	21.83	3.02	59.14	0.24	7.91	0.18	0.02	1.45	0.04	0.12	0.10	0.11	0.50	0.64	0.06	0.10	1.06	0.52	0.82	2.14	0.02	40.86
CF	1.30	3.21	0.19	44.81	4.45	4.60	1.35	3.39	2.27	2.81	2.03	0.90	3.49	4.35	2.99	1.58	2.85	2.25	7.32	3.86	0.01	55.19
CU	6.24	10.18	3.73	2.78	28.03	3.82	1.57	3.26	3.25	3.17	2.31	0.22	2.93	3.26	4.06	1.86	2.83	1.19	4.25	11.02	0.03	71.97
EG	0.84	4.10	0.09	3.13	4.09	30.68	1.85	4.78	3.38	4.47	4.31	0.45	11.15	1.84	4.84	2.07	4.35	0.62	9.43	3.52	0.01	69.32
FG	0.52	2.32	0.01	1.27	2.27	2.56	42.44	0.61	5.68	6.07	6.43	1.06	4.65	0.19	7.31	11.13	0.24	0.79	2.17	2.21	0.08	57.56
FU	1.17	2.60	0.80	2.29	3.62	4.79	0.42	31.00	1.41	1.59	1.44	1.15	3.89	5.20	1.59	0.41	20.13	1.99	11.96	2.51	0.04	69.00
I	0.66	2.64	0.02	1.60	3.70	3.48	4.17	1.55	31.54	8.32	6.76	0.48	4.50	1.36	14.88	5.07	1.30	0.97	3.42	3.36	0.21	68.46
J	0.58	3.37	0.05	1.71	2.96	3.81	3.78	1.37	6.89	26.17	18.17	0.33	5.50	1.47	11.60	4.52	1.21	0.54	2.68	3.15	0.14	73.83
JM	0.62	3.23	0.05	1.26	2.44	3.93	4.29	1.34	6.03	19.33	27.80	0.51	5.81	0.91	10.17	5.06	1.16	0.66	2.68	2.67	0.04	72.20
M	0.53	1.38	0.04	1.94	0.65	1.24	1.87	2.72	1.08	0.74	1.15	74.69	0.60	2.87	1.29	1.08	1.39	2.07	1.59	0.85	0.24	25.31
MA	0.88	4.28	0.23	2.27	2.91	10.60	3.22	3.69	4.16	6.18	6.09	0.23	29.28	1.88	6.07	4.27	3.72	0.54	6.29	3.19	0.01	70.72
P	1.44	4.07	0.50	4.24	4.99	2.63	0.13	7.30	1.87	2.41	1.39	1.54	2.82	43.52	2.80	0.96	6.51	1.80	5.82	2.98	0.27	56.48
RB	0.62	4.21	0.02	1.70	3.75	4.08	4.44	1.37	12.53	11.64	9.46	0.45	5.58	1.63	25.93	5.09	0.91	0.43	2.95	3.10	0.09	74.07
SA	0.55	3.04	0.05	1.37	2.58	2.64	10.27	0.51	6.40	6.68	7.12	0.55	5.77	0.83	7.49	39.06	0.24	0.67	1.92	2.23	0.03	60.94
SC	1.09	2.43	0.56	1.99	3.25	4.66	0.09	21.09	1.19	1.39	1.20	0.52	4.13	4.86	1.09	0.18	32.59	1.74	13.73	2.20	0.01	67.41
SR	1.56	1.13	0.77	3.25	2.56	1.27	1.12	4.03	1.63	1.17	1.23	1.76	1.07	2.45	1.07	1.34	3.41	64.04	3.46	1.60	0.08	35.96
TA	1.22	3.34	0.40	4.44	4.14	8.51	1.38	10.69	2.91	2.84	2.52	0.47	5.96	3.52	3.08	1.32	11.73	1.41	27.65	2.38	0.09	72.35
ZN	3.11	10.93	1.16	2.82	12.75	3.76	1.70	2.68	3.48	3.87	3.11	0.37	3.58	2.25	3.97	1.79	2.19	0.85	2.82	32.78	0.03	67.22
CEA	0.00	0.25	0.02	0.01	0.11	0.04	0.03	0.06	0.45	0.20	0.04	0.29	0.00	0.16	0.16	0.03	0.00	0.00	0.29	0.10	97.74	2.26
TO	48.08	74.39	27.41	41.84	90.72	71.94	43.93	76.25	68.10	87.88	79.15	12.27	77.79	44.18	90.60	50.96	69.08	21.06	89.26	67.87	1.51	1234.27
NET	−5.67	4.98	−13.45	−13.35	18.75	2.62	−13.63	7.24	−0.36	14.05	6.95	−13.05	7.07	−12.30	16.53	−9.98	1.67	−14.89	16.91	0.64	−0.74	TCI = 58.77
NPDC	3	14	2	5	16	13	5	12	10	20	15	2	15	6	19	8	9	1	18	10	7
Panel B. Short-term frequency (1–5 days)
AG	38.09	3.77	14.02	1.19	8.36	1.10	0.48	1.53	0.66	0.79	0.75	0.20	1.17	1.33	0.89	0.62	1.32	1.17	1.67	3.66	0.01	44.68
AL	3.01	25.63	1.50	1.81	9.68	3.45	1.42	2.21	2.26	3.35	2.86	0.51	3.81	2.62	4.18	2.01	1.97	0.74	3.01	9.01	0.07	59.47
AU	17.99	2.46	47.86	0.19	6.47	0.16	0.02	1.23	0.03	0.08	0.07	0.08	0.45	0.57	0.06	0.10	0.95	0.44	0.71	1.85	0.01	33.90
CF	1.10	2.67	0.17	37.08	3.55	3.89	1.12	2.97	1.75	2.28	1.74	0.75	2.92	3.58	2.49	1.32	2.51	1.89	6.30	3.03	0.00	46.02
CU	5.30	8.52	3.12	2.33	23.58	3.34	1.41	2.82	2.74	2.65	1.89	0.20	2.62	2.82	3.42	1.59	2.46	1.10	3.65	9.47	0.03	61.49
EG	0.72	3.23	0.08	2.50	3.36	24.97	1.54	4.02	2.79	3.81	3.62	0.37	9.08	1.49	3.99	1.68	3.58	0.54	7.78	2.82	0.01	57.02
FG	0.43	1.81	0.00	1.03	1.98	2.01	34.86	0.55	4.79	4.92	5.08	0.85	3.80	0.18	6.04	9.30	0.24	0.70	1.89	1.72	0.08	47.40
FU	0.94	2.05	0.59	1.78	2.76	3.94	0.35	25.50	1.14	1.35	1.20	1.06	3.24	4.15	1.24	0.37	16.83	1.77	9.87	1.98	0.02	56.63
I	0.61	2.10	0.02	1.37	3.14	2.89	3.48	1.40	26.09	6.88	5.65	0.43	3.75	1.15	12.40	4.24	1.21	0.95	2.95	2.81	0.21	57.63
J	0.52	2.74	0.04	1.24	2.36	2.95	3.21	1.20	5.61	20.97	14.58	0.32	4.50	1.26	9.24	3.48	1.12	0.51	2.26	2.39	0.14	59.67
JM	0.59	2.81	0.04	0.94	2.16	3.30	3.69	1.17	5.11	15.90	22.78	0.49	4.89	0.80	8.56	4.06	1.08	0.64	2.38	2.26	0.04	60.92
M	0.50	1.17	0.02	1.85	0.60	1.14	1.46	2.48	0.93	0.65	1.01	61.21	0.55	2.61	1.06	0.97	1.30	1.60	1.52	0.75	0.21	22.41
MA	0.77	3.40	0.20	1.79	2.44	8.69	2.71	3.12	3.48	5.24	5.16	0.16	24.45	1.52	4.90	3.51	3.12	0.51	5.28	2.55	0.01	58.56
P	1.14	3.17	0.35	3.55	4.06	2.02	0.10	5.97	1.48	1.89	1.17	1.29	2.27	35.44	2.33	0.83	5.38	1.65	5.08	2.40	0.18	46.30
RB	0.52	3.57	0.01	1.34	3.16	3.46	3.72	1.21	10.96	10.07	8.10	0.39	4.92	1.37	22.04	4.47	0.81	0.40	2.57	2.49	0.09	63.63
SA	0.46	2.55	0.03	1.09	2.18	2.15	8.68	0.43	5.52	5.47	5.88	0.43	4.87	0.69	6.26	32.06	0.23	0.56	1.66	1.96	0.02	51.14
SC	0.93	2.04	0.44	1.63	2.59	3.98	0.08	17.33	1.03	1.25	1.05	0.45	3.45	3.97	0.92	0.18	26.74	1.50	11.16	1.90	0.01	55.87
SR	1.29	0.84	0.51	2.53	2.29	1.05	0.90	3.47	1.56	1.04	1.09	1.45	0.95	1.87	1.02	1.28	2.90	52.61	3.09	1.32	0.06	30.50
TA	1.08	2.78	0.36	3.52	3.34	7.18	1.17	8.97	2.39	2.42	2.11	0.36	5.06	2.84	2.57	1.08	9.97	1.22	23.15	1.98	0.06	60.47
ZN	2.52	8.69	0.96	2.25	10.49	3.14	1.38	2.29	2.77	3.10	2.51	0.33	2.98	1.80	3.16	1.44	1.84	0.75	2.29	27.11	0.03	54.73
CEA	0.00	0.21	0.01	0.01	0.10	0.03	0.03	0.05	0.37	0.16	0.03	0.24	0.00	0.13	0.13	0.03	0.00	0.00	0.24	0.08	79.42	1.85
TO	40.42	60.58	22.50	33.93	75.08	59.88	36.96	64.42	57.36	73.32	65.54	10.35	65.29	36.76	74.86	42.54	58.81	18.64	75.36	56.41	1.29	1030.27
NET	−4.25	1.10	−11.41	−12.09	13.59	2.87	−10.44	7.78	−0.27	13.64	4.62	−12.06	6.73	−9.54	11.23	−8.60	2.94	−11.86	14.89	1.69	−0.55	TCI = 49.06
NPDC	3	10	2	5	15	13	5	15	10	20	14	2	16	6	18	8	10	1	18	12	7
Panel C. Long-term frequency (more than 5 days)
AG	8.16	0.89	3.04	0.18	1.91	0.17	0.09	0.25	0.18	0.14	0.12	0.06	0.19	0.21	0.22	0.07	0.22	0.09	0.30	0.74	0.00	9.07
AL	0.31	4.96	0.16	0.36	1.61	0.62	0.25	0.37	0.35	0.60	0.59	0.07	0.68	0.35	0.80	0.38	0.33	0.02	0.68	1.38	0.01	9.94
AU	3.84	0.56	11.28	0.05	1.44	0.02	0.00	0.22	0.01	0.03	0.03	0.03	0.05	0.07	0.00	0.00	0.10	0.08	0.11	0.30	0.01	6.96
CF	0.21	0.53	0.02	7.73	0.90	0.71	0.23	0.42	0.52	0.52	0.29	0.16	0.56	0.77	0.49	0.26	0.34	0.36	1.02	0.84	0.00	9.16
CU	0.94	1.65	0.61	0.45	4.45	0.48	0.15	0.43	0.51	0.52	0.42	0.03	0.32	0.43	0.65	0.26	0.38	0.09	0.60	1.55	0.00	10.49
EG	0.12	0.86	0.01	0.63	0.73	5.71	0.31	0.76	0.59	0.66	0.69	0.08	2.07	0.35	0.84	0.40	0.77	0.08	1.65	0.70	0.00	12.31
FG	0.09	0.51	0.00	0.25	0.30	0.55	7.58	0.06	0.88	1.15	1.35	0.21	0.85	0.00	1.27	1.83	0.00	0.08	0.28	0.49	0.00	10.16
FU	0.23	0.55	0.21	0.51	0.86	0.85	0.07	5.49	0.27	0.24	0.24	0.09	0.65	1.04	0.34	0.05	3.30	0.22	2.09	0.53	0.02	12.37
I	0.04	0.55	0.00	0.24	0.56	0.59	0.70	0.15	5.45	1.44	1.11	0.05	0.75	0.20	2.48	0.83	0.09	0.02	0.47	0.55	0.01	10.83
J	0.06	0.63	0.01	0.46	0.60	0.86	0.57	0.18	1.29	5.20	3.59	0.01	1.00	0.21	2.36	1.04	0.09	0.03	0.42	0.76	0.00	14.16
JM	0.04	0.42	0.00	0.32	0.29	0.63	0.59	0.17	0.91	3.43	5.02	0.02	0.92	0.11	1.61	1.00	0.08	0.03	0.30	0.41	0.00	11.28
M	0.02	0.21	0.01	0.08	0.05	0.10	0.41	0.25	0.16	0.10	0.14	13.48	0.04	0.26	0.23	0.12	0.09	0.46	0.07	0.09	0.02	2.91
MA	0.11	0.88	0.04	0.48	0.47	1.91	0.51	0.57	0.68	0.94	0.92	0.07	4.83	0.36	1.17	0.76	0.61	0.03	1.02	0.64	0.00	12.16
P	0.30	0.90	0.15	0.69	0.92	0.61	0.03	1.33	0.39	0.52	0.22	0.25	0.55	8.08	0.47	0.14	1.13	0.15	0.74	0.58	0.09	10.17
RB	0.10	0.64	0.00	0.36	0.60	0.62	0.72	0.15	1.57	1.57	1.37	0.06	0.66	0.27	3.89	0.62	0.10	0.03	0.39	0.62	0.00	10.44
SA	0.09	0.50	0.02	0.28	0.40	0.49	1.59	0.08	0.87	1.21	1.24	0.12	0.90	0.14	1.23	6.99	0.01	0.11	0.26	0.27	0.00	9.81
SC	0.16	0.40	0.12	0.36	0.66	0.68	0.01	3.76	0.16	0.14	0.15	0.08	0.69	0.89	0.17	0.01	5.85	0.24	2.57	0.30	0.00	11.54
SR	0.26	0.28	0.26	0.73	0.27	0.22	0.21	0.56	0.07	0.13	0.15	0.31	0.12	0.58	0.05	0.07	0.51	11.44	0.36	0.28	0.01	5.46
TA	0.13	0.56	0.04	0.91	0.79	1.33	0.21	1.72	0.53	0.41	0.41	0.12	0.90	0.69	0.51	0.24	1.77	0.19	4.50	0.40	0.03	11.88
ZN	0.59	2.24	0.20	0.57	2.27	0.61	0.32	0.39	0.71	0.77	0.59	0.04	0.61	0.45	0.81	0.35	0.34	0.09	0.53	5.67	0.01	12.49
CEA	0.00	0.05	0.00	0.00	0.02	0.01	0.01	0.01	0.08	0.03	0.01	0.05	0.00	0.03	0.03	0.01	0.00	0.00	0.05	0.02	18.32	0.41
TO	7.66	13.82	4.92	7.91	15.64	12.05	6.97	11.83	10.75	14.57	13.62	1.92	12.50	7.41	15.75	8.42	10.27	2.42	13.90	11.45	0.22	204.00
NET	−1.41	3.87	−2.04	−1.25	5.16	−0.25	−3.19	−0.54	−0.08	0.41	2.34	−0.99	0.34	−2.76	5.30	−1.38	−1.27	−3.04	2.02	−1.04	−0.19	TCI = 9.71
NPDC	5	17	5	8	17	11	8	7	14	13	18	7	13	4	19	3	7	2	15	11	6

Notes: Each panel reports the static (full-sample) connectedness. The ij-th entry is the share of the H-step-ahead forecast-error variance of market i explained by innovations to market j. FROM and TO denote the total directional connectedness received from and transmitted to all other markets; NET = TO − FROM, with a positive (negative) value indicating a net transmitter (receiver); NPDC is the net pairwise directional connectedness; and TCI is the total connectedness index. Panels A, B, and C correspond to the overall, short-term (1–5 days), and long-term (more than 5 days) frequency bands, respectively.

and

Table A5. Static connectedness (q = 0.95).

Panel A. Overall Frequency
	AG	AL	AU	CF	CU	EG	FG	FU	I	J	JM	M	MA	P	RB	SA	SC	SR	TA	ZN	CEA	FROM
AG	7.87	5.00	6.04	4.37	5.52	4.67	4.43	4.73	4.27	4.49	4.44	3.78	4.77	4.45	4.40	4.15	4.40	4.43	4.55	5.04	4.19	92.13
AL	4.71	7.57	4.09	4.36	5.76	4.83	4.43	4.73	4.52	4.94	4.80	3.66	5.05	4.47	4.86	4.36	4.43	4.05	4.82	5.75	3.82	92.43
AU	6.76	4.79	8.84	4.30	5.30	4.48	4.36	4.84	3.97	4.32	4.26	3.69	4.66	4.37	4.11	4.14	4.47	4.50	4.68	4.77	4.39	91.16
CF	4.51	4.70	4.06	8.08	4.75	4.89	4.70	4.78	4.45	4.70	4.59	4.07	4.87	4.82	4.67	4.18	4.58	4.48	5.23	4.90	3.99	91.92
CU	5.21	5.59	4.48	4.39	7.55	4.97	4.23	4.75	4.77	4.68	4.61	3.50	4.70	4.46	4.81	4.32	4.49	4.19	4.78	5.79	3.71	92.45
EG	4.35	4.85	3.67	4.61	4.84	7.47	4.53	4.91	4.74	4.87	4.88	3.75	5.85	4.30	4.78	4.46	4.70	4.15	5.42	4.87	4.00	92.53
FG	4.37	4.64	3.85	4.58	4.56	4.90	7.64	4.50	4.82	5.27	5.28	3.99	4.97	4.21	5.05	5.50	3.98	4.23	4.56	4.71	4.38	92.36
FU	4.45	4.65	4.01	4.42	4.70	5.01	4.19	7.58	4.32	4.56	4.36	3.93	5.11	4.87	4.33	3.83	6.55	4.58	5.91	4.68	3.95	92.42
I	4.24	4.56	3.59	4.26	4.96	5.03	4.58	4.54	7.43	5.42	5.27	3.77	5.01	4.34	6.06	4.71	4.34	4.27	4.75	4.83	4.03	92.57
J	4.14	4.81	3.59	4.23	4.60	4.82	4.91	4.46	5.33	7.40	6.62	3.50	5.14	4.27	5.82	4.85	4.21	4.05	4.59	4.77	3.90	92.60
JM	4.14	4.71	3.61	4.23	4.59	4.95	4.90	4.34	5.25	6.71	7.44	3.69	5.19	4.03	5.70	4.97	4.05	4.22	4.50	4.71	4.07	92.56
M	4.43	4.57	3.89	4.54	4.40	4.74	4.73	4.89	4.49	4.51	4.54	9.53	4.58	4.72	4.41	4.26	4.55	4.70	4.68	4.55	4.28	90.47
MA	4.38	4.91	3.75	4.42	4.62	5.78	4.70	4.98	4.72	5.13	5.06	3.61	7.40	4.30	5.01	4.63	4.73	4.15	5.12	4.78	3.83	92.60
P	4.60	4.84	3.97	4.95	4.88	4.73	4.15	5.29	4.48	4.68	4.34	4.08	4.73	8.27	4.59	4.08	5.16	4.34	5.12	4.76	3.96	91.73
RB	4.21	4.77	3.58	4.38	4.77	4.87	4.77	4.57	5.90	5.78	5.47	3.57	5.13	4.23	7.19	4.73	4.35	4.14	4.88	4.77	3.94	92.81
SA	4.34	4.79	3.72	4.22	4.82	4.87	5.87	4.19	5.08	5.36	5.47	3.78	4.99	4.20	5.17	8.12	3.77	4.15	4.40	4.59	4.12	91.88
SC	4.34	4.59	3.91	4.46	4.71	5.02	3.93	6.92	4.33	4.57	4.32	3.84	5.10	5.00	4.22	3.64	8.01	4.43	6.14	4.70	3.83	91.99
SR	4.68	4.45	4.05	4.70	4.74	4.71	4.52	5.12	4.53	4.58	4.65	4.25	4.77	4.47	4.41	4.34	4.73	8.52	4.81	4.68	4.28	91.48
TA	4.23	4.72	3.80	4.71	4.77	5.41	4.41	5.93	4.61	4.60	4.43	3.73	5.20	4.66	4.59	4.03	5.84	4.27	7.61	4.66	3.78	92.39
ZN	4.77	5.69	4.03	4.63	5.84	4.88	4.44	4.70	4.69	4.87	4.73	3.64	4.87	4.40	4.76	4.18	4.49	4.15	4.71	7.65	3.87	92.35
CEA	4.73	4.63	4.15	4.41	4.48	4.91	4.72	4.66	4.67	4.73	4.68	4.06	4.63	4.45	4.53	4.45	4.33	4.51	4.58	4.66	9.04	90.96
TO	91.58	96.27	79.84	89.17	97.60	98.48	91.50	97.84	93.95	98.77	96.78	75.87	99.32	89.01	96.29	87.83	92.15	86.00	98.24	96.99	80.31	1933.78
NET	−0.55	3.84	−11.32	−2.75	5.16	5.95	−0.86	5.42	1.38	6.17	4.22	−14.60	6.72	−2.71	3.48	−4.05	0.16	−5.48	5.85	4.64	−10.65	TCI = 92.08
NPDC	7	12	1	6	13	16	7	16	9	18	15	0	20	6	14	4	11	3	17	13	2
Panel B. Short-term frequency (1–5 days)
AG	6.56	4.12	4.96	3.65	4.61	3.92	3.73	3.96	3.57	3.76	3.71	3.13	3.97	3.70	3.65	3.52	3.69	3.73	3.84	4.20	3.56	76.97
AL	4.08	6.42	3.58	3.70	5.00	4.09	3.77	4.09	3.87	4.30	4.15	3.16	4.35	3.82	4.17	3.69	3.83	3.54	4.18	4.96	3.23	79.57
AU	6.22	4.42	7.98	3.98	4.85	4.19	4.09	4.51	3.67	3.95	3.91	3.38	4.35	4.06	3.80	3.90	4.14	4.22	4.37	4.38	4.17	84.58
CF	4.12	4.26	3.76	7.22	4.31	4.44	4.35	4.32	4.03	4.27	4.17	3.77	4.41	4.29	4.22	3.82	4.15	4.03	4.79	4.40	3.65	83.58
CU	4.22	4.40	3.70	3.52	6.16	4.07	3.36	3.94	3.92	3.83	3.78	2.84	3.88	3.61	3.97	3.48	3.68	3.39	3.93	4.72	2.95	75.18
EG	3.57	3.93	2.99	3.67	3.97	6.12	3.71	4.02	3.84	4.00	4.00	3.11	4.75	3.49	3.88	3.63	3.85	3.41	4.41	3.91	3.29	75.42
FG	3.14	3.32	2.78	3.22	3.23	3.50	5.66	3.19	3.51	3.79	3.75	2.91	3.59	2.93	3.63	4.00	2.82	3.04	3.34	3.33	3.16	66.16
FU	3.77	3.94	3.32	3.70	3.98	4.18	3.53	6.35	3.61	3.82	3.63	3.33	4.30	4.11	3.63	3.23	5.51	3.81	4.97	3.97	3.32	77.64
I	3.87	4.13	3.32	3.87	4.52	4.60	4.07	4.16	6.68	4.88	4.74	3.46	4.57	3.97	5.48	4.21	3.98	3.95	4.31	4.41	3.65	84.16
J	3.54	4.15	3.09	3.61	3.91	4.12	4.19	3.85	4.55	6.23	5.54	2.96	4.45	3.70	4.93	4.09	3.61	3.55	3.99	4.07	3.39	79.29
JM	3.59	4.07	3.17	3.69	3.95	4.31	4.21	3.78	4.55	5.74	6.32	3.23	4.56	3.50	4.92	4.23	3.51	3.78	3.96	4.08	3.62	80.43
M	3.73	3.81	3.27	3.76	3.70	3.95	3.89	4.09	3.66	3.69	3.75	7.76	3.77	3.92	3.61	3.53	3.80	3.87	3.91	3.77	3.54	75.02
MA	3.97	4.39	3.32	3.92	4.18	5.15	4.25	4.43	4.19	4.60	4.55	3.22	6.55	3.85	4.46	4.14	4.23	3.65	4.57	4.27	3.45	82.79
P	3.99	4.16	3.45	4.23	4.23	4.03	3.61	4.50	3.86	4.00	3.69	3.47	4.00	7.01	3.91	3.50	4.39	3.74	4.44	4.03	3.37	78.60
RB	4.03	4.52	3.45	4.18	4.54	4.65	4.53	4.39	5.58	5.47	5.15	3.41	4.90	4.02	6.76	4.49	4.20	3.99	4.70	4.54	3.78	88.53
SA	2.95	3.26	2.53	2.86	3.25	3.37	4.11	2.88	3.65	3.79	3.82	2.58	3.57	2.80	3.66	5.84	2.57	2.92	3.06	3.13	2.80	63.54
SC	3.51	3.72	3.15	3.58	3.84	4.00	3.12	5.63	3.42	3.60	3.38	3.06	4.07	4.08	3.34	2.85	6.57	3.54	5.00	3.81	3.05	73.74
SR	3.99	3.80	3.37	3.99	4.06	4.02	3.91	4.38	3.94	3.97	4.07	3.66	4.10	3.82	3.83	3.78	4.06	7.12	4.10	4.04	3.71	78.59
TA	3.59	3.99	3.15	3.88	4.04	4.46	3.67	4.97	3.80	3.81	3.68	3.15	4.28	3.91	3.86	3.41	4.90	3.61	6.35	3.88	3.09	77.13
ZN	3.96	4.70	3.38	3.87	4.90	4.08	3.72	3.94	3.90	4.06	3.94	3.06	4.04	3.68	3.95	3.50	3.77	3.49	4.00	6.39	3.28	77.23
CEA	3.60	3.52	3.20	3.28	3.46	3.69	3.61	3.51	3.65	3.69	3.58	3.21	3.51	3.36	3.52	3.38	3.30	3.51	3.45	3.57	7.25	69.61
TO	77.44	80.62	66.94	74.20	82.52	82.79	77.43	82.57	78.76	83.01	80.98	64.11	83.41	74.61	80.40	74.38	77.97	72.77	83.32	81.46	68.06	1627.77
NET	0.47	1.06	−17.63	−9.38	7.34	7.37	11.28	4.93	−5.40	3.72	0.54	−10.91	0.62	−3.99	−8.12	10.84	4.23	−5.82	6.19	4.23	−1.56	TCI = 77.51
NPDC	8	10	0	1	17	18	20	15	4	12	9	2	10	6	3	19	13	5	15	15	8
Panel C. Long-term frequency (more than 5 days)
AG	1.30	0.88	1.08	0.72	0.92	0.75	0.70	0.76	0.71	0.73	0.74	0.65	0.80	0.75	0.75	0.64	0.71	0.71	0.71	0.84	0.63	15.16
AL	0.63	1.15	0.51	0.66	0.76	0.74	0.67	0.64	0.65	0.63	0.65	0.50	0.69	0.66	0.69	0.67	0.60	0.51	0.64	0.80	0.58	12.86
AU	0.53	0.37	0.85	0.32	0.45	0.29	0.27	0.33	0.30	0.37	0.35	0.31	0.31	0.32	0.31	0.24	0.33	0.28	0.31	0.39	0.22	6.59
CF	0.39	0.44	0.30	0.86	0.44	0.46	0.35	0.46	0.42	0.42	0.41	0.30	0.46	0.52	0.45	0.36	0.43	0.45	0.43	0.50	0.34	8.34
CU	0.99	1.19	0.78	0.86	1.39	0.90	0.87	0.82	0.85	0.85	0.83	0.67	0.83	0.85	0.84	0.83	0.82	0.79	0.86	1.07	0.76	17.26
EG	0.77	0.92	0.69	0.94	0.87	1.35	0.83	0.89	0.90	0.87	0.87	0.64	1.10	0.81	0.90	0.83	0.85	0.74	1.01	0.97	0.71	17.11
FG	1.23	1.33	1.07	1.36	1.33	1.41	1.98	1.32	1.31	1.48	1.53	1.09	1.38	1.28	1.42	1.50	1.16	1.19	1.22	1.37	1.22	26.21
FU	0.68	0.71	0.69	0.72	0.72	0.83	0.66	1.23	0.72	0.74	0.73	0.59	0.81	0.77	0.70	0.60	1.05	0.77	0.94	0.71	0.64	14.78
I	0.37	0.43	0.27	0.39	0.43	0.44	0.51	0.38	0.76	0.54	0.53	0.31	0.44	0.37	0.58	0.50	0.36	0.32	0.43	0.43	0.38	8.40
J	0.60	0.66	0.49	0.61	0.69	0.70	0.71	0.61	0.77	1.17	1.08	0.53	0.69	0.57	0.89	0.77	0.59	0.50	0.60	0.70	0.51	13.31
JM	0.55	0.65	0.44	0.54	0.64	0.64	0.69	0.56	0.70	0.97	1.12	0.45	0.63	0.53	0.78	0.74	0.54	0.45	0.54	0.64	0.45	12.13
M	0.70	0.76	0.62	0.77	0.70	0.79	0.84	0.80	0.83	0.82	0.79	1.77	0.81	0.80	0.80	0.73	0.74	0.83	0.77	0.78	0.73	15.45
MA	0.42	0.52	0.43	0.50	0.44	0.63	0.46	0.55	0.53	0.53	0.51	0.39	0.85	0.45	0.55	0.48	0.50	0.50	0.55	0.51	0.37	9.81
P	0.61	0.68	0.52	0.72	0.65	0.70	0.54	0.79	0.62	0.68	0.65	0.61	0.73	1.26	0.68	0.57	0.77	0.60	0.68	0.73	0.59	13.13
RB	0.17	0.24	0.13	0.20	0.23	0.22	0.24	0.18	0.31	0.31	0.31	0.16	0.24	0.21	0.44	0.25	0.15	0.15	0.19	0.23	0.15	4.28
SA	1.39	1.53	1.19	1.35	1.57	1.50	1.76	1.30	1.44	1.57	1.65	1.20	1.43	1.40	1.51	2.28	1.20	1.23	1.34	1.46	1.32	28.34
SC	0.83	0.86	0.77	0.88	0.87	1.03	0.81	1.29	0.91	0.98	0.94	0.78	1.03	0.91	0.88	0.79	1.44	0.89	1.14	0.89	0.78	18.24
SR	0.69	0.64	0.68	0.71	0.68	0.69	0.61	0.73	0.59	0.61	0.58	0.59	0.67	0.65	0.58	0.57	0.67	1.40	0.71	0.64	0.57	12.89
TA	0.64	0.73	0.65	0.83	0.73	0.95	0.74	0.96	0.82	0.80	0.75	0.57	0.92	0.74	0.74	0.62	0.94	0.66	1.26	0.78	0.69	15.26
ZN	0.81	0.99	0.65	0.75	0.94	0.80	0.71	0.76	0.79	0.82	0.79	0.58	0.83	0.72	0.81	0.68	0.72	0.66	0.71	1.26	0.59	15.12
CEA	1.13	1.10	0.95	1.13	1.01	1.22	1.11	1.15	1.03	1.03	1.10	0.84	1.12	1.09	1.01	1.07	1.03	1.01	1.14	1.09	1.79	21.34
TO	14.14	15.65	12.90	14.97	15.08	15.68	14.07	15.27	15.18	15.76	15.80	11.76	15.91	14.40	15.88	13.45	14.17	13.23	14.92	15.53	12.25	306.00
NET	−1.02	2.78	6.31	6.63	−2.18	−1.43	−12.14	0.49	6.78	2.45	3.68	−3.68	6.10	1.28	11.61	−14.89	−4.07	0.34	−0.34	0.41	−9.09	TCI = 14.57
NPDC	7	14	17	18	5	6	1	11	19	13	15	4	16	10	20	0	3	10	9	10	2

Notes: Each panel reports the static (full-sample) connectedness. The ij-th entry is the share of the H-step-ahead forecast-error variance of market i explained by innovations to market j. FROM and TO denote the total directional connectedness received from and transmitted to all other markets; NET = TO − FROM, with a positive (negative) value indicating a net transmitter (receiver); NPDC is the net pairwise directional connectedness; and TCI is the total connectedness index. Panels A, B, and C correspond to the overall, short-term (1–5 days), and long-term (more than 5 days) frequency bands, respectively.

); the main text discusses the summary statistics together with the block bootstrap confidence intervals (

Table 3. Connectedness measures and cross-quantile difference tests.

Panel A. Connectedness Levels by Quantile.
Quantile	Total TCI	Short-Run TCI (1–5 d)	Long-Run TCI (5–∞ d)	CEA NET (Aggregate)
q = 0.05	92.17 [91.79, 92.41]	75.30 [69.22, 79.56]	16.87 [12.62, 22.97]	−13.96 [−19.11, −8.40]
q = 0.50	58.77 [55.48, 62.58]	49.06 [45.86, 52.28]	9.71 [8.97, 11.00]	−0.74 [−3.60, 0.63]
q = 0.95	92.08 [91.71, 92.26]	77.51 [72.69, 80.56]	14.57 [11.48, 19.35]	−10.65 [−16.47, −5.96]
Panel B. Cross-quantile difference tests.
Comparison	Δ Total TCI		Δ CEA NET (Aggregate)
q = 0.05 − q = 0.50	32.86 [29.55, 36.08]		−12.85 [−18.77, −6.43]
q = 0.95 − q = 0.50	32.65 [29.49, 36.14]		−9.90 [−16.09, −4.42]

Notes: Brackets report [2.5%, 97.5%] confidence intervals obtained from a moving block bootstrap (B = 1000; block length = 20 trading days). TCI denotes the total connectedness index and NET the net directional connectedness; the short-run and long-run bands cover 1–5 days and more than 5 days, respectively. Panel A reports connectedness levels by quantile; Panel B reports cross-quantile differences (Δ), each obtained by paired moving block bootstrap, so an interval excluding zero indicates a significant difference.

) and the directional-network representation.

Table A3 reports the static connectedness matrix of the CEA and 20 commodity futures under the extreme downside quantile q = 0.05. Over the aggregate band, the system’s total connectedness index (TCI) reaches 92.17%, meaning that more than 90% of each asset’s variance is contributable to cross-market connectedness and reflecting a near-saturated linkage under extreme-downside conditions. The frequency decomposition shows that the short-term component (one to five days) contributes 75.30 percentage points (81.70% of the total), whereas the long-term component (more than five days) contributes only 16.87 percentage points (18.30% of the total), indicating that return transmission under extreme-downside conditions is highly concentrated in the high-frequency channel within one week [6].

Over the aggregate band, RB (NET = 7.24), TA (7.14), and MA (6.21) rank among the leading net transmitters, while M (−15.68), AU (−14.26), and CEA (−13.96) rank among the leading net receivers. The frequency decomposition reveals a short- versus long-run sign change in net directional connectedness: in the short term, FU (13.23), TA (10.99), RB (9.69), and CF (8.23) are net transmitters, while CEA (−24.11), AU (−12.84), M (−11.33), and AL (−7.54) are net receivers; in the long term, FU switches from 13.23 to −7.65 and CF from 8.23 to −11.59—most industrial commodities reverse the sign of their NET—whereas AL and I reverse into net transmitters (AL from −7.54 to 13.32, I from −6.02 to 10.32). This short- versus long-run sign change is consistent with the short- and long-term bands being associated with different types of shocks: the short-term component is associated mainly with the rapid diffusion of high-frequency information and price shocks, whereas the long-term component is consistent with the cumulative transmission of structural and persistent shocks through the low-frequency channel [6].

Under q = 0.05, the CEA exhibits a role configuration markedly different from that of the commodity system. Over the aggregate band, the CEA’s NET = −13.96 (95% bootstrap CI [−19.11, −8.40]), placing it among the leading net receivers together with M and AU. Under the direct constraint of the allowance system, the CEA mainly acts in the short term as a net receiver of high-frequency shocks from the energy, chemical, and ferrous-metal sectors, consistent with Jiang and Chen’s [2] finding of strong short-term frequency–domain linkages among carbon, energy, and material markets; the long-term band is more associated with the low-frequency, cumulative influence of persistent and structural factors.

Table A4 reports the static connectedness matrix of the 21 assets under the median condition q = 0.50. Over the aggregate band, the TCI is 58.77%, a marked decline from 92.17% under q = 0.05, reflecting that cross-market return transmission under normal market conditions is substantially weaker than at the extreme tails. The frequency decomposition shows that the short-term component contributes 49.06 percentage points (83.48% of the total) and the long-term component contributes 9.71 percentage points (16.52%), a band-share structure similar to that under q = 0.05 but with markedly lower absolute levels in both bands.

Over the aggregate band, CU (NET = 18.75), TA (16.91), RB (16.53), and J (14.05) rank among the leading net transmitters, while SR (−14.89), FG (−13.63), AU (−13.45), CF (−13.35), and M (−13.05) rank among the leading net receivers. The frequency decomposition shows that the net-spillover directions are highly consistent between the short and long run: in the short term, TA (14.89), J (13.64), CU (13.59), and RB (11.23) remain net transmitters, while CF (−12.09), M (−12.06), and SR (−11.86) remain net receivers; in the long term, CU (5.16), RB (5.30), and TA (2.02) continue to transmit shocks, while SR (−3.04) and FG (−3.19) continue to receive them. In sharp contrast to the widespread short- versus long-run sign changes under q = 0.05, the system under the median condition exhibits stable frequency consistency, reflecting that under normal market conditions, the directions of transmission channels are highly consistent and structurally stable.

Under the median condition q = 0.50, the CEA exhibits a role configuration markedly decoupled from the commodity system. Over the aggregate band, the CEA’s NET is −0.74 (close to zero), with outward transmission TO = 1.51 and reception FROM = 2.26, both among the lowest in the entire table, indicating that under the median state the CEA neither meaningfully transmits to nor receives from the commodity system. Under the frequency decomposition, both the short- and long-term NET values are close to zero (−0.55 and −0.19), showing none of the frequency-band sign changes observed under q = 0.05. This decoupling reflects the CEA’s policy-driven nature and relatively low liquidity: as an allowance asset directly constrained by the allowance system and still at an early, thinly traded stage of development, the CEA has only limited capacity to absorb or transmit cross-market shocks, so that under normal market conditions its linkage with the commodity system contracts markedly. This median decoupling is consistent in direction with Chen et al.’s [28] finding that the quantile connectedness of carbon–energy–metal markets is far higher at the extreme tails than at the median.

Table A5 reports the static connectedness matrix of the 21 assets under the extreme upside quantile q = 0.95. Over the aggregate band, the TCI reaches 92.08%, almost equal to the 92.17% under q = 0.05, reflecting tail symmetry in the system’s linkage under extreme market states. The frequency decomposition shows that the short-term component contributes 77.51 percentage points (84.18% of the total) and the long-term component contributes 14.57 percentage points (15.82%), a band-share structure similar to that under the other two quantiles.

Over the aggregate band, MA (NET = 6.72), J (6.17), EG (5.95), TA (5.85), and FU (5.42) rank among the leading net transmitters, while M (−14.60), AU (−11.32), and CEA (−10.65) rank among the leading net receivers. The frequency decomposition shows that, under q = 0.95, the system again exhibits widespread short- versus long-run sign changes in net directional connectedness: in the short term, FG (11.28), SA (10.84), EG (7.37), and CU (7.34) are net transmitters, while AU (−17.63), M (−10.91), CF (−9.38), and RB (−8.12) are net receivers; entering the long term, FG switches from 11.28 to −12.14 and SA from 10.84 to −14.89—most former short-term transmitters reverse into long-term receivers—whereas AU, CF, RB, and I reverse into long-term net transmitters (AU from −17.63 to 6.31, RB from −8.12 to 11.61, CF from −9.38 to 6.63, I from −5.40 to 6.78). The structural feature of short- versus long-run sign changes exists under both q = 0.05 and q = 0.95, but the specific set of assets involved differs, consistent with Wu and Huang’s [10] evidence on the quantile–frequency heterogeneity of carbon–energy–metal markets.

Under the extreme-upside quantile q = 0.95, the CEA exhibits a role configuration asymmetric to that under q = 0.05. Over the aggregate band, the CEA’s NET = −10.65, placing it among the leading net receivers with M and AU, of a magnitude similar to its −13.96 under q = 0.05. However, the frequency decomposition shows that under q = 0.95, unlike at q = 0.05, the CEA is a net receiver in both frequency bands (short-term NET = −1.56, long-term NET = −9.09), with its long-term reception strength even exceeding its short-term reception. Descriptively, the CEA’s long-term net position is somewhat less negative under extreme-downside than under extreme-upside conditions. However, because the band-level net measures are estimated imprecisely—the bootstrap confidence intervals for the CEA’s short- and long-run net connectedness contain zero, as discussed for Table 3 below—we interpret this pattern as descriptive rather than as evidence of a statistically established frequency-band directional change. This finding is highly consistent with Zhao and Yang’s [7] evidence on the downside/upside asymmetry of risk spillovers in China’s carbon–commodity markets.

Table 3 reports 95% block bootstrap confidence intervals for the headline connectedness statistics. The total connectedness index is estimated precisely at every quantile, and the interval for the difference between the two tail indices, [−0.21, 0.46], contains zero, so the null of tail symmetry cannot be rejected. The short-run band accounts for the larger share of total connectedness at all quantiles. The CEA’s aggregate net connectedness is significantly negative at both tails and statistically indistinguishable from zero at the median, consistent with the interpretation that the CEA behaves as a net receiver under tail conditions while remaining largely decoupled under normal conditions. A formal cross-quantile difference test (Table 3, Panel B) confirms these contrasts: both the total connectedness index and the CEA’s net connectedness differ significantly between each tail and the median (the corresponding intervals exclude zero), so the amplification of integration under extreme conditions and the CEA’s tail-specific role as a net receiver are statistically established rather than asserted. At the band level, by contrast, the net measures are estimated less precisely: the confidence intervals for the CEA’s short- and long-run net connectedness, and for their short-minus-long-run difference (e.g., −34.3 [−44.1, 12.0] at q = 0.05), all contain zero; we therefore do not interpret the frequency-band pattern as a statistically significant directional change. Confidence bands for the dynamic total connectedness index are reported in Appendix A Figure A1, where the two tail-quantile bands overlap throughout the sample, reinforcing the tail-symmetry result.

Figure 2 depicts the dynamic total connectedness index (TCI) of the system comprising the CEA and 20 commodity futures over the July 2021–February 2026 sample period at the three quantile levels q = 0.05, q = 0.50, and q = 0.95. Throughout the sample, the TCI under extreme-downside (q = 0.05) and extreme-upside (q = 0.95) conditions remains within a high and narrow band of 90–96%, with the two tail curves closely overlapping and exhibiting clear tail symmetry, whereas the median (q = 0.50) TCI fluctuates within a range of 54–70%, markedly below the tail levels. This dynamic pattern, in which tail connectedness exceeds the median, indicates that cross-market connectedness under extreme states is substantially stronger than during normal periods [10,28]. Because each estimate uses a 200-day rolling window, the dynamic series begins in May 2022; the February 2022 onset of the Russia–Ukraine conflict therefore predates the dynamic sample, so the dynamic figures capture only the conflict’s prolonged energy–commodity repercussions from the second half of 2022 onward, not its initial outbreak.

The median TCI exhibits a pronounced cyclical pattern over the sample. In the second half of 2022, the TCI climbed from about 60% to a sample peak of about 70% at the end of 2022, accompanying the global energy–commodity shock triggered by the Russia–Ukraine conflict. From the second half of 2024 to the second half of 2025, the TCI rose again to the 62–66% range, corresponding to the public consultation draft of the expansion reform in September 2024 and its first formal implementation in March 2025. Notably, the amplitude of the tail TCI over the sample is markedly smaller than that of the median: even in the face of cascading shocks such as the SVB collapse and the UBS takeover of Credit Suisse in March 2023, it shows no sharp rise or fall. This pattern of the dynamic tail TCI approaching its ceiling corroborates the earlier static analysis (Table A3 and Table A5), in which the TCI reaches 92.17%/92.08% under q = 0.05/0.95, indicating that in tail states the TCI is already near its ceiling and has limited marginal room to respond to individual events.

Figure 3 reports the time-varying paths of the short-term (one to five days) and long-term (more than five days) band components of the TCI under the three quantiles. Under the median condition q = 0.50 (Figure 3b), the short-term component dominates throughout (about 80–86% of the total), and no episode of the long-term component overtaking the short-term component is observed over the sample, reflecting that under normal market conditions return transmission is dominated by high-frequency information diffusion.

Under extreme-downside conditions q = 0.05 (Figure 3a), the switches in which the long-term component overtakes the short-term component are concentrated in windows of persistent external shocks. The most pronounced switch occurs during the cascading SVB–Credit Suisse crisis in the first quarter of 2023, when the long-term share rises to about 65–85%, constituting the most persistent long-term-dominated period in the sample. The second-half-2022 energy–commodity shock associated with the Russia–Ukraine conflict also coincides with a brief long-term-dominated switch. This pattern is consistent with the interpretation that cross-week persistent external shocks are transmitted more through the low-frequency channel, whereas transient information shocks are concentrated in the short-term channel [6].

Under extreme-upside conditions q = 0.95 (Figure 3c), the switching pattern exhibits a different event distribution: long-term-dominated switches concentrate in windows related to policy expectations and compliance, mainly the first formal expansion implementation in March 2025. This ‘policy expectations lifting the long-term component’ pattern is consistent with the contemporaneous rebound path of the median TCI in Figure 2, revealing the asymmetry in the event contexts associated with the frequency switches under q = 0.05 and q = 0.95: the downside tail is accompanied by persistent external shocks and the upside tail by policy expectations, and the pattern in which the upside tail is accompanied by policy implementation is consistent in direction with He’s [29] finding that the upside tail of China’s carbon market is associated with climate policy implementation.

Figure 4 reports the dynamic NET paths of the CEA and 20 commodity futures under the three quantiles q = 0.05, q = 0.50, and q = 0.95. A positive NET indicates that an asset is a net transmitter in the system, and a negative NET indicates a net receiver. Overall, the NET of each asset switches between positive and negative over the sample, indicating the contagion source/receiver roles of the assets continuously evolve over time, with the frequency and magnitude of switching differing significantly across quantiles.

Under the median q = 0.50, the CEA persistently acts as a net receiver, with its path fluctuating tightly within a narrow range below the zero line. Under extreme-downside conditions, q = 0.05, the CEA’s NET exhibits several pronounced positive spikes, most notably concentrated during the cascading SVB–Credit Suisse crisis in the first quarter of 2023, when the CEA briefly switches into a contagion source. Under extreme-upside q = 0.95, the CEA mostly maintains a net receiver role but shows pronounced upward jumps at the beginning of the dynamic sample in the second half of 2022, when the market was still in its early post-launch phase, in September 2024 around the public consultation draft of the expansion reform, and in March 2025 around the first formal expansion implementation. The activation of the downside tail is concentrated in windows of external macro shocks, and that of the upside tail in windows related to policy expectations and compliance, forming an asymmetric structure in the event contexts associated with the downside/upside tails, consistent with Zhao and Yang’s [7] evidence on the downside/upside asymmetry of risk spillovers in China’s carbon–commodity markets; the pattern in which the upside tail is accompanied by policy implementation is consistent in direction with He’s [29] finding.

An event window analysis provides additional identification-oriented evidence on these channels (Appendix A 

Table A1. Event-window regressions of the dynamic total connectedness index.

Panel A. Pooled Event Categories (Window ±10 Trading Days).
Quantile	β_EXT (External)		β_POL (Policy)
q = 0.05	0.185 *** [0.031]		−0.228 ** [0.106]
q = 0.50	0.046 [0.030]		0.104 [0.069]
q = 0.95	−0.248 *** [0.054]		−0.156 [0.196]
Panel B. Individual events (window ±10 trading days).
Quantile	SVB	Draft	Plan
q = 0.05	0.185 *** [0.031]	−0.234 [0.166]	−0.223 ** [0.109]
q = 0.50	0.045 [0.030]	0.128 [0.093]	0.082 [0.099]
q = 0.95	−0.256 *** [0.056]	−0.491 *** [0.076]	0.168 [0.186]

Notes: The dependent variable is the dynamic Baruník–Křehlík total connectedness index at each quantile. Each regression includes a constant and one lag of the dependent variable; Newey–West HAC standard errors are in brackets. β_EXT uses a ±10 trading-day window around the SVB collapse (10 March 2023); β_POL uses a ±10-day window around the September 2024 public consultation draft and the March 2025 formal expansion work plan; SVB, Draft and Plan are the corresponding individual-event dummies. The external shock coefficients are robust to ±5 and ±20 windows. *** p < 0.01, ** p < 0.05.

). Regressing the dynamic total connectedness index on event window dummies, while controlling for its own lag and using Newey–West standard errors, shows that the external shock window (the March 2023 SVB–Credit Suisse turmoil) is associated with significantly higher connectedness in the downside tail (q = 0.05) and significantly lower connectedness in the upside tail (q = 0.95), with no systematic effect at the median; this directional, tail-specific pattern is consistent with the interpretation that extreme-downside connectedness is particularly sensitive to external financial shocks, though the magnitudes are modest given that tail connectedness is already high. Policy-related events exhibit weaker and less consistent effects: while the formal expansion work plan of March 2025 is associated with higher post-event upside connectedness in before-after comparisons, the event window coefficients are statistically insignificant once persistence is controlled for, suggesting that policy effects may be gradual and partially anticipated rather than concentrated around a single date. The event window evidence thus provides stronger support for the external shock channel than for the policy channel, and we interpret the policy–tail association as suggestive rather than conclusive. To be explicit about the source of each result, the significant external shock effects (positive at q = 0.05, negative at q = 0.95) come from the event-window regressions in Table A1, whereas the higher upside connectedness around the March 2025 plan appears only in the raw before-after comparison and loses significance in the regression once persistence is controlled for. Because the signs and significance of the policy events are mixed across events and quantiles, we treat the policy–tail association as suggestive.

Under the median q = 0.50, the roles of other assets are relatively stable: CU, RB, and J act as net transmitters most of the time, while M, SR, and AU act as net receivers most of the time. Under extreme-downside q = 0.05, J and RB remain net transmitters most of the time, and M, SR, and AL remain net receivers most of the time; however, AU and P—stable receivers under the median—switch into net transmitters here, exhibiting a clear change in directional role. Under extreme-upside conditions, q = 0.95, J, CU, and RB remain net transmitters most of the time, and M and SR remain net receivers most of the time; the stable receivers under the median largely remain receivers here, with none of the widespread role changes seen under q = 0.05. System-level role changes are highly concentrated in the downside tail, indicating that such role changes are more frequent in the downside tail.

To move beyond this descriptive reading and quantify how stable these directional roles are, we further assess the cross-window stability of the NET rankings: for each quantile and band, the 200-day window is rolled across the sample, and the concordance of the resulting asset rankings is measured by Kendall’s W and by the average Spearman correlation between each window’s ranking and the full-sample ranking (Appendix A 

Table A7. Cross-window stability of the directional (NET) rankings.

Quantile	Band	Kendall’s W	Mean Spearman ρ
q = 0.05	Aggregate	0.023	0.060
	Short-run (1–5 d)	0.018	0.040
	Long-run (>5 d)	0.015	0.037
q = 0.50	Aggregate	0.705	0.779
	Short-run (1–5 d)	0.657	0.766
	Long-run (>5 d)	0.361	0.463
q = 0.95	Aggregate	0.110	0.267
	Short-run (1–5 d)	0.041	0.078
	Long-run (>5 d)	0.038	0.136

Notes: For each quantile and frequency band the 200-day rolling window is moved across the sample and the asset NET rankings are computed in each window. Kendall’s W (∈[0, 1]) measures the concordance of these rankings across windows; the mean Spearman ρ is the average rank correlation between each window’s ranking and the full-sample ranking. Higher values indicate more stable rankings. The rankings are highly stable under the median state but unstable in both tails.

). The rankings are highly stable under the median state (Kendall’s W = 0.705 and average Spearman ρ = 0.779 in the aggregate band) but become unstable at both tails (W = 0.023 and 0.110, ρ = 0.060 and 0.267 at q = 0.05 and q = 0.95, respectively), confirming that the identities of net transmitters and receivers vary substantially across stress episodes, consistent with the view that connectedness intensifies and the transmitter–receiver structure reconfigures during systemic stress [11]. We therefore do not base the tail-state conclusions on rolling window directional rankings; instead, the tail results rely on the full-sample bootstrap inference reported in Table 3.

Figure 5 reports the decomposed dynamic NET paths of the CEA and 20 commodity futures on the short-term (one to five days) and long-term (more than five days) bands under the three quantiles. A positive NET indicates that an asset is a net transmitter on that band, and a negative NET indicates that it is a net receiver.

Under the median q = 0.50, the CEA’s short-term NET is negative most of the time, acting stably as a short-term net receiver; its long-term NET is also predominantly negative, with no significant role change or strength shift observed in either band within event windows. Under extreme-downside q = 0.05, the CEA’s short-term NET switches from net transmitter to net receiver around the cascading SVB–Credit Suisse crisis in 2023, with its strength rising markedly to a sample high after the public consultation draft of the expansion reform in September 2024; its long-term NET switches from around the zero line to a deep net receiver around the 2023 SVB–Credit Suisse crisis, and reverses from net receiver to net transmitter—accompanied by a pronounced jump in strength—around the first formal expansion implementation in March 2025. Under extreme-upside conditions, q = 0.95, the CEA’s short-term NET maintains a high net-transmitter role during the second-half-2022 energy–commodity shock associated with the Russia–Ukraine conflict and turns into a net receiver around the 2023 SVB–Credit Suisse crisis; its long-term NET reverses from net receiver to net transmitter during this second-half-2022 shock window, reverses back to net receiver around the 2023 SVB–Credit Suisse crisis, and turns into a net transmitter again after the public-consultation draft of the expansion reform in September 2024. These band-level directional movements trace the time path of imprecisely estimated rolling NET measures; consistent with the full-sample bootstrap evidence discussed for Table 3—where the confidence intervals for the CEA’s short- and long-run net connectedness contain zero—the CEA’s band-level net positions are not statistically distinguishable from zero, so they are read as suggestive dynamics rather than established frequency band reversals.

The band roles of other assets are quantile-dependent. Under the median q = 0.50, in the short-term band, CU, J, RB, and TA—upstream industrial chain commodities—are stable net transmitters, while M, SR, and AU are stable net receivers; in the long-term band, AL, CU, I, J, and RB remain net transmitters and AU and SR remain net receivers, with most assets showing consistent judgments across the two bands. Under extreme-downside conditions, q = 0.05, in the short-term band only P is a net transmitter most of the time, while most other assets exhibit a time-varying pattern; in the long-term band AU reverses from a median receiver to a net transmitter, and CF, EG, and SR lean overall toward receivers. Around the first formal expansion implementation in March 2025, in the short-term band AU, M, and SA switch from net transmitters to net receivers, while FG, I, JM, and SC switch from net receivers to net transmitters; in the long-term band EG, I, MA, and SR switch from net transmitters to net receivers, while JM and P switch from net receivers to net transmitters, with the long-term NET of P and AU exhibiting a pronounced jump in strength in that window. Under extreme-upside conditions, q = 0.95, in the short-term band AG and CU are net transmitters most of the time, and M maintains a receiver role; in the long-term band I, MA, EG, and J are net transmitters most of the time, while most other assets exhibit a time-varying pattern. Around the 2023 SVB–Credit Suisse crisis, the divergence between the short- and long-term NET directions of assets such as AL, RB, CF, and SC reaches its sample high before gradually subsiding. The cross-quantile role change revealed in Figure 4 and the within-quantile short- versus long-run sign divergence shown in this figure constitute two independent structural features; the overall band pattern is consistent with Wu and Huang’s [10] evidence on the quantile–frequency heterogeneity of carbon–energy–metal markets.

Figure 6b shows that under the median state q = 0.50, upstream industrial chain commodities such as CU, TA, RB, and J systematically act as core net transmitters across the three bands, while SR, FG, AU, CF, and M systematically act as the main net receivers, with node roles highly consistent across bands. The network is relatively dense in the aggregate and short-term bands, the most prominent transmission paths being AG → AU, CU → AU, and CU → AG (strong connections within precious metals and between non-ferrous and precious metals), as well as the outflows of industrial commodities to chemicals, glass, and soda ash, such as TA → CF, RB → FG, and RB → SA. In the long-term band, the network density drops sharply, with most cross-asset connections falling below the threshold and being omitted, leaving only a few weak connections such as CU → AG, AL → ZN, and RB → I. Across all three bands, the CEA is a node of very small magnitude that does not enter the leading ranks of net transmitters or receivers, and in the long-term band, it is almost fully decoupled from the system, reflecting the lack of a stable low-frequency linkage between the CEA and the commodity system under normal conditions.

Figure 6a shows that under the downside tail q = 0.05, the network density is markedly higher than under the median state. In the aggregate band, RB, TA, MA, AL, and J rank among the leading net transmitters, while M, AU, and CEA rank among the leading net receivers. In the short-term band, FU, TA, RB, and CF are the main net transmitters, whereas the CEA is the largest net receiver in the entire network—almost all of the strongest edges point toward the CEA (FU → CEA, RB → CEA, TA → CEA, MA → CEA, EG → CEA, CF → CEA, etc.), meaning that the energy, chemical, and ferrous-metal sectors collectively channel shocks into the CEA through the high-frequency channel under extreme-downside conditions, exhibiting a typical ‘many-to-one’ pattern. In the long-term band, a widespread short- versus long-run sign change in net directional connectedness occurs: AL and I reverse from short-term net receivers into long-term net transmitters, and the main low-frequency transmission paths shift to AL → CF, I → CF, CEA → CF, and AL → FU, meaning that energy-intensive metals in turn transmit shocks to the chemical and fuel oil sectors through the low-frequency channel. Zhou et al. [30], using a quantile-VAR network, find significant extreme risk spillovers among the carbon, energy, and metal markets and pronounced differences in the network centrality of individual markets; this paper further characterizes the CEA’s role along the frequency dimension: its net reception is concentrated in the short-term high-frequency channel, whereas its long-term net position is not statistically distinguishable from zero (see the band-level bootstrap intervals discussed for Table 3).

Figure 6c shows that under the upside tail q = 0.95, the network density is similar to that under q = 0.05 (tail symmetry), but the node role configuration is asymmetric with that of the downside tail. In the aggregate band, MA, J, EG, TA, and FU collectively assume the net-transmitter role, while M is the single largest net receiver in the entire network—almost all of the strongest edges point toward M (J → M, EG → M, MA → M, FU → M, TA → M, etc.), constituting a ‘many-to-one’ inflow pattern. In the short-term band, FG, SA, EG, and CU are the main net transmitters, and AU becomes the largest net receiver, with the strongest edges concentrated toward AU (SA → AU, FG → AU, AG → AU, TA → AU, etc.). In the long-term band, widespread sign changes reappear: FG and SA switch from short-term net transmitters into the largest long-term net receivers (with RB → SA, RB → FG, CF → FG, AU → SA, etc., pointing toward SA and FG), while AU, RB, CF, and I reverse into long-term net transmitters. Unlike under q = 0.05, the CEA remains a net receiver in both the aggregate and long-term bands and is close to zero in the short term, showing none of the downside tail pattern of short-term reception reversing into long-term transmission, which corroborates the upside/downside asymmetry of the CEA’s tail role. Across the three quantiles, the ‘sparse median, dense tails’ difference in network density is consistent with Chen et al.’s [28] evidence that quantile connectedness is far higher at the tails than at the median; and the asymmetric pattern of different dominant sinks across the two tails (inflow to CEA in the downside short term, to M in the upside aggregate, and to AU in the upside short term) is consistent with Gong et al.’s [31] finding of U-shaped asymmetric tail dependence in carbon finance risk.

4.3. Wavelet Coherence Analysis

Figure 7 shows that, in the long-term band (64–256 days), the CEA exhibits persistent and significant coherence with multiple high-emission industrial chain nodes, with arrows pointing up-right (↗︎) and the CEA tending to precede in an in-phase, positive relationship. The coherence regions of CEA–AL and CEA–ZN span from the second half of 2022 to 2024, coinciding in time with the window of the global energy–metal shock triggered by the Russia–Ukraine conflict in the second half of 2022—AL and ZN, both energy-intensive smelting products, may move synchronously with the CEA over long horizons in response to energy-price shocks and the carbon constraint cycle. The CEA’s long-term coherence with JM and J, as well as FG, MA, and SA is likewise significant, with the CEA tending to precede over a relatively long span; the further strengthening of coherence coincides in time with two policy windows—the September 2024 consultation draft of the carbon market expansion plan (covering steel, cement, and aluminium) and the first formal expansion implementation in March 2025—where AL is a commodity directly covered by this expansion, JM and J as upstream raw materials of the steel chain are indirectly affected by expansion expectations, and FG, MA, and SA are high-emission potential nodes under discussion for subsequent coverage. This low-frequency lead–lag pattern is consistent in direction with Zhou et al.’s [30] finding of long-term spillovers among the carbon, energy, and non-ferrous metal markets.

In contrast to the pattern of the CEA tending to precede the above industrial commodities, CEA–SC shows significant coherence in the long term but with arrows close to horizontal rightward (→), indicating near-synchronous movement—possibly reflecting that SC and the CEA are jointly driven by the macroeconomic cycle, energy price expectations, and policy expectations, rather than the carbon price actively leading industrial commodities in a transmission chain. Long and Cao [32], over the 2014–2021 sample, find a regime switch around 2019 in the CEA–SC lead–lag relationship; this paper further reveals that, in the long-term band, this relationship has evolved into near-synchrony, a pattern that also complements He’s [29] evidence on the asymmetric structure of tail risk spillovers between the CEA and energy markets in the low-frequency channel. In the medium-term band (16–64 days), the CEA exhibits directionally heterogeneous anti-phase lags with agricultural products: for CEA–SR, the arrow points up-left (↖︎) with the CEA tending to precede SR in anti-phase, and the coherence is concentrated during the period of surging international sugar prices and tight domestic sugar supply in 2023–2024, possibly reflecting that rising carbon prices reversely suppress SR’s medium-term expectations through cost transmission; for CEA–SA, the arrow points down-left (↙︎) with SA tending to precede the CEA in anti-phase, suggesting a reverse SA → CEA feedback channel in the medium-term band; and for CEA–P, the arrow points up-right (↗︎) with the CEA tending to precede in-phase. This directional differentiation is consistent with Yao et al.’s [4] finding of heterogeneous spillovers between China’s CEA and agricultural futures.

In contrast to the above coherence groups, the CEA exhibits almost no significant long-term coherence with several assets. The long-term coherence of CEA–AU largely disappears, with only an arrow down-left (↙︎) at 64–128 days (AU tending to precede the CEA in anti-phase), reflecting that AU’s low-frequency price logic is mutually independent of the CEA’s policy drivers; the long-term coherence of CEA–AG is likewise sparse. The long-term coherence of CEA–CU, CEA–FU, CEA–RB, CEA–TA, and CEA–I largely disappears, indicating that the CEA’s long-term influence does not cover the entire industrial chain but is highly structured around the nodes most directly exposed to emission costs. The long-term coherence of CEA–M and CEA–CF is similarly sparse, possibly reflecting global supply factors more than carbon price signals. This structured decoupling pattern is consistent with Wu and Huang’s [10] finding of quantile–frequency heterogeneity in carbon–energy–metal markets, revealing the market segmentation feature of carbon price transmission.

Across the three bands, the coherence between the CEA and the 20 commodity futures is frequency-stratified: in the short term (2–16 days) the arrows are scattered and the phase unstable, reflecting the dominance of intraday information flow and noise; in the medium term (16–64 days) significant coherence is more stable, with the agricultural anti-phase–lag pattern concentrated here; and in the long term (64–256 days) the coherence regions are stable, with the CEA tending to precede nodes such as AL, ZN, JM, J, SA, MA, and FG and moving almost synchronously with SC, while decoupling from AU, CU, FU, RB, TA, I, and most agricultural products. Wavelet phase difference arrows summarize average relative timing and may partly reflect common drivers rather than direct influence. Accordingly, the results are interpreted as evidence consistent with lead–lag patterns rather than proof of economic leadership. The long-term coherence regions span the large 2022–2024 window, aligning in time with the late tail of the Russia–Ukraine shock and the September 2024–March 2025 policy windows, consistent with Gong et al.’s [31] finding that carbon–finance tail-risk transmission exceeds its normal level—the increase in long- and medium-frequency fluctuations during crisis and policy windows is the main source of the rise in coherence. The CEA’s low-frequency linkage with the commodity markets is structurally concentrated around the industrial chain nodes most directly exposed to carbon emission costs, revealing the structured and selective nature of the carbon price signal transmission path.

4.4. Wavelet Quantile Correlation Analysis

In Figure 8, the short-term (2–16 days) and medium-term (16–64 days) bands show very low overall color saturation, with almost no prominent color blocks in most panels in these bands, reflecting that the correlation structure between the CEA and commodity futures is overall weak at monthly or shorter cycles. Only SA and CF show horizontal light red bands in the lower part of the medium-term band, and EG and TA show localized light red at 16–32 and 32–64 days, but their intensities are clearly lower than those of the main correlation regions in the long- or super long-term bands of the same panel. This feature of the overall weak short- and medium-term correlation structure is also consistent in direction with Sun et al.’s [33] finding that carbon-related market linkages concentrate mainly at medium-to-long scales.

The 128–256-day region of the long-term band is where positive correlation is most concentrated on the CEA–commodity WQC plane. AL, ZN, AG, and CU exhibit, at 128–256 days and between q = 0.3 and 0.7, the most prominent red bands in the entire panel, reflecting strong positive correlation with the CEA at the median quantiles in this location. In particular, ZN’s red band further extends synchronously to 64–128 and 256–512 days, forming a wide band spanning all three time intervals of the long-term band and showing a stable positive correlation distribution between zinc futures and the CEA in the long-term band. This band-dominated median-dependence pattern is consistent in direction with Qi et al.’s [3] finding that the cross-quantile dependence between China’s carbon and commodity markets strengthens as the frequency lengthens; this paper further shows that this long-term dependence is concentrated mainly in the median quantile interval (q = 0.3–0.7) and exhibits clear heterogeneity across commodities.

The other two time intervals of the long-term band display the features of a few commodities deviating from the dominant band. At 64–128 days, only the red block for I concentrates here (q = 0.3–0.8), indicating that the positive correlation between iron ore and the CEA is most concentrated at 64–128 days rather than 128–256 days. At 256–512 days, the red block P concentrates alone in the lower quantiles (q = 0.2–0.4), J shows a light red wide band covering most quantiles, and SA instead appears light blue (negative correlation). Together, these three observations indicate that a few commodities’ correlation structures with the CEA are distributed more across longer bands, and that some commodities’ correlation directions differ from those of most commodities.

The super long-term band (Smooth, ≥512 days), although not the main cluster, concentrates high-intensity correlation structures at the tail quantiles of the WQC plane and exhibits a clear deep red–deep blue directional polarization. The most prominent features on the deep blue side are the deep blue blocks of AU and AG at the upper quantiles of the Smooth band (around q = 0.7), constituting the most prominent negative correlation region among the 20 panels; M likewise shows a deep blue block at the lower quantiles (around q = 0.2), exhibiting negative correlation with the CEA in this band; and CU shows a medium-intensity blue block in the upper tail of the Smooth band, although it is less prominent than AU and AG. The deep red side covers three groups of commodities at differing positions: the deep red blocks of SC and FU concentrate mainly at the lower-to-median quantiles, MA and EG concentrate at the median-to-upper quantiles, and the positive correlations of SR and SA are distributed mainly at the median and lower quantiles. CF, JM, and J are relatively pale in this band, showing no clear correlation structure with the CEA. This quantile heterogeneity of super long-term tail dependence is also consistent in direction with Maghyereh and Abdoh’s [34] finding that tail dependence in commodity markets varies heterogeneously across quantiles and frequencies.

4.5. Robustness Tests

To examine the sensitivity of the main conclusions to model specification and method choice, this paper conducts robustness checks along four dimensions: the rolling window width, the forecast horizon, common driver control, and the mother wavelet replacement.

Figure 9a reports the dynamic TCI series after shortening the QVAR rolling-window width from the baseline w = 200 to w = 150. Across the three quantiles (q = 0.05, 0.50, 0.95), the TCI series retain the baseline ‘tail-symmetric, median-heterogeneous’ structure: the tail quantile TCI remains stable between 93% and 95%, while the median quantile TCI exhibits pronounced time variation within the range of 55–72%, continuing the baseline ‘high–decline–rebound’ dynamic path. As the overall connectedness measure of the QVAR variance decomposition, the stability of the TCI indicates that this paper’s QVAR results are robust to the rolling window width specification.

Figure 9b reports the dynamic TCI series after shortening the variance decomposition forecast horizon from the baseline H = 20 to H = 10. The TCI series at the three quantiles are overall consistent with the baseline in both magnitude and time-varying shape: the tail quantile TCI remains stable between 93% and 94%, and the median quantile TCI follows the same ‘high–decline–rebound’ path within the range of 58–70%. This indicates that this paper’s QVAR results remain stable under different forecast horizon specifications.

Beyond the parameter settings, this paper further checks the robustness of the connectedness and quantile dependence results from two angles: potential common driver control and mother wavelet replacement.

Figure 10 reports the partial wavelet coherence (PWC) results controlling for crude oil (SC) [35]. After removing SC—identified in Figure 7 as a potential common driver strongly coherent with the CEA—the coherence structure between the CEA and most commodities still retains clear red coherence regions in the long-term band (about 64–128 days), and their temporal distribution largely overlaps with the baseline WTC coherence regions over 2022–2024. This indicates that the CEA–commodity long-term linkage reported in Figure 7 is not fully explained by the crude oil channel, and that a relatively stable long-band linkage structure remains between the CEA and the commodity markets.

We further extend this common-driver control beyond crude oil to a broad equity market proxy, since the carbon and commodity markets may also co-move because of common macro-financial forces rather than only through direct bilateral transmission. Specifically, we compute the partial wavelet coherence between the CEA and each commodity, controlling for the CSI 300 index (Appendix A Figure A2). The long-horizon (64–256 days) coherence between the CEA and the high-emission commodities (e.g., aluminium, zinc, and coking coal) remains substantial after partialling out the equity market, declining only modestly relative to the unconditional coherence; this indicates that the carbon–commodity linkage is not merely a by-product of common equity market movements.

Figure 11 re-estimates the WQC after replacing the mother wavelet from LA(8) with Daubechies-4. The image structures of the 20 panels remain overall consistent with the Figure 8 baseline in three core features: the median quantile red bands at 128–256 days in the long-term band remain clear for AL, ZN, AG, and CU; the deep blue blocks of AU and AG at the upper quantiles and the deep red blocks of SC and FU at the lower quantiles in the super long-term band still appear simultaneously; and CF, JM, and J still show weak correlation structures in this band. This indicates that the main quantile–frequency dependence patterns reported in Figure 8 are preserved under the alternative mother wavelet specification.

Beyond the four checks above, we further assess whether the conclusions are driven by a particular part of the sample by splitting the data at the September 2024 public consultation draft and re-estimating the static connectedness in each subperiod (Appendix A 

Table A2. Subsample stability of the static connectedness measures.

Panel A. Total Connectedness Index (TCI).
Quantile	Pre	Post	Full
q = 0.05	92.26	95.23	92.17
q = 0.50	60.06	59.57	58.77
q = 0.95	92.06	92.04	92.08
Panel B. CEA Net Connectedness (Aggregate).
Quantile	Pre	Post	Full
q = 0.05	−15.17	−73.81	−13.96
q = 0.50	0.30	−1.79	−0.74
q = 0.95	−10.87	−8.72	−10.65

Notes: Pre = July 2021 to the September 2024 public consultation draft (764 observations); Post = thereafter (342 observations); Full = full sample (1106 observations). Entries are static Baruník–Křehlík connectedness measures (lag order p = 1, forecast horizon 100). The shorter post-reform subsample yields less precise tail estimates, particularly for single-asset measures such as the CEA’s net connectedness (e.g., the q = 0.05 value); emphasis is therefore on qualitative consistency rather than exact numerical equality.

). Three of the four main findings remain qualitatively unchanged across subperiods: tail connectedness stays substantially higher than median state connectedness (about 92–95% versus roughly 60%); the CEA remains a net receiver at both tails (its net connectedness is negative in both subsamples); and the median state stays close to disconnectedness (the CEA’s net connectedness is near zero). The symmetry between the lower- and upper-tail connectedness is broadly preserved but becomes somewhat weaker in the post-reform subsample, in which the lower tail is somewhat more connected than the upper tail. Because the post-reform subsample is shorter (342 observations), its tail estimates are less precise—particularly for single-asset measures such as the CEA’s net connectedness—so we emphasize qualitative consistency rather than exact numerical equality. In particular, the post-reform q = 0.05 CEA net connectedness (about −73.8, versus −14.0 in the full sample) is estimated with substantially greater sampling uncertainty in this short post-reform subsample; we therefore interpret it as small-sample imprecision rather than an economically meaningful change and rely on the full-sample estimates.

5. Conclusions

Within a unified framework integrating quantile connectedness, frequency decomposition, and wavelet analysis, this paper examines the return connectedness between China’s national carbon emission allowance (CEA) market and 20 representative commodity futures. We find that cross-market return transmission is highly state-dependent: connectedness is near-saturated and symmetric across the upper and lower tails but falls markedly under normal conditions; the CEA is largely decoupled from the commodity system under normal conditions and is drawn in only at the tails as a net receiver. The event contexts associated with the downside and upside tails are mutually asymmetric—the former accompanied mainly by external financial shocks and the latter mainly by domestic carbon market policy expectations; wavelet analysis further shows that the CEA tends to precede high-emission commodities such as aluminium, zinc, and coking coal over long horizons, with the linkage highly structured around the most emission-intensive industrial chain nodes. This evidence indicates that, at the current stage, CEA price formation is still largely shaped by institutional and policy factors, and its market-based financial attributes have yet to strengthen. This is consistent with broader evidence that financial behavior can respond strongly to institutional reform and social channels rather than to market fundamentals alone [36].

These results carry direct implications for carbon market regulation. First, the CEA’s low connectedness with the commodity system under normal conditions and its very low outward connectedness indicate that its transmission channels with the real commodity markets are still relatively limited; as expansion proceeds toward steel, cement, and aluminium smelting, efforts should focus on strengthening the transmission and absorption of real-sector risk through the carbon price. Second, given that the CEA passively receives external shocks from energy and high-emission industrial chains in the downside tail, monitoring and disclosure of abnormal carbon price fluctuations should be reinforced during windows of global financial turbulence. Third, the activity of the upside tail is accompanied by expectations around expansion and compliance, suggesting that the pace and transparency of policy releases themselves amplify the long-horizon carbon–commodity linkage; regulators should therefore emphasize the predictability of policy communication when advancing expansion, so as to prevent expectation shocks from spilling over to the real commodity markets via the carbon price. Ultimately, these patterns speak to the carbon market’s role in the low-carbon transition: because carbon pricing can steer real-economy decarbonization only if its signal reaches the high-emission sectors, deepening the integration of the carbon market with the real commodity economy matters for its capacity to advance China’s dual-carbon goals and sustainable low-carbon development.

For investors and hedgers, our findings provide a state-dependent and frequency-dependent basis for risk management. First, under normal market conditions, the CEA can offer some diversification benefit to a commodity portfolio; however, under extreme states, this diversification effect weakens markedly, so investors should adopt a hedging framework that adjusts dynamically with the market state rather than using static weights. Second, the CEA’s long-horizon lead over high-emission commodities such as aluminium, zinc, and coking coal can serve as a low-frequency reference for managing exposure to these commodities, whereas the short-term high-frequency channel mainly reflects noise and should not be used for frequent rebalancing. We stress, however, that this lead–lag pattern is a descriptive empirical regularity rather than a validated, exploitable signal: because the national CEA market is young and strongly policy-driven, the estimated linkage may not be stable out of sample and should be interpreted as a qualitative indication of market interdependence rather than a mechanical rule for portfolio allocation or exposure management. Third, given that the upside tail linkage is accompanied by carbon market policy expectations, investors holding the relevant exposures should closely follow expansion and compliance policy arrangements and pay particular attention to the potential changes in the carbon–commodity linkage around major policy windows.

More broadly, the implications above should be read as descriptive interpretations of the estimated connectedness, lead–lag, and event window patterns rather than as actionable trading or regulatory rules. In particular, this study does not test out-of-sample forecasting or hedging performance, so whether the documented state- and frequency-dependent linkages possess economically meaningful forecasting or hedging value remains an open empirical question. These implications should therefore be treated as indicative guidance for risk monitoring and policy design, to be validated in future work as the national carbon market matures and longer samples accumulate.

This study also has limitations that point to directions for future research. The national CEA market was established only recently, and the sample period is relatively limited; as expansion deepens and data accumulate, the conclusions warrant further testing over longer samples. This paper focuses on 20 representative individual futures; future work could incorporate a wider range of commodity varieties, spot markets, and other financial assets to depict a more complete connectedness network. In addition, introducing high-frequency data, structural-break tests, or cross-country comparisons with mature markets such as the EU ETS would help to further clarify the mechanisms of carbon–commodity return transmission.