Developing a Sustainable Risk Warning Framework for Short-Term Cross-Border Capital Flows: Empirical Analysis Based on Heterogeneous Exchange Rate Expectations

Abstract

The supervision of and early warning about cross-border capital flows are crucial for maintaining financial stability. This study develops a sustainable risk warning framework that incorporates the heterogeneous exchange rate expectations of foreign exchange market participants into a comprehensive indicator system. Using the KLR signal analysis method and data for China covering the period from July 2005 to June 2022, the framework is empirically evaluated for its ability to predict short-term capital inflow and outflow risks. The results show that incorporating heterogeneous expectations significantly enhances the accuracy and robustness of early warning performance. Regardless of the specific estimation method, the proposed Weighted Heterogeneous Expectation Indicator demonstrates stable and effective predictive capacity across different market environments, underscoring its time-varying adaptability and robustness. Early warning indicators exhibit varying sensitivities, highlighting the importance of a holistic assessment that captures multiple market dimensions. Overall, the proposed sustainable framework strengthens the monitoring of short-term cross-border capital flow risks in China and provides methodological insights for improving risk warning systems in other economies.

1. Introduction

Since the 2008 global financial crisis, the global economic and political landscape has undergone profound transformations, accompanied by increasing uncertainty in international financial markets and heightened volatility in cross-border capital movements. The acceleration of globalization and financial liberalization has enabled capital to flow more freely across borders, amplifying both opportunities for investment and exposure to systemic financial risks. Short-term cross-border capital flows, in particular, are characterized by high sensitivity to market expectations and policy changes. While surges in inflows can stimulate asset price growth and economic expansion, abrupt reversals often trigger exchange rate pressures and destabilize domestic financial systems [1,2]. Given these developments, developing a sustainable risk warning framework for short-term cross-border capital flows has become essential for enhancing global financial resilience. Sustainable risk management emphasizes not only timely identification and response to emerging risks but also the establishment of adaptive and data-driven monitoring systems that can function effectively under evolving macroeconomic and policy environments. Such a framework supports long-term financial stability by improving early warning capacity, enhancing policy coordination, and strengthening the overall resilience of the international financial system.

China offers a particularly relevant empirical setting for exploring such a framework. As one of the world’s largest recipients and sources of international capital, China has undergone rapid market liberalization alongside gradual RMB exchange rate reform and deeper financial openness. These reforms, together with the macroeconomic and policy responses to the COVID-19 shock, have magnified the scale and complexity of short-term capital movements and increased the likelihood of speculative inflows and sudden reversals. For these reasons, China serves as a representative case for testing how heterogeneous market expectations and an adaptive warning architecture interact in an open emerging-market environment.

Existing research on the monitoring and risk warning of cross-border capital flows frequently identifies exchange rate expectations as a critical indicator. However, a common limitation in these studies is the assumption of homogeneous exchange rate expectations among foreign exchange market participants, often relying on a single expectation measure to represent the entire market. In reality, the heterogeneity of exchange rate expectations and the resulting divergence in trading behaviors have gained increasing relevance in the discourse on short-term cross-border capital flows. These factors are too significant to be overlooked in risk warning research. This paper contributes to the literature in several ways. First, it integrates heterogeneous exchange rate expectations into the empirical analysis of short-term cross-border capital flow risk warning, thereby capturing the dynamic and multifaceted nature of the foreign exchange market. Second, it constructs a weighted exchange rate expectation index that reflects both the heterogeneity and market influence of different types of traders, enhancing the informativeness of expectation-based indicators. Third, and most importantly, this study enhances the traditional KLR early-warning framework by embedding a nonlinear exchange rate equilibrium model that captures the dynamic and heterogeneous expectations of foreign exchange market participants. Rather than merely adding an individual indicator, the approach integrates expectation-weighted measures derived from the heterogeneous agent model into the KLR signal-generation mechanism, allowing the early-warning system to reflect market dynamics more accurately and to identify expectation-driven speculative pressures that the standard KLR structure cannot detect. Finally, in line with this research motivation, we advance the central hypothesis that incorporating heterogeneous exchange rate expectations into the early warning system significantly improves the accuracy, robustness, and sustainability of short-term capital flow risk prediction.

The remainder of this paper is structured as follows. Section 2 reviews the literature on risk warning of cross-border capital flows as well as heterogeneous exchange rate expectations, and highlights the existing research gaps. Section 3 develops the short-term cross-border capital flow early warning model, detailing the design of the early warning mechanism and the selection of indicators. Section 4 presents the construction of the Weighted Heterogeneous Expectation Indicator using the foreign exchange market equilibrium model, covering data description, parameter estimation, and empirical results. Section 5 presents an empirical analysis of the early-warning system for short-term cross-border capital flows using Chinese market data, including the early-warning analysis and robustness checks. Section 6 concludes with the main findings and policy implications.

2. Literature Review

2.1. Risk Warning of Cross-Border Capital Flows

Research on cross-border capital flow risk warning can be broadly categorized into two main areas: studies on currency crisis warnings triggered by abnormal capital flows and studies on the construction of monitoring and early warning systems. Currency crisis warning models mainly include the KLR signal analysis method, the FR probability model, the STV cross-sectional regression model, and neural network (NN) approaches.

The KLR signal analysis method, which identifies key indicators and threshold values to monitor financial market fluctuations and predict currency crises within a 24-month horizon, was pioneered [3]. Subsequent studies have extended and refined this approach. For example, the early warning process has been divided into short-, medium-, and long-term stages, and a composite warning indicator incorporating both external and internal economic factors has been developed [4,5]. For example, 15 early warning indicators have been employed to identify financial crisis trends similar to those preceding the 2008 global financial crisis [6]. The FR probability model, which treats currency crises as discrete events influenced by multiple factors and estimates their likelihood using cumulative probability distributions, was introduced [7,8]. This framework later evolved into Probit and Logit models. To enhance prediction accuracy, the KLR and FR models have been combined. A financial stress early warning system using the Logit model has been constructed [9], and its application in Nigeria demonstrated a significant link between exchange rate misalignment and crisis risk [9,10]. Emerging markets were found to face increasing crisis probabilities after 2020 [11]. The STV cross-sectional regression model, incorporating cross-country variations to analyze the determinants of financial crises, has also been developed [12]. Neural network models, inspired by human brain processes, have gained traction in crisis warning research; artificial neural network (ANN) techniques have been applied to currency crisis prediction, while a neuro-fuzzy hybrid causal model has outperformed traditional methods in predicting crises and identifying underlying causal mechanisms, offering a more prescriptive framework for crisis prevention [13,14]. Comparative studies on model performance remain inconclusive; for example, ANN has exhibited superior out-of-sample predictive performance [15]. The random forest model has been shown to achieve higher accuracy than the Logit model, and BP neural networks improve corporate financial risk forecasting, outperforming traditional methods in accuracy and reliability [16,17]. Machine learning, especially NARX neural networks, has also been demonstrated to effectively forecast energy prices, outperforming traditional methods and supporting market stability and informed decision-making under uncertainty [18].

Research on China’s cross-border capital flow monitoring and early warning systems has employed diverse methodologies, reflecting the field’s increasing complexity and evolving analytical perspectives. Both the STV and KLR models have been applied to China, identifying external shocks as key destabilizing factors [19]. Building on earlier work, the scale of short-term cross-border capital flows has been quantified, and a comprehensive early warning index constructed using principal component analysis [20]. The study of capital flow risks in emerging economies has been expanded by developing an indicator system covering economic fundamentals, investor sentiment, exchange rate movements, and contagion, highlighting contagion as a key trigger of financial instability [21]. A refined early-warning framework has also been developed by selecting indicators across macroeconomic, external financing, foreign debt, and financial market dimensions, constructing a PCA-based monitoring index, and emphasizing the role of gray channels and illicit cross-border capital flows [22]. The procyclical nature of China’s short-term cross-border capital flows has been incorporated into a KLR-based model, integrating bank foreign exchange positions, capital and financial account flows, and cross-border payment willingness, with model validity confirmed via the prosperity index method [23]. Machine learning approaches, using Lasso-PCA, have been applied to identify key indicators of abnormal cross-border capital flows in China, effectively forecasting tail risks and highlighting macro-financial factors driving inflows and outflows [24].

2.2. Heterogeneous Exchange Rate Expectations

Early studies on exchange rate expectations assumed homogeneous trader behavior. Heterogeneity in survey data was later identified, a finding subsequently confirmed [25,26]. The idea was further developed using chaos theory, showing that interactions between fundamental and technical traders can generate complex, nonlinear dynamics in exchange rates [27].

Building on these, a “herd effect” from trend extrapolation has been documented [28], while discrepancies between individual forecasts and market consensus have been noted to be influenced by economic events and forecast horizons [29]. Short-term volatility is primarily driven by technical traders [30]. Subsequent studies explored the sources of heterogeneity more deeply: differences in information access and adaptive strategies were analyzed, and traders’ subjective interpretations of information were highlighted [31,32]. Time-varying effects on exchange rate movements due to carry traders and variations in information processing across trader types have also been examined [33,34]. Learning models have been introduced to reveal nonlinear mechanisms underlying expectation heterogeneity [35]. More recently, evolving heterogeneous expectations have been shown to continue driving market fluctuations, emphasizing the persistent impact of trader diversity [36]. Exchange rate responses to monetary policy surprises exhibit heterogeneity, with informational effects and other factors explaining deviations from standard predictions, highlighting the limitations of conventional models in capturing currency behavior [37]. Sectoral heterogeneity has been shown to significantly shape the impact of real exchange rate movements on manufacturing exports in emerging economies, with low- and medium-complexity sectors being most sensitive, illustrating the limitations of aggregate RER measures [38].

Turning to the RMB market, research on heterogeneous exchange rate expectations has deepened understanding of their dynamics and drivers. The formation mechanisms and the nature of heterogeneity have been reviewed, distinguishing between rational and boundedly rational expectations [39]. Central bank interventions and rational versus adaptive expectations have been examined, confirming the heterogeneity of trader behavior [40]. An equilibrium model incorporating expectation heterogeneity and psychological coefficients has been developed, providing a more refined analytical framework [41]. The role of carry traders in driving deviations of exchange rates from their fundamental values has been highlighted, emphasizing the influence of diverse trading strategies [42]. Increased central bank communication has been shown to amplify expectation heterogeneity, underscoring the role of policy transparency [43]. Further evidence suggests that interest rate spread traders exacerbate deviations between market-clearing and fundamental exchange rates, highlighting the destabilizing effects of speculative activity [44]. Heterogeneous trader behavior has been linked to cross-border capital flows, showing that fundamental traders dominate short-term flows, whereas interest rate spread and technical traders influence longer-term dynamics, highlighting the crucial role of trader composition in shaping capital flow patterns [45]. Heterogeneous agent models have been demonstrated to effectively capture RMB exchange rate dynamics, with stabilizers mitigating excessive volatility and aligning market rates with fundamentals through timely expectation management [46].

2.3. Research Gaps

Existing research has explored the early warning and management of cross-border capital flows, as well as the role of heterogeneous exchange rate expectations, from multiple perspectives. However, several important gaps remain. First, although extensive research has been conducted on both cross-border capital flow risk warning and heterogeneous exchange rate expectations, existing studies have rarely integrated heterogeneous expectations and their influence on capital flows into the analysis of capital flow risk warning frameworks. Second, most existing warning models rely heavily on static macroeconomic indicators, which limits their capacity to capture dynamic market expectations and evolving financial conditions. Consequently, such models often lack sustainability and adaptability in rapidly changing global environments. Third, limited attention has been given to how heterogeneous exchange rate expectations shape the timing, intensity, and persistence of short-term capital flow risks.

This study aims to address the aforementioned research gaps by incorporating the heterogeneous exchange rate expectations of foreign exchange market participants to explore a sustainable and dynamic framework for risk warning. By doing so, it enhances the forecasting and management of China’s cross-border capital flow risks. The proposed framework not only improves the predictive accuracy of early warning systems but also provides actionable insights for policymakers and market participants, deepening the understanding of the dynamic behavioral mechanisms through which exchange rate expectations influence cross-border capital flows.

3. Establishment of a Short-Term Cross-Border Capital Flow Early Warning Model

3.1. Model Selection and Early Warning Principles

Existing studies commonly employ several early-warning models, including the KLR signal analysis method, the FR probability model, the STV cross-sectional regression model, and the neural network model, each with distinct characteristics. The FR probability model is structurally simple but highly dependent on sample size for accuracy, while the STV cross-sectional regression model assesses crisis probability but cannot predict the timing of crises. Neural network models demonstrate strong stability and adaptability but are abstract and prone to overfitting. In contrast, the KLR signal analysis method generates early-warning signals based on multi-level indicators, enabling monetary authorities to proactively prevent and manage market disruptions. Its noise-to-signal ratio minimization principle provides an intuitive and practical framework for indicator selection, and the threshold-search mechanism inherently provides robustness by optimizing indicator cut-offs. Compared with alternative approaches, such as the FR probability model or neural networks, the KLR method is particularly suitable for this study due to the limited number of short-term cross-border capital flow events and the focus on directional early-warning signals rather than probability forecasts. Therefore, the KLR signal analysis method is adopted here as the most appropriate approach for assessing cross-border capital flow risks and constructing the early-warning model.

Building on the discussions above and the established early warning indicator system, this study develops a short-term cross-border capital flow risk early warning model by closely following the standard KLR framework. Specifically, the procedure involves four main steps: first, identifying risk events and defining the crisis episodes for cross-border capital outflows and inflows (Section 3.1.1); second, screening the optimal thresholds for each selected early warning indicator based on the noise-to-signal ratio (Section 3.1.2); third, generating individual early-warning signals for each indicator by comparing historical data with the optimal thresholds (Section 3.1.3); fourth, aggregating these signals into a composite early-warning index using both simple and weighted methods (Section 3.1.4). This stepwise procedure ensures that each indicator, including the Weighted Heterogeneous Expectation measure, is fully integrated into the KLR framework, providing a transparent and systematic mechanism for early-warning analysis.

3.1.1. Risk Event Identification

A core function of the early warning model is to signal potential crises. This requires identifying periods characterized by abnormal short-term cross-border capital flows. Risk events are defined based on the historical behavior of short-term cross-border capital flows, following the widely used crisis-identification approach in the literature [47]. Specifically, the upper and lower thresholds are set at the historical mean plus and minus 1.5 times the standard deviation, respectively. This threshold balances the detection of meaningful stress episodes against the avoidance of excessive noise. A ±1 SD threshold would generate too many spurious signals, while a ±2 SD threshold would miss several recognized episodes of capital flow stress. Therefore, the ±1.5 SD threshold is adopted as the most suitable criterion for the Chinese context. When capital flows exceed these bounds, they are classified as risk events. If short-term cross-border capital inflows surpass the upper threshold, an inflow risk is identified; if short-term cross-border capital outflows fall below the lower threshold, an outflow risk is identified.

3.1.2. Optimal Threshold Screening of Early Warning Indicators

Abnormal fluctuations in early warning indicators can signal potential cross-border capital flow risks. To assess whether an indicator exhibits abnormal changes, a critical threshold must be established. If an indicator’s value exceeds this threshold, it generates an early warning signal; otherwise, no signal is issued. The more indicators that signal within the early warning system, the higher the likelihood of a cross-border capital flow crisis within the next 24 months. To determine optimal thresholds systematically, this study employs the grid search method, following existing literature and adhering to the principle of minimizing the noise-to-signal ratio (NSR). A lower NSR indicates a higher proportion of accurate signals, enhancing the predictive effectiveness of the model.

The NSR calculation involves four possible scenarios based on whether an early warning indicator signals and whether a crisis occurs within the next 24 months: (A) true signal, the indicator signals and a risk event occurs; (B) false signal, the indicator signals but no risk event occurs; (C) missed event, the indicator does not signal, yet a risk event occurs; (D) correct non-signal, the indicator does not signal and no risk event occurs. The NSR for the i-th indicator is then calculated as:

$${\mathrm{N}\mathrm{S}\mathrm{R}}_i={\displaystyle \frac{N_{B_i}/N_{B_i}+N_{D_i}}{N_{A_i}/N_{A_i}+N_{C_i}}}$$

(1)

where $N_{A_i}$, $N_{B_i}$, $N_{C_i}$, and $N_{D_i}$ denote the historical frequencies of scenarios A–D, respectively.

3.1.3. Signal Generation Based on Optimal Thresholds

Building on the identification of risk events (Section 3.1.1) and the optimal thresholds determined for each early warning indicator (Section 3.1.2), this subsection describes how individual indicator signals are generated within the KLR framework. For each selected indicator, the historical data are examined on a period-by-period basis. If the indicator value in a given period exceeds the optimal threshold corresponding to either short-term cross-border capital outflow or inflow risk, a risk signal is triggered for that period. This procedure is applied separately to all indicators, ensuring that each contributes appropriately to the early-warning analysis. The generated signals are then aggregated according to the methods described in Section 3.1.4 to form the composite early-warning index. By explicitly linking the optimal threshold to the signal generation process, this step ensures a transparent and systematic application of the KLR methodology across all indicators.

3.1.4. Constructing the Early Warning Signal Aggregation Composite Index

It should be noted that the early-warning analysis in this study is conducted based on the composite indices, constructed through both simple and weighted aggregation methods, rather than individual indicators. By aggregating signals from multiple indicators, the composite indices inherently capture the joint effects of different indicators, reflecting the overall early-warning strength for short-term cross-border capital outflow and inflow risks. While potential nonlinear interactions between indicators (e.g., multiplicative effects) are not explicitly modeled, the aggregation approach already accounts for the combined influence of all indicators. Exploring explicit interactions among indicators represents a promising avenue for future research, but it does not affect the validity of the current early-warning analysis.

Simple Aggregation Method

The Simple Aggregation Composite Index is constructed by first determining the optimal threshold for each early warning indicator, as described in the preceding methodology. Using these established thresholds, the number of early warning signals generated by each indicator for both short-term cross-border capital outflow and inflow risks is quantified over the historical period. The Simple Aggregation Composite Index is then calculated as follows:

$$S_t^j={\sum }_{i=1}^n{I}_{\left(j_t\right)}^i$$

(2)

In this equation, $S_t^j$ represents the sum of early warning signal values from n indicators at time t. Here, $j=1$ indicates short-term cross-border capital outflow risk, and $j=2$ indicates inflow risk. $I_{\left(j_t\right)}^i$ takes a value of 1 or 0, indicating whether the $i$-th indicator issued a warning signal for the $j$-type risk at time $t$. A higher $S_t^j$ value corresponds to a stronger overall early warning signal intensity, implying a greater likelihood of the respective short-term cross-border capital flow risk occurring within the next 24 months.

Weighted Aggregation Method

To account for differences in predictive performance among indicators, a weighted aggregation composite index is constructed, with each indicator’s weight determined by its ${\mathrm{N}\mathrm{S}\mathrm{R}}_i$. The weighted index is calculated as follows:

$$S_t^{j^{\prime }}={\sum }_{i=1}^n\left({\displaystyle \frac{I_{\left(j_t\right)}^i}{{\mathrm{N}\mathrm{S}\mathrm{R}}_i}}\right)$$

(3)

Here, $S_t^{\left(j^{\prime }\right)}$ denotes the weighted composite index value of the warning signals generated by $n$ indicators at time $t$. A higher $S_t^{\left(j^{\prime }\right)}$ indicates a stronger collective warning signal from the system, reflecting an increased probability of a short-term cross-border capital flow crisis within the next 24 months.

3.2. Selection of Early Warning Indicators

To construct a comprehensive early warning model for short-term cross-border capital flows, this study selects indicators that capture both market-driven and traditional macro-financial factors. Accordingly, the indicators are divided into two categories. The first category introduces a Weighted Heterogeneous Expectation Indicator, which integrates the heterogeneous expectations of foreign exchange market participants and represents the core innovation of this study. The second category comprises traditional indicators, including macroeconomic and financial variables commonly used in early warning models.

3.2.1. Weighted Heterogeneous Expectation Indicator

Under a floating exchange rate system, changes in exchange rate expectations among foreign exchange market participants significantly affect the arbitrage behavior of international investors [48]. Anticipated currency appreciation tends to attract capital inflows, while expectations of depreciation often trigger outflows. In the RMB foreign exchange market, the 2015 exchange rate reform strengthened market-based pricing mechanisms, thereby amplifying the influence of exchange rate expectations on cross-border capital flows [49].

Existing studies generally assume homogeneity among market participants and commonly use the one-year non-deliverable forward (NDF) rate as a proxy for overall market expectations [23,49,50]. However, research indicates significant heterogeneity in market participants, suggesting that a single homogeneous measure cannot fully capture the diversity of expectations and trading behaviors. To address this limitation, this study constructs a Weighted Heterogeneous Expectation Indicator (WE). For each period, the expected RMB exchange rate changes of the three trader types are multiplied by their respective market shares and then summed to form a weighted series. This indicator captures the aggregate market expectation while incorporating trader heterogeneity and serves as a replacement for the conventional NDF-based measure in the short-term cross-border capital flow early-warning system. The predictive performance of WE is compared with that of the traditional NDF-based indicator to evaluate improvements in forecasting accuracy. A detailed description of the measurement procedure is provided in Section 4.

Heterogeneous exchange rate expectations influence cross-border capital flows through the way heterogeneous traders process information and adjust their portfolios. Traders form exchange rate expectations based on their distinct beliefs and respond to market information accordingly. Under risk aversion and utility maximization, they rebalance their foreign exchange portfolios and positions, thereby making specific trading decisions. When they expect the domestic currency to appreciate, they tend to increase holdings of domestic assets and reduce foreign currency positions, generating capital inflows. When they anticipate depreciation, they reduce domestic asset holdings and increase foreign currency positions, resulting in capital outflows. This mechanism transforms trading decisions shaped by heterogeneous expectations into actual cross-border capital movements. Moreover, heterogeneous traders not only make different decisions under the same information set but also update their beliefs and trading behavior in subsequent periods based on past investment outcomes. As a result, the market shares of different trader types adjust dynamically with changes in information. A weighted expectation measure that incorporates these time-varying market shares therefore captures traders’ dynamic responses to information and the interactive effects of their decisions more comprehensively, providing a more effective and consistent indicator for monitoring capital inflows and outflows driven by heterogeneous exchange rate expectations.

Building on the Weighted Heterogeneous Expectation indicator described above, this study further extends the traditional KLR early-warning framework by embedding these model-based measures into the signal-generation process. In the standard KLR approach, crisis signals are generated by comparing individual macro-financial indicators with their respective thresholds, treating all indicators as exogenous and independent of traders’ dynamic behavior. By incorporating the expectation-weighted measures derived from the heterogeneous agent model, the KLR framework is enriched with real-time information on market participants’ belief dispersion and dynamic trading responses. This integration enables the early-warning system to capture expectation-driven speculative pressures and shifts in capital-flow risks that cannot be identified under the conventional KLR structure, thereby enhancing the accuracy, robustness, and practical relevance of the short-term cross-border capital-flow risk predictions.

For each historical period, the Weighted Heterogeneous Expectation indicator generates an early-warning signal by comparing its value with the optimal threshold corresponding to either capital inflow or outflow risk, as determined in Section 3.1.2. If the indicator exceeds the threshold, a risk signal is triggered for that period. These signals are subsequently incorporated into the composite early-warning index described in Section 3.1.4, ensuring that expectation-driven speculative pressures are fully reflected in the final early-warning system.

3.2.2. Traditional Indicators

Following the principles of comprehensiveness, representativeness, scientific rigor, and data availability, this study selects a set of traditional indicators for cross-border capital flow risk monitoring, drawing on related studies [23]. The indicators cover three levels of macroeconomic fundamentals, foreign exchange market conditions, and micro-level transaction behaviors to capture the multidimensional drivers of capital flow fluctuations.

At the macro level, the Manufacturing Purchasing Managers’ Index (${PMI}_t$) reflects China’s economic performance and investor confidence, where expansion or contraction signals affect the direction of cross-border capital flows [51]. (China Manufacturing Purchasing Managers’ Index: referred to as PMI. This index can reflect the overall macroeconomic situation of the country. The higher the index value, the better the macroeconomic environment.) The current account balance (${CA}_t$) captures the external position and overall international transaction trends [52]. Arbitrage investment Balance (${SI}_t$), measured by the variation in securities and other financial investments, indicate short-term speculative capital movements driven by financial account activities. The interest rate differential between China and the United States (${IR}_t$) represents global interest rate arbitrage incentives influencing international capital allocation.

At the market and micro levels, indicators describe foreign exchange operations and expectations of market participants. The trade deviation index (${TD}_t$) measures the mismatch between the trade value and banks’ foreign exchange settlements, reflecting the settlement behaviors of importers and exporters [23]. The calculation formula is as follows:

$${TD}_t=[\left({FE}_t^a-O_t\right)-\left({FE}_t^b-I_t\right)]/(O_t+I_t)$$

(4)

where ${FE}_t^a$ represents the amount of foreign exchange settled by banks on behalf of customers in period t, $O_t$ denotes the export trade value in period t, ${FE}_t^b$ represents the amount of foreign exchange sold by banks on behalf of customers in period t, and $I_t$ denotes the import trade value in period t. The willingness of market participants to pay foreign exchange (${FE}_t^p$) (the foreign exchange purchase rate, also known as the import sales rate, is the ratio of the foreign exchange sold by a bank on behalf of a customer to the foreign exchange paid by the bank on behalf of a customer) and to hold foreign exchange (${FE}_t^s$) (the foreign exchange income settlement rate, also known as the export settlement rate, is the ratio of the bank’s foreign exchange settlement on behalf of customers and the bank’s foreign-related income on behalf of customers), respectively, proxy importers’ and exporters’ behavioral responses to exchange rate expectations, jointly indicating capital inflow and outflow pressures [52]. A summary of these indicators is provided in

Table 1. Summary of Traditional Indicators.

Indicator Name	Symbol	Measurement	Key References
Weighted Heterogeneous Exchange Rate Expectation	${WE}_t$	Weighted index reflecting heterogeneous RMB expectations among FX market participants (see Section 4)	[35,45,53]
Manufacturing Purchasing Managers’ Index	${PMI}_t$	Monthly PMI value reflecting macroeconomic conditions	[51]
Trade Deviation Index	${\mathrm{T}\mathrm{D}}_t$	Calculated as Equation (1)	[23]
Current Account Balance	${CA}_t$	Current account value in balance of payments	[52]
Arbitrage Investment Balance	${SI}_t$	Δ(Securities investment + Other investments)	[52]
Interest Rate Differential	${IR}_t$	Domestic interest rate minus U.S. rate	[51]
Willingness to Pay Foreign Exchange	${FE}_t^p$	Foreign exchange payment purchase rate	[54]
Willingness to Hold Foreign Exchange	${FE}_t^s$	Foreign exchange income settlement rate	[54]

.

Building on the above framework, data for all early warning indicators, except for Weighted Heterogeneous Exchange Rate Expectation, can be obtained directly. Following the methodology of the literature, this study develops a nonlinear foreign exchange market equilibrium model that incorporates the heterogeneous exchange rate expectations of market participants [45]. The model is grounded in existing theoretical frameworks on exchange rate determination and heterogeneous expectations, and is employed to quantify the heterogeneous expectations of participants in the RMB foreign exchange market [27,53]. All data processing and empirical analyses were conducted using MATLAB R2017b, EViews 10, and Microsoft Excel (Office 2016).

4. Construction of the Weighted Heterogeneous Exchange Rate Expectation Indicator

This section focuses on constructing a Weighted Heterogeneous Exchange Rate Expectation by capturing the heterogeneous expectations of participants in the RMB foreign exchange market. To this end, a nonlinear foreign exchange market equilibrium model is first developed to characterize traders’ heterogeneous expectations. The following subsections describe the data and its descriptive statistics, outline the parameter estimation process of the equilibrium model, and report the resulting Weighted Heterogeneous Exchange Rate Expectation.

4.1. Foreign Exchange Market Equilibrium Model Construction

4.1.1. Heterogeneous Exchange Rate Expectations of Foreign Exchange Traders

Based on existing literature, this study assumes that the foreign exchange market comprises three types of traders: fundamental traders, chartists, and carry traders, who differ in the beliefs through which they form expectations. These three types of traders represent the commonly adopted classification in heterogeneous agent models of the foreign exchange market, reflecting the heterogeneous beliefs and corresponding exchange rate expectations observed among market participants [27,45,52]. This classification provides the foundation for constructing the weighted heterogeneous exchange rate expectation indicators.

First, fundamental traders formulate their exchange rate expectations based on macroeconomic fundamentals. They assume that exchange rates fluctuate around their fundamental equilibrium values. Consequently, their exchange rate expectations can be expressed as follows:

$${\widehat{E}}_t^1(∆{\epsilon }_{t+1})={\overline{\delta }}_1({\epsilon }_{t-1}^{\ast }-{\epsilon }_{t-1})$$

(5)

Here, ${\widehat{E}}_t^1(∆{\epsilon }_{t+1})$ represents the expected change in the RMB exchange rate from time $t$ to $t+1$ as anticipated by fundamental traders. The parameter ${\overline{\delta }}_1$ denotes the expected speed of adjustment of the RMB exchange rate toward its fundamental value. Additionally, ${\epsilon }_{t-1}^{\ast }$ denotes the fundamental exchange rate at time $t-1$, while ${\epsilon }_{t-1}$ indicates the spot exchange rate at time $t-1$.

Second, chartists (technical analysis traders) focus on the direct relationship between exchange rate trends and historical movements. They assume that future exchange rate changes follow patterns observed in historical data. Consequently, their exchange rate expectations can be expressed as:

$${\widehat{E}}_t^2(∆{\epsilon }_{t+1})={\overline{\delta }}_2({\epsilon }_{t-1}-{\epsilon }_{t-2})$$

(6)

where ${\widehat{E}}_t^2(∆{\epsilon }_{t+1})$ represents the expected change in the exchange rate from time $t$ to $t+1$ as anticipated by technical analysis traders. ${\overline{\delta }}_2$ denotes the reaction coefficient capturing traders’ sensitivity to past exchange rate movements, and ${\epsilon }_{t-2}$ denotes the spot exchange rate at time $t-2$.

Third, carry traders base their strategies on the uncovered interest parity (UIP) theory, assuming that exchange rate fluctuations are primarily driven by interest rate differentials between domestic and foreign markets. Their exchange rate expectations can be expressed as:

$${\widehat{E}}_t^3(∆{\epsilon }_{t+1})={\overline{\delta }}_3(i_{t-1}^f-i_{t-1}^d)$$

(7)

where ${\widehat{E}}_t^3(∆{\epsilon }_{t+1})$ represents the expected exchange rate change from time $t$ to $t+1$ as anticipated by carry traders. ${\overline{\delta }}_3$ denotes the sensitivity coefficient reflecting the impact of interest rate differentials on exchange rate expectations, $i_{t-1}^f$ denotes the foreign interest rate at time $t-1$; and $i_{t-1}^d$ denotes the domestic interest rate at time $t-1$.

4.1.2. Optimal Foreign Currency Asset Holdings

Assume that the foreign exchange market comprises two types of monetary assets: one denominated in domestic currency and the other in foreign currency. Let $C_t^i$ denote the total funds available to the i-th type of trader at time t, where $i=1, 2, 3$ corresponds to fundamental traders, technical analysis traders, and carry traders, respectively. The amount of funds available to the i-th trader at time t + 1, denoted $C_{t+1}^i$, can be expressed as:

$$C_{t+1}^i=V_t^i(1+i_t^f){\epsilon }_{t+1}+(C_t^i-{\epsilon }_t{V}_t^i)(1+i_t^d)$$

(8)

Here, $V_t^i$ denotes the investment in foreign currency-denominated assets by the i-th trader, $i_t^f$ and $i_t^d$ denote the risk-free interest rates for foreign and domestic currency assets, respectively, and ${\epsilon }_t$ and ${\epsilon }_{t+1}$ denote the domestic currency spot exchange rates at times $t$ and $t+1$. The term $C_t^i-{\epsilon }_t{V}_t^i$ represents the portion of the trader’s funds allocated to domestic currency assets.

Following existing research, the expected utility of the trader’s disposable amount at time $t+1$ is assumed to increase with the size of the disposable amount and decrease with investment risk. Accordingly, the expected utility function for the i-th trader can be formulated as:

$$U_t^i(C_{t+1}^i)={\widehat{E}}_t^i(C_{t+1}^i)-{\displaystyle \frac{1}{2}}{\widehat{\mu }}_i{\widehat{\sigma }}_t^i(C_{t+1}^i)$$

(9)

Here, $U_t^i(C_{t+1}^i)$ denotes the expected utility of the i-th trader’s disposable amount at time $t+1$, ${\widehat{E}}_t^i(C_{t+1}^i)$ denotes its expected value, ${\widehat{\mu }}_i$ is the risk aversion coefficient of the i-th trader, and ${\widehat{\sigma }}_t^i(C_{t+1}^i)$ denotes the conditional variance of the disposable amount. By substituting $C_{t+1}^i$ into the utility function, we obtain:

$$U_t^i(C_{t+1}^i)=(1+i_t^f){\widehat{E}}_t^i({\epsilon }_{t+1})V_t^i+(C_t^i-{\epsilon }_t{V}_t^i)(1+i_t^d)-{\displaystyle \frac{1}{2}}{\widehat{\mu }}_i{[(1+i_t^f)V_t^i]}^2{\widehat{\sigma }}_t^i({\epsilon }_{t+1})$$

(10)

To determine the optimal investment in foreign currency-denominated assets, we set the first-order derivative of $U_t^i(C_{t+1}^i)$ with respect to $V_t^i$ to zero. This yields the optimal investment:

$$V_t^i={\displaystyle \frac{1}{{(1+i_t^f)}^2}}·{\displaystyle \frac{(1+i_t^f){\widehat{E}}_t^i({\epsilon }_{t+1})-(1+i_t^d){\epsilon }_t}{{\widehat{\mu }}_i{\widehat{\sigma }}_t^i({\epsilon }_{t+1})}}$$

(11)

Among these, ${\widehat{\sigma }}_t^i({\epsilon }_{t+1})$ denotes the conditional variance of the spot exchange rate at time $t+1$. A higher ${\widehat{\sigma }}_t^i({\epsilon }_{t+1})$ indicates a higher investment risk. The variance is calculated as:

$${\widehat{\sigma }}_t^i({\epsilon }_{t+1})={[{\widehat{E}}_{t-2}^i({∆\epsilon }_{t-1})]}^2$$

(12)

4.1.3. Dynamic Adjustment of Heterogeneous Traders’ Proportions

Following the literature, in the foreign exchange market, traders continuously adjust their heterogeneous beliefs based on profits realized in the previous period. This dynamic adjustment reflects the principle that market influence is not static but depends on the relative success of each trader type over time. Specifically, when the current profit of trader type $i$ falls below that of the previous period, their proportion in the market decreases; conversely, when the current profit exceeds the previous level, their proportion increases. This adaptive learning mechanism allows the composition of trader types in the foreign exchange market to evolve dynamically, generating a time-varying market share for each trader type. These time-varying proportions serve as weights in constructing the weighted heterogeneous exchange rate expectation indicators, which are then used as core variables in the early-warning analysis. The adjustment process is governed by the following equations:

$${\tilde{\delta }}_t^i=\left\{\begin{array}{c}{\displaystyle \frac{e^{\phi {\tilde{p}}_{t-1}^i}}{e^{\phi {\tilde{p}}_{t-1}^1}+e^{\phi {\tilde{p}}_{t-1}^2}+e^{\phi {\tilde{p}}_{t-1}^3}}} if \left|i_t^d-i_t^f\right|>\tau \\ {\displaystyle \frac{e^{\phi {\tilde{p}}_{t-1}^i}}{e^{\phi {\tilde{p}}_{t-1}^1}+e^{\phi {\tilde{p}}_{t-1}^2}}} if \left|i_t^d-i_t^f\right|\le \tau \end{array} i=1,2\right.$$

(13)

$${\tilde{\delta }}_t^i=\left\{\begin{array}{c}{\displaystyle \frac{e^{\phi {\tilde{p}}_{t-1}^i}}{e^{\phi {\tilde{p}}_{t-1}^1}+e^{\phi {\tilde{p}}_{t-1}^2}+e^{\phi {\tilde{p}}_{t-1}^3}}} if \left|i_t^d-i_t^f\right|>\tau \\ 0 if \left|i_t^d-i_t^f\right|\le \tau \end{array} i=3\right.$$

(14)

Here, ${\tilde{\delta }}_t^i$ denotes the proportion of trader type $i$ at time $t$. The parameter $\phi$ captures the intensity of belief adaptation among traders: a smaller value of $\phi$ indicates weaker adaptability, whereas a larger value reflects stronger responsiveness to profit differentials.

The threshold parameter $\tau$ represents the critical level of the domestic–foreign interest rate differential $\left|i_t^d-i_t^f\right|$. When this differential exceeds $\tau$, carry traders enter the market. Following existing literature, $\tau$ is set to 0.03. The term ${\tilde{p}}_{t-1}^i$ represents the risk-adjusted profit of trader type $i$ at time $t-1$, defined as:

$${\tilde{p}}_t^i=p_t^i-{\widehat{\mu }}_i{\widehat{\sigma }}_t^i({\epsilon }_{t+1})$$

(15)

where $p_t^i$ denotes the unadjusted profit of trader type i at time t, calculated as:

$$p_t^i=[(1+i_{t-1}^f){\epsilon }_{t-1}-(1+i_{t-1}^d){\epsilon }_{t-2}]sgn[{\widehat{E}}_{t-2}^i({∆\epsilon }_{t-1})+i_{t-1}^f{\widehat{E}}_{t-2}^i({\epsilon }_{t-1})-i_{t-1}^d{\epsilon }_{t-2}]$$

(16)

The first term, $(1+i_{t-1}^f){\epsilon }_{t-1}-(1+i_{t-1}^d){\epsilon }_{t-2}$ represents investment profits. The function $sgn\left(x\right)$ is an indicator function that determines whether the direction of the exchange rate change aligns with traders’ expectations:

$$sgn(x)=\left\{\begin{array}{c}1 if x>0\\ -1 if x<0 \\ 0 if x=0 \end{array}\right.$$

(17)

4.1.4. Model Solution

In the foreign exchange market equilibrium, the total demand for foreign currency must equal the total supply. As described earlier, total demand is determined by the weighted sum of the foreign exchange demands of heterogeneous traders. Conversely, total supply in the foreign exchange market is jointly influenced by the net value of the current account and the central bank’s foreign exchange interventions. This relationship can be expressed as follows:

$$\left\{\begin{array}{c}{D}_t=\sum {\tilde{\delta }}_t^i({\tilde{p}}_t^i)V_t^i[{\widehat{E}}_t^i({\epsilon }_{t+1})]\\ S_t=W_t+I_t \end{array} \right.$$

(18)

where $D_t$ denotes the total demand for foreign currency at time $t$, while $S_t$ represents the total supply at the same time. The total supply depends on the net value of the current account ($W_t$) and the value of the central bank’s foreign exchange intervention $\left(I_t\right)$, with ${\eta }_1$ and ${\eta }_2$ as their respective coefficients.

By equating the total demand and total supply of foreign currency, the equilibrium exchange rate ${\epsilon }_t$ at time $t$ can be determined, ensuring market clearing in the foreign exchange market.

$${\epsilon }_t={\displaystyle \frac{{(1+i_t^f)}^2\left\{{\sum }_{i=1,2,3}\left[\frac{{\widehat{E}}_t^i({\epsilon }_{t+1})}{1+i_t^f}·\frac{{\tilde{\delta }}_t^i}{{\widehat{\mu }}_i{\widehat{\sigma }}_t^i({\epsilon }_{t+1})}\right]-{(\eta }_1{W}_t+{\eta }_2{I}_t)\right\}}{{\sum }_{i=1,2,3}\left[(1+i_t^d)·\frac{{\tilde{\delta }}_t^i}{{\widehat{\mu }}_i{\widehat{\sigma }}_t^i({\epsilon }_{t+1})}\right]}}$$

(19)

At this stage, a nonlinear foreign exchange market equilibrium model incorporating heterogeneous exchange rate expectations and accounting for anchoring-induced expectation bias has been fully established.

4.2. Data and Descriptive Statistics

Based on the exchange rate model developed above, the variables required to measure heterogeneous traders’ exchange rate expectations include the RMB spot exchange rate (${\epsilon }_t$), the domestic and foreign risk-free interest rates ($i_t^d$ and $i_t^f$), the RMB fundamental exchange rate (${\epsilon }_t^{\ast }$), the net current account value ($W_t$), and foreign exchange intervention ($I_t$). The RMB spot exchange rate is represented by the RMB-USD central parity rate. The domestic risk-free interest rate is proxied by the one-month bond yield in the Chinese interbank bond market, while the foreign risk-free rate is represented by the one-month U.S. Treasury yield. The net current account value is calculated from China’s import–export balance. The RMB fundamental exchange rate (${\epsilon }_t^{\ast }$) is estimated using a time-varying model that incorporates inflation and interest rate assumptions, following an established methodology for fundamental exchange rate estimation [55]. Foreign exchange intervention ($I_t$) is measured by changes in foreign exchange reserves, adjusted for interest income, consistent with the standard approach in the literature [56]. The sample period spans from July 2005 to June 2022. All original data are obtained from the Wind database. Descriptive statistics for all variables are reported in

Table 2. Descriptive Statistics of Variables Used in the Foreign Exchange Equilibrium Model.

Variable	Mean	S.D.	Minimum	Maximum	ADF t-Statistic
${\epsilon }_t$	6.732	0.497	6.104	8.076	−2.797 *
${\epsilon }_t^{\ast }$	6.839	0.374	6.257	7.865	−2.828 *
$i_t^f$	0.010	0.015	0.000	0.052	−2.180
$i_t^d$	0.034	0.013	0.010	0.078	−4.276 ***
$W_t$	303.075	205.932	−320.020	979.410	0.176
$I_t$	−88.486	458.663	−1156.598	1090.417	−3.128 **

Note: *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

.

According to Table 2, the descriptive statistics reveal several key characteristics of the variables. On average, the RMB spot exchange rate is lower than the RMB fundamental exchange rate, while the mean risk-free interest rate of U.S. dollar assets is lower than that of RMB assets. The positive mean of the import–export balance indicates an overall trade surplus, whereas the negative mean of foreign exchange intervention suggests a net decline in foreign exchange reserves over the sample period. In terms of volatility, the RMB spot exchange rate displays greater fluctuations than the RMB fundamental exchange rate, as reflected in its higher standard deviation. Likewise, the U.S. risk-free interest rate shows relatively high variability. Examining the extremes, the minimum value of the RMB spot exchange rate is below that of the RMB fundamental exchange rate, and the maximum value of the U.S. risk-free interest rate is lower than that of the Chinese risk-free rate. Augmented Dickey–Fuller (ADF) unit root tests were conducted for all variables. The results indicate that most indicator series are stationary at the 10% significance level, while a few series exhibit a unit root. It should be noted that stationarity is not a prerequisite for the nonlinear least squares estimation of the foreign exchange market equilibrium model, which focuses on minimizing the nonlinear fitting error rather than relying on the asymptotic properties of linear regression.

4.3. Parameter Estimation of the Equilibrium Model

This study employs the damped least squares method to estimate the parameters of the foreign exchange market equilibrium model. The estimation results are reported in

Table 3. Estimated Parameters of the Foreign Exchange Equilibrium Model.

Parameter	Coefficient Estimate	Standard Error	t-Statistic	p-Value
${\tilde{\delta }}_t^1$	0.706 ***	0.096	7.369	0.000
${\tilde{\delta }}_t^2$	1.559 ***	0.032	48.274	0.000
${\tilde{\delta }}_t^3$	−6.764 ***	0.289	−23.377	0.000
${\widehat{\mu }}_1$	0.088 **	0.038	2.303	0.022
${\widehat{\mu }}_2$	6.915 ***	1.948	3.551	0.000
${\widehat{\mu }}_3$	−0.201 **	0.097	−2.080	0.039
$\phi$	−17.812 ***	2.004	−8.888	0.000
${\eta }_1$	−0.002 *	0.001	−1.704	0.090
${\eta }_2$	0.001	0.000	1.505	0.134
Taylor inequality coefficients		0.008
$R^2$	0.949
Adj. $R^2$	0.946

Note: *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

. As shown in the table, the Taylor inequality coefficient is 0.008, indicating a high level of model accuracy. Both the $R^2$ and adjusted $R^2$ values are close to 1, further confirming the model’s strong overall fit. From the perspective of exchange rate expectation parameters, carry traders exhibit the strongest belief that exchange rate expectations are anchored to the interest rate differential between domestic and foreign markets. Regarding risk preferences, technical traders display the highest degree of risk aversion, while carry traders tend to exhibit risk-seeking behavior. In terms of dynamic adjustment parameters, heterogeneous foreign exchange traders demonstrate a high degree of adaptability in updating their expectations and trading strategies in response to market fluctuations. Finally, the estimated coefficients associated with the current account and foreign exchange intervention are below 0.002 in absolute value, suggesting that their direct influence on market equilibrium is relatively limited.

4.4. Measurement Results of Weighted Heterogeneous Exchange Rate Expectation

Using the estimated parameters from the foreign exchange market equilibrium model, we computed the expected RMB exchange rates changes for three types of heterogeneous traders. To construct a weighted market-based expectation indicator for the early-warning system, the expected RMB exchange rate changes of the three trader types are combined using their respective market shares. Specifically, for each period, the expected change of each trader type is multiplied by its corresponding market weight, and the resulting products are summed across all trader types to obtain a weighted series of expected exchange rate changes. This weighted series reflects the aggregate market expectation of RMB movements and serves as a key input indicator in the short-term cross-border capital flow early-warning system. Figure 1 presents individual traders’ expectations by type alongside the weighted expectation series, highlighting market heterogeneity and the resulting aggregated signal.

As shown in Figure 1, between 2005 and 2007, all trader types anticipated RMB appreciation, though chartists’ expectations were more moderate. Leading up to the 2008 global financial crisis, both fundamental and carry traders turned toward depreciation expectations, while chartists maintained a relatively optimistic outlook. Following the 2008–2009 crisis, all trader groups shifted decisively toward depreciation expectations, with carry traders projecting the sharpest decline. During the period from 2010 to 2015, which encompassed the European and U.S. debt crises, fundamental and carry traders predominantly expected RMB depreciation, whereas chartists exhibited alternating expectations between appreciation and depreciation. The “8.11 reform” (the “8.11 reform”, referring to the exchange rate regime adjustment announced by the People’s Bank of China on 11 August 2015, aimed to enhance the market orientation of the RMB central parity formation mechanism; the reform resulted in a sudden depreciation of the RMB and signaled a shift toward greater exchange rate flexibility) in 2015, which increased RMB exchange rate flexibility, further widened the heterogeneity of expectations. Fundamental and carry traders continued to forecast depreciation, while chartists displayed a more balanced stance. The weighted expected exchange rate series fluctuates within the range of the three trader groups’ expectations, capturing the overall direction of market sentiment while smoothing extreme individual biases. It tends to align more closely with chartists’ expectations during stable periods but moves toward fundamental and carry traders’ forecasts when market uncertainty intensifies, indicating that shifts in trader composition play a crucial role in shaping aggregate market expectations.

5. Empirical Analysis of an Early-Warning System for Short-Term Cross-Border Capital Flows in China

5.1. Data Description

Prior to the empirical analysis of the early-warning system, China’s short-term cross-border capital flows are quantified. An indirect measurement approach is employed, following a standard methodology proposed in the literature [57]:

$${STCF}_t={FO}_t-T_t-{FDI}_t$$

(20)

where ${STCF}_t$ denotes short-term cross-border capital flows, with positive values indicating capital inflows and negative values indicating outflows; ${FO}_t$ represents changes in foreign exchange deposits; $T_t$ is the trade balance, calculated as exports minus imports; and ${FDI}_t$ indicates the actual utilization of foreign direct investment.

Building on the previously developed early-warning system, key indicators are processed as follows. The current account balance and arbitrage investment balance, originally available as quarterly data, are converted to monthly values using a quadratic interpolation method. The interest rate differential between domestic and foreign markets is measured by the spread between the three-month Eurodollar deposit rate and the three-month Shanghai Interbank Offered Rate (SHIBOR). Market participants’ exchange rate expectations are quantified by a weighted average of expected RMB exchange rate changes, based on the previously derived expectations of the three heterogeneous trader types and their respective market shares. To assess the predictive capability of this market-based expectation indicator, a comparative analysis is conducted using the NDF-based rate. The empirical analysis uses monthly data from December 2005 to June 2022, sourced from the Wind database.

Table 4. Descriptive Statistics of Indicators for the Short-Term Cross-Border Capital Flow Early-Warning System.

Indicator	Symbol	Mean	S.D.	Min	Max	Skewness	Kurtosis	ADF t-Statistic
Short-Term Cross-Border Capital Flows	${STCF}_t$	−1825.224	3779.254	−15,651.900	5231.253	−1.023	1.729	−5.059 ***
Weighted Heterogeneous Exchange Rate Expectation	${WE}_t$	0.0943	0.147	−0.165	0.526	0.448	−0.455	−2.779 *
NDF-based forward premium	${NDF}_t$	−0.005	0.076	−0.213	0.251	0.701	1.420	−3.960 ***
Manufacturing Purchasing Managers’ Index	${PMI}_t$	51.386	2.718	35.700	59.200	−1.152	7.913	−6.005 ***
Trade Deviation Index	${\mathrm{T}\mathrm{D}}_t$	−0.050	0.160	−0.756	0.286	−0.881	2.239	−4.166 ***
Current Account Balance	${CA}_t$	195.416	112.018	−139.259	461.719	−0.324	0.542	−2.280
Arbitrage Investment Balance	${SI}_t$	−25.191	152.121	−382.049	283.221	−0.410	−0.456	−4.510 ***
Interest Rate Differential	${IR}_t$	−0.011	0.337	−1.264	1.229	−0.357	3.348	−10.637 ***
Willingness to Pay Foreign Exchange	${FE}_t^p$	0.518	0.082	0.331	0.768	−0.038	−0.127	−3.410 **
Willingness to Hold Foreign Exchange	${FE}_t^s$	0.569	0.112	0.362	0.815	−0.053	−1.228	−0.782

Note: *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

presents descriptive statistics for all indicators.

According to Table 4, substantial differences exist in the dispersion and distributional characteristics of the early warning indicators. The standard deviations of the current account balance (${CA}_t$) and arbitrage investment balance (${SI}_t$) are relatively high, suggesting pronounced fluctuations and heterogeneity in these variables. In contrast, the NDF-based forward premium (${NDF}_t$) and willingness to pay foreign exchange (${FE}_t^p$) show smaller standard deviations, indicating greater stability over time. In terms of skewness, most indicators exhibit right-skewed distributions, including the trade deviation index (${\mathrm{T}\mathrm{D}}_t$), interest rate differential (${IR}_t$), and non-deliverable forward exchange rate (${NDF}_t$), implying that extreme positive deviations occur more frequently. However, the weighted expected exchange rate change (${WE}_t$), arbitrage investment balance (${SI}_t$), and willingness to hold foreign exchange (${FE}_t^s$) display left-skewness, suggesting that negative shocks or depreciation expectations are relatively more pronounced among these indicators. Regarding kurtosis, the manufacturing purchasing managers’ index (${PMI}_t$) shows the highest kurtosis value, reflecting a highly peaked distribution with more frequent extreme observations. In contrast, the willingness to pay foreign exchange (${FE}_t^p$) and weighted expected exchange rate change (${WE}_t$) have relatively low kurtosis, indicating flatter and more dispersed distributions. Overall, these results suggest that macroeconomic indicators are prone to sharp fluctuations during economic cycles, while market-based expectation indicators display smoother dynamics. Augmented Dickey–Fuller (ADF) unit root tests were conducted for all variables included in the early-warning system. The results indicate that most series are stationary at the 10% significance level, while the Current Account Balance and Willingness to Hold Foreign Exchange series exhibit a unit root. It should be noted that the construction of the early-warning system, which relies on threshold-based signal aggregation rather than regression estimation, does not require all series to be strictly stationary.

5.2. Risk Events Identification

To identify risk events related to short-term cross-border capital flows, it is first necessary to define what constitutes a risk event. Following the methodology outlined above, the normal range of short-term cross-border capital flows is determined by the sample-period average plus or minus 1.5 times the standard deviation [47]. Any short-term cross-border capital flows falling outside this range are classified as risk events. Specifically, risk events are defined as follows:

$$\left|{STCF}_t-{\mu }_{STCF}\right|>1.5{\sigma }_{STCF}$$

(21)

Here, ${STCF}_t$ represents China’s short-term cross-border capital flows in period $t$, ${\mu }_{STCF}$ denotes the monthly average of China’s short-term cross-border capital flows over the sample period, and ${\sigma }_{STCF}$ is the corresponding standard deviation. A cross-border capital outflow risk event is identified when ${STCF}_t$ falls below ${\mu }_{STCF}-1.5{\sigma }_{STCF}$, indicating that short-term capital flows are lower than the lower risk limit. Conversely, a cross-border capital inflow risk event occurs when ${STCF}_t$ exceeds ${\mu }_{STCF}+1.5{\sigma }_{STCF}$, indicating that short-term capital flows surpass the upper risk limit. Using this methodology, risk events in China’s short-term cross-border capital flows from December 2005 to June 2022 were identified, as illustrated in Figure 2.

It is worth noting that the COVID-19 period (January 2020–June 2022) does not distort risk identification under the ±1.5 SD criterion. Capital flows remained within the normal range throughout most of the pandemic, and only May–June 2022 fell below the lower threshold. These two episodes coincide with well-documented capital outflow pressures triggered by the Federal Reserve’s aggressive tightening cycle. Therefore, the use of a unified threshold across the full sample does not generate false signals or affect the identification of true risk events.

From Figure 2, a total of 11 short-term cross-border capital flow risk events were identified during the sample period. Specifically, China’s short-term cross-border capital flows fell below the lower threshold, indicating outflow risk events, during the following periods: August–September 2015; November 2015–January 2016; July 2016; September-December 2016; July 2018; May 2019; August 2019; and May-June 2022. Conversely, inflow risk events, where capital flows exceeded the upper limit, occurred in January–February 2008, October 2010, and January 2011. Based on the timing of these events, the 24 months preceding each are defined as risk warning periods. Given the differences between inflow and outflow events, the subsequent empirical analysis of the early warning system distinguishes between these two types of risks.

5.3. Optimal Threshold Analysis of Early Warning Indicators

To identify the optimal threshold for each early warning indicator in the context of short-term cross-border capital flow risk, the following procedure is employed. First, all historical data for each indicator are used to construct a comprehensive library of potential thresholds. Next, the noise-to-signal ratio for each indicator is calculated at every possible threshold using the methodology outlined above. The optimal threshold is then determined according to the principle that a lower noise-to-signal ratio corresponds to stronger early warning capability. This procedure is applied separately to assess both cross-border capital outflow and inflow risks. As a result, the optimal thresholds, noise-to-signal ratios, and corresponding early warning capabilities of each indicator are derived for China’s short-term cross-border capital outflow and inflow risk early warning systems. The results are summarized in

Table 5. Optimal Thresholds and Noise-to-Signal Ratios of Early Warning Indicators for China’s Short-Term Capital Outflow Risk.

Indicator	Symbol	Optimal Threshold	Noise-to Signal Ratio	Effective-Signal Probability	Noise-Signal Probability	Early Warning Capability
Weighted Heterogeneous Exchange Rate Expectation	${WE}_t$	0.287	0.391	0.203	0.079	0.652
NDF-based forward premium	${NDF}_t$	0.038	0.440	0.338	0.149	0.625
Manufacturing Purchasing Managers’ Index	${PMI}_t$	52.000	0.422	0.987	0.416	0.635
Trade Deviation Index	${\mathrm{T}\mathrm{D}}_t$	−0.178	0.023	0.432	0.010	0.970
Current Account Balance	${CA}_t$	62.367	0.314	0.189	0.059	0.700
Arbitrage Investment Balance	${SI}_t$	−320.947	0.122	0.081	0.010	0.857
Interest Rate Differential	${IR}_t$	0.630	0.550	0.054	0.030	0.571
Willingness to Pay Foreign Exchange	${FE}_t^p$	0.688	0.733	0.014	0.010	0.500
Willingness to Hold Foreign Exchange	${FE}_t^s$	0.573	0.100	0.892	0.089	0.880

and

Table 6. Optimal Thresholds and Noise-to-Signal Ratios of Early Warning Indicators for China’s Short-Term Capital Inflow Risk.

Indicator	Symbol	Optimal Threshold	Noise-to Signal Ratio	Effective-Signal Probability	Noise-Signal Probability	Early Warning Capability
Weighted Heterogeneous Exchange Rate Expectation	${WE}_t$	−0.083	0.089	0.365	0.033	0.826
NDF-based forward premium	${NDF}_t$	−0.113	0.141	0.115	0.016	0.750
Manufacturing Purchasing Managers’ Index	${PMI}_t$	54.300	0.037	0.442	0.016	0.920
Trade Deviation Index	${\mathrm{T}\mathrm{D}}_t$	0.070	0.259	0.596	0.155	0.620
Current Account Balance	${CA}_t$	394.691	0.141	0.058	0.008	0.750
Arbitrage Investment Balance	${SI}_t$	209.335	0.071	0.115	0.008	0.857
Interest Rate Differential	${IR}_t$	−0.939	0.141	0.058	0.008	0.750
Willingness to Pay Foreign Exchange	${FE}_t^p$	0.387	0.211	0.039	0.008	0.667
Willingness to Hold Foreign Exchange	${FE}_t^s$	0.640	0.198	0.904	0.179	0.681

, respectively.

As shown in Table 5, several observations can be made. First, the noise-to-signal ratio for each early warning indicator of cross-border capital outflow risk is below 1, indicating that all indicators are suitable as leading indicators for short-term cross-border capital outflow risk warnings. Second, the indicator capturing import and export foreign exchange payment behavior exhibits the lowest noise-to-signal ratio, reflecting the strongest early warning capability for cross-border capital outflow risks. This is followed by indicators measuring arbitrage investment balance and market entities’ willingness to hold foreign exchange. Market entities’ exchange rate expectations demonstrate an intermediate level of early warning capability, while their willingness to pay foreign exchange shows relatively weaker performance. Third, a comparison between the Weighted Heterogeneous Exchange Rate Expectation constructed in this study and the NDF-based forward premium reveals that the heterogeneous exchange rate expectation indicators not only have significantly lower noise-to-signal ratios than the NDF-based forward premium but also provide superior early warning capability for short-term cross-border capital outflow risks. Specifically, the Noise-to-Signal Ratio of the Weighted Heterogeneous Expectation indicator is 0.391, compared with 0.440 for the NDF-based indicator, representing a 11.1% reduction in noise. Its Early Warning Capability rises from 0.625 (NDF) to 0.652, an improvement of 4.3%, further confirming the superior predictive performance of the weighted indicator. Overall, these improvements clearly demonstrate that the Weighted Heterogeneous Expectation indicator provides a more effective early-warning signal for capital-outflow risks than the conventional NDF-based measure.

According to Table 6, several conclusions can be drawn. First, the noise-to-signal ratios of all early warning indicators for cross-border capital inflow risk are below 1, indicating that each indicator is suitable as a leading indicator for short-term inflow risk warnings. Second, macroeconomic-level indicators exhibit the lowest NTSR, suggesting the strongest early warning capability for cross-border capital inflow risks. This is followed by indicators capturing changes in arbitrage investment and market participants’ exchange rate expectations. Indicators such as domestic–foreign interest rate differentials and changes in the current account show a moderate level of early warning performance, whereas the indicator reflecting import and export foreign exchange payment behavior demonstrates relatively weaker predictive ability. Third, the Weighted Heterogeneous Exchange Rate Expectation developed in this study, based on heterogeneous exchange rate expectations, significantly outperforms the NDF-based forward premium in both NTSR and early warning effectiveness for China’s short-term cross-border capital inflow risks. Quantitatively, the Noise-to-Signal Ratio decreases from 0.141 (NDF) to 0.089, a reduction of 38.9%, while the Early Warning Capability increases from 0.750 to 0.826, an improvement of 10.1%. These results highlight the robustness and effectiveness of the Weighted Heterogeneous Expectation indicator across inflow risk scenarios. Together, these improvements underscore that incorporating heterogeneous expectations materially enhances the indicator’s ability to capture capital inflow pressures, outperforming the NDF-based benchmark in both accuracy and stability.

Both analyses of risk early warning for short-term cross-border capital outflows and inflows suggest that the weighted indicators remain effective across different periods, providing a more stable and sustainable basis for risk monitoring. Moreover, the Weighted Heterogeneous Exchange Rate Expectation demonstrates superior performance compared with the NDF-based forward premium. Given this, the subsequent empirical analysis focuses exclusively on this weighted indicator.

5.4. Early Warning Analysis

Building on the aggregation methods introduced earlier, this section applies the optimal thresholds to evaluate whether each indicator signaled short-term cross-border capital outflow or inflow risk over the sample period. The individual indicator signals are then integrated into composite indices through both simple and weighted aggregation approaches. The following analysis presents and compares the empirical results obtained under these two approaches.

5.4.1. Using Simple Aggregation Composite Index

The early warning signals based on the simple aggregation composite index for China’s short-term cross-border capital outflows are presented in Figure 3. Prior to 2008, the system did not issue any signals of potential cross-border capital outflows over the following 24 months. Starting in July 2008, various indicators began generating early warning signals, although the number of signals remained relatively low. These signals occurred primarily during the following periods: July 2008–February 2009, July–August 2010, and January 2011–February 2012. From May 2012 onwards, certain indicators began issuing continuous signals, which gradually accumulated and intensified. By January 2014, the total number of signals had increased substantially, indicating persistent early warnings and a high likelihood of cross-border capital outflows over the following 24 months. China’s “8.11 reform” in 2015 heightened market participants’ expectations of RMB depreciation, and the 2016 stock market crash, triggered by global financial turbulence, coincided with a significant outflow of cross-border capital. During this period, the early warning system consistently issued signals for cross-border capital outflow risks.

Further analysis of individual indicators reveals the following patterns regarding short-term cross-border capital outflow risks. At the macroeconomic level, early warnings were first issued in 2008, followed by more frequent signals beginning in 2013. Concerning market participants’ exchange rate expectations, early warning signals intensified after 2014. Similarly, the behavior of import and export foreign exchange settlements, as well as market participants’ willingness to hold foreign exchange, generated continuous signals over the 24 months following 2014. In contrast, the willingness of market participants to make foreign exchange payments and the domestic–foreign interest rate differential exhibited relatively limited effectiveness as early warning indicators for short-term cross-border capital outflow risks.

The early warning signals based on the simple aggregation composite index for China’s short-term cross-border capital inflow risks into a composite indicator, as shown in Figure 4, which highlights three distinct warning phases. During 2006–2007, multiple indicators consistently issued signals of potential capital inflow risks over a 24-month horizon. From 2009 onward, the system again generated concentrated warnings of future risks. Between 2014 and 2019, warning activity was minimal, with almost no risk signals detected. However, from February 2020 to June 2022, selected indicators resumed issuing warnings for short-term cross-border capital inflow risks. These warning patterns correspond closely with actual capital flow developments in the Chinese market. The concentrated signals in 2007 coincided with substantial capital inflows influenced by the US quantitative easing policy in 2008, during which the inflow volume significantly exceeded the warning threshold. Similarly, the increased warning frequency in 2009 aligned with strong capital inflows during 2010–2011, a period marked by robust growth in emerging economies and sustained macroeconomic recovery both domestically and internationally. More recently, the COVID-19 pandemic has introduced greater volatility in short-term cross-border capital flows since 2020. Although these fluctuations have not reached crisis levels, the early warning system’s signals underscore the importance of continuous monitoring and proactive measures to mitigate potential capital inflow risks.

5.4.2. Using Weighted Aggregation Composite Index

The early warning system constructs the weighted aggregation composite index for China’s short-term cross-border capital flows, with individual indicators weighted by the inverse noise-to-signal ratio. This index systematically integrates signals from each indicator to assess both outflow and inflow risks.

Figure 5 illustrates the temporal pattern of the weighted aggregation composite index for short-term cross-border capital outflow risks, revealing distinct phases of market volatility. As shown in the figure, during the initial phase of the international financial crisis in December 2008, the system issued a strong warning signal in the weighted composite index, indicating potential capital outflows over the following 24 months and reflecting accumulating risk factors. From 2010 onward, the system generated intermittent warnings of relatively lower intensity. A significant escalation occurred in October 2014, when persistent strong warnings appeared, effectively anticipating several capital outflow events between September 2015 and 2016. The predictive capability of the weighted composite index remained robust during 2017–2019. Strong warnings issued between April and July 2017 preceded actual outflow events in April 2018 and July 2019, both falling within the 24-month warning horizon. Although the intensity of warnings decreased after late 2017, their persistence indicated ongoing, albeit sub-critical, outflow risks. This pattern was further supported by notable surges in the index in November and December 2018, which accurately captured two subsequent outflow events within a 12-month period. Since 2019, both the intensity and frequency of warnings from the weighted composite index have declined. However, significant increases were observed in July and December 2020, successfully predicting a capital outflow event in June 2022 within the 24-month forecast window, demonstrating the index’s continued relevance for monitoring financial stability.

The weighted aggregation composite index also serves as a reliable signal for short-term cross-border capital inflow risks, as shown in Figure 6. The index exhibited intermittent but notable increases in early 2006. Beginning in September 2006, the system generated frequent warnings over the following 24 months, accurately anticipating cross-border capital inflow events in January and February 2008. From mid-2008 onward, the intensity of the weighted composite index gradually declined. A minor uptick was observed in November 2011, but the change was negligible. Notably, in October 2009, the index experienced another significant surge, signaling potential inflow risks over the subsequent 24 months. This warning proved highly accurate, coinciding with two inflow events in October 2010 and January 2011. Since 2011, both the frequency and intensity of warnings from the weighted composite index have decreased substantially. Sporadic warnings were issued, but their low values indicated that short-term cross-border capital inflows remained below critical risk thresholds. From 2020 to 2022, the density and intensity of the index increased noticeably, emphasizing the need for enhanced monitoring and preemptive measures to address potential abnormal capital inflows over the next 24 months.

Overall, the early warning system for cross-border capital flow risks constructed in this study generates several alert signals for inflow and outflow risks during the sample period that align with the major risk episodes identified in existing research. For instance, the outflow pressures during the 2008 global financial crisis, the episodic volatility following the 2015 exchange rate reform, and the risk signals observed during the COVID-19 shock in 2020 are all documented in recent studies [24,50]. This consistency suggests that the proposed system can effectively capture common patterns in cross-border capital movements during periods of stress.

In terms of methodological comparison, empirical evidence confirms the important role of exchange rate expectations in forecasting inflow risks, which is consistent with this study’s emphasis on trader expectations [24]. In contrast, although some studies also incorporate market expectations into their indicator set, the use of the NDF-based forward premium as a proxy combined with machine learning techniques does not reveal a significant early-warning effect of expectations [50]. A plausible explanation is that differences in participant structure and pricing mechanisms between the NDF and onshore markets imply that the NDF-based forward premium may contain risk premia or market frictions. As a result, it may not fully reflect the actual expectations of domestic and foreign traders engaged in daily settlement and position adjustments, which can weaken the contribution of micro-level expectations within their framework. By contrast, the Weighted Heterogeneous Exchange Rate Expectation proposed in this study is derived from the optimal estimation of an exchange rate equilibrium model featuring three heterogeneous trader types, namely fundamentals, chartists, and carry traders. Parameter estimation yields the expectation series and market weights of each trader group, and their weighted combination is used as the proxy for market-based exchange rate expectations. Because this measure is directly grounded in differences in beliefs, risk preferences, and behavioral weights across trading agents, it provides a closer representation of expectations formed through actual trading behavior.

Empirically, the noise-to-signal ratio results show that the Weighted Heterogeneous Exchange Rate Expectation outperforms the NDF-based forward premium in terms of both signal identification and stability. Moreover, the composite index constructed using this indicator exhibits greater timeliness and persistence in early warning performance during several key episodes. These findings indicate that incorporating the micro-level behavioral characteristics of heterogeneous traders helps enhance the identification and monitoring of short-term cross-border capital flow risks. Overall, compared with studies that rely primarily on macro variables or single market-based proxies, the approach in this paper offers complementary insights by capturing capital flow dynamics driven by trading behavior and provides valuable implications for policy-oriented early intervention.

5.4.3. Robustness Checks of the Early-Warning System

To assess the robustness of the early-warning system, two alternative data adjustments were implemented. First, quarterly variables were converted to monthly series using the Constant interpolation method to examine whether the choice of interpolation technique affects the system’s signals. Second, for indicators that were found to be non-stationary based on the Augmented Dickey–Fuller (ADF) tests, including Current Account Balance and Willingness to Hold Foreign Exchange, first differences were taken to achieve stationarity.

Early-warning signals were then regenerated using these adjusted datasets within the original analytical framework. The results are presented in Figure A1, Figure A2, Figure A3, Figure A4, Figure A5, Figure A6, Figure A7 and Figure A8 in Appendix A.1 and Appendix A.2. Specifically, Figure A1, Figure A2, Figure A3 and Figure A4 in Appendix A.1 show the signals obtained using the Constant-interpolated data under the simple and weighted aggregate indices, while Figure A5, Figure A6, Figure A7 and Figure A8 in Appendix A.2 illustrate the signals generated from the stationarity-adjusted indicators.

Comparison with the original signals indicates that replacing the interpolation method with the Constant approach does not alter the overall performance of the early-warning system for either capital inflows or outflows. Regarding the stationarity-adjusted indicators, both types of warning signals deviate from the baseline results. The deviations for capital outflow risk are relatively modest despite the presence of some noise signals, whereas those for capital inflow risk are considerably more pronounced. These deviations are primarily driven by the two stationarity-adjusted indicators, particularly the Willingness to Hold Foreign Exchange indicator, which generates a higher number of false signals after stationarity adjustment. In summary, the robustness checks confirm that the substantive findings of the early-warning system do not depend on the choice of interpolation method, and that its overall effectiveness does not hinge on all indicator series being strictly stationary.

5.5. Sustainable Features of the Short-Term Cross-Border Capital Flow Risk Warning Framework

Building on the previous empirical analysis, this section discusses the sustainable characteristics of the proposed risk warning framework for short-term cross-border capital flows. Although the empirical analysis focuses on China as a representative case, the framework is broadly applicable and could be adapted to other emerging and developed markets. A key innovation of the framework lies in incorporating a composite market-effect indicator based on heterogeneous exchange rate expectations. By capturing the diverse anticipations of market participants, this indicator contributes significantly to the framework’s predictive capability and underpins its sustainable characteristics.

First, the system demonstrates temporal stability, a core aspect of its sustainable design. Both the simple and weighted aggregation composite indices consistently identified periods of heightened outflow and inflow risks across multiple years, including major events such as the 2008 global financial crisis, the “8.11 reform” in 2015, and the COVID-19 pandemic. By incorporating the heterogeneous exchange rate expectations indicator, the system better captures shifts in market sentiment, supporting persistent and reliable early warning signals over extended periods without frequent recalibration, which reinforces its long-term monitoring sustainability.

Second, the framework exhibits robustness across different types of capital flows and risk scenarios, further highlighting its sustainable performance. The weighted composite index effectively captures both inflow and outflow patterns, integrating traditional macroeconomic and market-based indicators with the heterogeneous expectation-based weighted indicator to consider diverse sources of risk. This design ensures that predictive effectiveness is maintained even under extreme or rapidly changing market conditions, demonstrating resilience and adaptability, key elements of a sustainable early warning framework

Third, the system provides enduring policy relevance, an important dimension of sustainability. The alignment between early warning signals and actual capital flow events in China indicates that the framework can support timely policy interventions. By offering policymakers nuanced insights into potential market pressures, the heterogeneous expectation-based indicator facilitates proactive risk mitigation, contributing to the framework’s long-term applicability and its role in maintaining financial stability.

Overall, the empirical results indicate that the proposed risk warning system delivers reliable short-term forecasts while embodying sustainable characteristics through stability, robustness, and policy relevance. The composite indicator based on heterogeneous expectations is central to achieving these sustainable features, providing a practical and potentially generalizable approach for ongoing monitoring of short-term cross-border capital flows.

6. Conclusions and Implications

This study develops an early warning indicator system for short-term cross-border capital flows by incorporating the Weighted Heterogeneous Exchange Rate Expectation of foreign exchange market participants. Using data spanning from July 2005 to June 2022, the study employs the KLR signal analysis method to empirically assess the performance of the short-term cross-border capital flow risk warning system in predicting both inflow and outflow risks, using China as a representative case. The main empirical findings are summarized as follows.

First, the Weighted Heterogeneous Exchange Rate Expectation, the indicator constructed in this study which integrates the heterogeneity of market participants’ expectations, demonstrates robust early-warning capabilities for both short-term cross-border capital outflows and inflows. Compared to the NDF-based forward premium commonly used in previous studies, the proposed weighted indicator shows superior effectiveness in monitoring abnormal short-term capital flows and provides enhanced predictive performance. Second, concerning the early-warning capacity of individual indicators, macroeconomic factors and the exchange rate expectations of market participants exhibit strong early-warning capabilities for both outflow and inflow risks. In contrast, indicators such as market participants’ willingness to pay, willingness to exchange, and the domestic–foreign interest rate differential show relatively weaker predictive power. Third, with respect to the overall effectiveness of the system, the weighted aggregation composite index constructed by assigning weights to individual early-warning signals outperforms the simple aggregation composite index, which is based on the unweighted sum of these signals, by providing more precise and concentrated early-warning results. The system issued frequent alerts for cross-border capital outflow risks between 2015 and 2019, though the frequency declined in 2022. Similarly, intensive early-warning signals for capital inflow risks were observed in 2008, while signals for inflows in 2010 were less pronounced. Fourth, based on the system’s signals, in mid-2022 the framework issued a strong warning regarding short-term cross-border capital outflow risks over the subsequent 24 months, highlighting the persistence of such risks. Furthermore, the proposed framework demonstrates sustainable characteristics. By integrating heterogeneous exchange rate expectations with traditional macroeconomic and market-based indicators, the framework achieves temporal stability and robustness under diverse market conditions, as well as practical policy relevance. The Weighted Heterogeneous Exchange Rate Expectation plays a central role in strengthening these sustainable features, ensuring that the system can sustain reliable performance over time and adapt to evolving market dynamics. Consequently, the framework represents a practical and potentially generalizable approach for monitoring short-term cross-border capital flows, applicable not only to China but also to other economies, offering methodological insights for enhancing their risk warning systems.

Drawing on these findings, several policy implications are proposed to strengthen the monitoring, early warning, and management of short-term cross-border capital flow risks. First, in monitoring short-term capital flows, it is important to consider the influence of heterogeneous exchange rate expectations among market participants, as these expectations guide cross-border capital movements. Specifically, high-frequency data and model-based measures may be used to track, in real time, the distribution and weight shifts in exchange rate expectations across different types of market participants. This enables regulators to promptly detect the overall direction of market expectations and the interactive effects arising from expectation divergence among various agents. Incorporating such heterogeneous expectation indicators into the daily monitoring system of foreign exchange authorities can further enhance the responsiveness of early-warning mechanisms. A deeper understanding of these dynamics can inform more effective risk management strategies.

Second, given the heterogeneity in expectations and the diverse responses of market participants to economic and financial policies, risk early-warning frameworks should incorporate these factors and their dynamic effects. In particular, regulators should not only assess how individual policy actions, such as interest rate adjustments, macroprudential measures, or foreign exchange management operations, affect the expectations of different types of traders, but also evaluate the joint effects of multiple policies implemented simultaneously on the formation of market beliefs. The cross-policy interactions may amplify or dampen traders’ expectation responses, potentially triggering abnormal capital inflows or outflows. Incorporating these dynamic interactions into early-warning systems can therefore improve the accuracy of risk identification. For instance, when the market anticipates a one-sided appreciation, monetary policy and macroprudential measures may release signals in opposite directions, producing more complex market reactions that must be assessed holistically. This will allow for a more nuanced and accurate assessment of capital flow risks and enhance predictive capability.

Third, since early-warning indicators at different levels exhibit varying sensitivities, policymakers should adopt a holistic approach, considering multiple indicators and the broader market context, to improve the accuracy and reliability of risk assessments. For example, econometric models can be employed to integrate macro-level capital flow indicators with micro-level behavioral data, such as trading volume structures, order flow characteristics, or position adjustments, to identify potential risk transmission mechanisms triggered by expectation shifts. This allows regulators to more effectively capture early signals of capital flow anomalies.

Fourth, while abnormal signals from a single indicator do not necessarily indicate excessive capital flows, attention should be paid to lagged and time-varying effects arising from interactions among market variables. This means that regulators should not focus solely on short-term risks identified by current indicators, but should also employ multi-dimensional data to identify lagged and time-varying factors that may trigger future capital flow disruptions. Assessing these latent drivers and their implications for the accumulation of risks enables the development of pre-emptive policy responses. For example, an intertemporal risk-monitoring module may be established to track evolving lagged relationships among key market variables. Careful monitoring of these effects can help mitigate potential risks and prevent systemic vulnerabilities.

Overall, these recommendations are intended to inform and strengthen the early-warning and management of short-term cross-border capital flow risks in China, based on insights derived from the empirical application of the framework. Moreover, the sustainable framework and policy insights developed in this study may provide valuable guidance for other economies seeking to strengthen their risk monitoring and management systems in the context of increasingly complex cross-border capital flows. Future research could further explore potential interactions among early-warning indicators, such as nonlinear or multiplicative effects between macroeconomic and market expectation indicators, which may provide additional insights into the dynamics of short-term cross-border capital flow risks.