Search Results (48)

This article presents the Asymmetric Cross-Market Dynamics Network (ACMD-Net), a forecasting framework built on the premise that commodity markets are fundamentally asymmetric. Three symmetry assumptions are statistically tested and rejected: volatility symmetry via the GJR-GARCH leverage test $\gamma >0$, $p<0.001$, coupling symmetry via the directional Granger causality DM statistic, 3.18–3.67, $p<0.001$, and cointegration symmetry via a likelihood ratio test, $p<0.01$. Each rejected hypothesis motivates a corresponding architectural component, yielding causally interpretable forecasts unavailable in black-box alternatives. The model is evaluated on daily CBOT futures for corn, wheat, and soybeans from January 2010 to December 2023, $T=3508$. ACMD-Net achieves RMSE reductions of 37–42% over ARIMA and 15–17% over standard LSTM. At short horizons ($h=1$), TFT achieves marginally lower point RMSE (3–4%, not statistically significant; DM $p>0.05$); at long horizons ($h=22$), TFT continues to report the lowest point RMSE across all commodities; differences versus ACMD-Net are not statistically significant DM $<1.96$ for all commodities. The architecture’s predictive value lies in economically grounded interpretability and superior directional accuracy rather than universal RMSE dominance. Directional accuracy ranges from 60 to 62% $p<0.001$, and net-positive trading returns are obtained for wheat and soybeans at 8–12-basis-point transaction costs. Ablation analysis identifies temporal attention as the primary performance driver, RMSE $+22.2\%$, upon removal, with econometric features contributing an additional 24.9% gain. Full article

This study examines the modelling and forecasting of South African macroeconomic and financial time series using a comparative framework based on Vector Autoregressive (VAR), Vector Autoregressive Moving Average (VARMA), and GARCH-type models. Quarterly data spanning 1970 to 2024 were analysed to determine GDP growth, exchange rates, interest rates, and household consumption expenditure. VAR and VARMA models were employed to capture conditional mean dynamics, while GARCH, EGARCH, and GJR-GARCH models, including ARMA-GARCH extensions, were used to model volatility behaviour. Optimal model specifications were selected using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Hannan–Quinn Criterion (HQ), and the Extended Cross-Correlation Matrix (ECCM), resulting in the estimation of VAR (4) and VARMA (1,1) models. The results reveal strong dynamic interdependencies among the variables. However, diagnostic tests indicate that the VAR (4) and VARMA (1,1) models do not fully capture the underlying data-generating process, as evidenced by residual autocorrelation, heteroskedasticity, and non-normality. Although the VARMA (1,1) model improved forecasting performance relative to the VAR (4) model, important nonlinear and higher-order dynamics remained unexplained. Volatility modelling revealed substantial persistence and clustering, particularly in exchange rates and interest rates. Initial GARCH, EGARCH, and GJR-GARCH specifications exhibited residual autocorrelation and remaining ARCH effects, suggesting model misspecification. The incorporation of an ARMA (1,1) term into the asymmetric GARCH models significantly improved model adequacy by eliminating residual autocorrelation and heteroskedasticity. Limited evidence of asymmetric volatility effects was found. Overall, the findings demonstrate that GARCH-ARMA specifications provide a more robust framework for modelling South Africa’s macroeconomic and financial dynamics. This study recommends future research incorporating nonlinear, regime-switching, and exogenous-variable models to enhance forecasting accuracy and policy relevance. Full article

This study investigates whether FinTech thematic assets achieve dynamic variance reduction for regional ESG market risk under clean-energy equity stress regimes, using daily data from March 2019 to August 2024 across five S&P ESG LargeMidCap markets spanning developed and emerging economies (North America, Europe, Asia Pacific Developed, Latin America Emerging, and Asia Pacific Emerging). Employing a DCC-GARCH framework with GJR-GARCH univariate specifications across four S&P Kensho FinTech channels—Democratized Banking, Alternative Finance, Future Payments, and Distributed Ledger—we estimate time-varying correlations and hedging effectiveness, and assess safe-haven properties via the Baur–Lucey framework. The most robust finding is that North America ESG shows the strongest dynamic variance reduction (59–76%), improving further during high clean-energy equity stress regimes (p < 0.01, bootstrap permutation test); Asia Pacific Developed ESG shows the weakest (7–9%) despite its developed-market status, while Latin America Emerging ESG’s comparatively high variance reduction (28–40%) is tempered by residual ARCH effects that point to incompletely modeled volatility rather than structural hedging capacity. All FinTech channels remain positive diversifiers rather than safe havens across every market and regime. Hedging capacity thus tracks market-specific volatility and correlation dynamics rather than a simple developed–emerging divide. The analysis is bounded by a single five-year sample window and two transition-risk proxies, warranting continued monitoring as FinTech and ESG regulatory frameworks evolve. Full article

This paper examines the structural changes that the Indian equity market has experienced between 2015 and 2025 under the influence of major macroeconomic and geopolitical shocks—including the November 2016 demonetisation, the IL&FS liquidity crisis of 2018, the COVID-19 pandemic of 2020–2021, the Russo–Ukrainian conflict of 2022, and the synchronised global monetary tightening of 2022–2024. The primary objective is to test whether the volatility-modelling architecture proposed by a 2017 benchmark study for the 1992–2016 period continues to hold under the structurally different post-2015 regime, and to identify how persistence, asymmetry, and ARCH-order properties have evolved across the BSE Sensex, NSE CNX Nifty, and twenty-seven sectoral indices. A unified GARCH-family framework comprising GARCH(1,1), GJR-GARCH(1,1), and GARCH(2,1) is estimated on daily log-returns over an eleven-year sample of approximately 2750 observations per index. The empirical evidence confirms that volatility clustering and persistence are pervasive in the post-2015 decade, with the persistence measure (α1 + β1) rising relative to the initial 2017 study for most indices. Asymmetric volatility has intensified—negative shocks generate disproportionately larger volatility responses than positive shocks, particularly in the banking, FMCG, and energy sectors. A higher-order GARCH(2,1) specification is the preferred model for four indices in which lag-2 ARCH effects remain significant or in which integrated-GARCH behaviour rules out the standard GARCH(1,1). The findings have direct implications for portfolio risk management, option pricing, and the design of prudential policy in an increasingly retail-driven and derivative-intensive market ecosystem. Full article

In frontier markets, financial volatility exhibits long-memory properties and regime-dependent asymmetries that standard linear models do not capture. This leads to inaccuracies in forecasting risk when a single model is applied across regimes. This study investigates the horizon- and regime-dependent performance of volatility models within a horizon- and regime-sensitive evaluation framework that applies single-regime Generalized Autoregressive Conditional Heteroscedasticity (GARCH) variants alongside a Hidden Markov Model (HMM). We evaluate the predictive accuracy of GARCH, Exponential GARCH (EGARCH), Glosten-Jagannathan-Runkle GARCH (GJR-GARCH), Asymmetric Power ARCH (APARCH), Fractionally Integrated GARCH (FIGARCH), and an HMM. Diebold–Mariano test statistics reveal that predictive superiority is sensitive to the chosen benchmark. When EGARCH is the benchmark, results highlight the importance of leverage effects, whereas a FIGARCH benchmark demonstrates that short-memory models are rejected as horizons increase. While short-memory models capture immediate clustering, FIGARCH maintains stable performance via hyperbolic decay. HMM provides a superior in-sample fit by capturing transitions between calm and turbulent regimes. Economic validation through Value-at-Risk (VaR) and Expected Shortfall (ES) backtesting indicates that FIGARCH and APARCH offer more reliable coverage for early warning systems during market stress. The findings emphasize that forecasting in a frontier market requires asset-specific approaches where benchmark selection dictates the interpretation of model superiority. Full article

This study examines the ability of asymmetric GARCH-family models, specifically EGARCH and GJR-GARCH, to capture and forecast the volatility of major decentralized cryptocurrencies. We analyzed the returns of seven leading assets (BTC, ETH, ADA, XRP, LTC, XLM, DASH). We used the Crypto Fear & Greed Index (CFGI) as a dummy variable, covering a period when all cryptocurrencies were active simultaneously. Notably, the Student-t distribution provided the best in-sample results with the lowest AIC and BIC for both models. When comparing the models directly, EGARCH consistently outperforms GJR-GARCH across in-sample metrics. The use of the CFGI dummy variable marginally improves in-sample results for only three of the seven cryptocurrencies, suggesting it may be adding noise to the models for some coins. Additionally, there is no clear rule of asymmetry across all cryptocurrencies, suggesting a fundamental structural difference from the traditional stock market. Out-of-sample metrics and performance vary more than in-sample metrics, with normal and GJR-GARCH models yielding better performance and lower QLIKE values for specific cryptocurrencies. This study contributes to the growing literature on volatility modeling and forecasting in cryptocurrencies, highlighting the importance of asset-specific valuation in the cryptocurrency market. It also provides a framework for integrating specific market indicators into the modeling framework. Full article

Against the backdrop of the expansion of sustainable finance and the growing relevance of ESG-related information, disclosure and regulation, this paper examines the dynamic relationship between sustainability-related uncertainty and ESG equity market volatility in a global framework. Sustainability-related uncertainty is proxied by the Global GDP-Weighted ESG-Based Sustainability Uncertainty Index (ESGUI), while ESG market volatility is measured through a monthly proxy constructed from estimated daily conditional variances obtained from GJR-GARCH(1,1) models with Student-t innovations. The paper explicitly distinguishes sustainability-related uncertainty, understood as ambiguity in the ESG information environment, from ESG market volatility, understood as market-pricing instability in ESG equity benchmarks. Empirically, the study combines bootstrap full-sample Granger-causality tests, parameter-stability diagnostics, and rolling-window bootstrap analysis. Robustness and extended analyses use an EGARCH-based volatility proxy, alternative rolling-window lengths, macro-financial controls, an emerging-market ESG benchmark, impulse-response analysis, forecast-error variance decomposition, and out-of-sample forecasting tests. The full-sample results indicate an asymmetric predictive pattern: ESG market volatility contains Granger-causal predictive information for changes in sustainability-related uncertainty, whereas the reverse direction is not supported on average. However, parameter-stability tests reject constancy, and rolling-window evidence shows that predictive effects arise episodically in both directions, with changes in sign, magnitude and significance. The uncertainty-to-volatility channel becomes statistically relevant and locally stronger during stress episodes, especially around 2019–2021, while macro-control results show that broader market stress absorbs part of the volatility-to-uncertainty linkage. The findings indicate a regime-dependent uncertainty–volatility nexus and support dynamic approaches to ESG risk monitoring, portfolio management and regulatory communication. All results are interpreted as predictive evidence, not structural causality. Full article

Brent crude oil prices are strategically important due to their sensitivity to geopolitical developments, financial market stress, and global monetary conditions. This study examines whether strategic risk indicators improve the forecasting performance of Brent crude oil returns within an integrated econometric and machine learning framework. Monthly data from January 2001 to December 2025 are employed, using the Global Geopolitical Risk Index (GPR), the CBOE Volatility Index (VIX), and the U.S. 10-year Treasury yield (DGS10) as key explanatory variables. Methodologically, the analysis first estimates benchmark econometric models, including ARIMAX (AutoRegressive Integrated Moving Average with Explanatory Variable) and ARIMAX-gjrGARCH (Glosten-Jagannathan-Runkle Generalized Autoregressive Conditional Heteroscedasticity, and then implements machine learning models, namely XGBoost (eXtreme Gradient Boosting), LightGBM (Light Gradient Boosting Machine), and Random Forest, to capture potential nonlinear relationships. Using sMAPE (Symmetric Mean Absolute Percentage Error), forecast performance is assessed over multiple forecast horizons under a rolling-origin framework. Across several forecasting horizons and train-test split configurations, the empirical results consistently show that machine learning techniques, especially LightGBM, offer superior out-of-sample forecasting accuracy. These findings suggest that the dynamics of Brent crude oil returns are influenced by complex and nonlinear relationships between macro-financial conditions, financial uncertainty, and geopolitical risk. The study concludes that flexible data-driven forecasting frameworks offer stronger predictive performance than benchmark econometric models under strategic risk conditions and provide useful implications for energy market risk management and policy decision-making. Full article

We introduce the Normalising Flow GARCH (NF-GARCH), a two-stage hybrid framework that enhances traditional GARCH models by replacing restrictive parametric innovation distributions with learned densities via normalising flows. Our approach preserves the interpretability of standard variance dynamics while addressing the common issue of innovation misspecification. In the first stage, we estimate standard GARCH variants (sGARCH, TGARCH, and gjrGARCH) to extract standardised residuals. In the second stage, a Masked Autoregressive Flow learns the underlying residual distribution, with samples from the flow subsequently driving the GARCH recursion for out-of-sample forecasting. Evaluated on 13 daily financial series (six FX pairs and seven equities), NF-GARCH demonstrates systematic, statistically significant improvements in forecast accuracy for skewed-t baselines. Wilcoxon signed-rank tests confirm superior performance specifically for gjrGARCH-sstd and sGARCH-sstd specifications. While the framework offers enhanced flexibility and generative realism, we observe that computational overhead is increased, and the log-variance specification of eGARCH exhibits instability when paired with flow-based innovations. These results suggest that while NF-GARCH effectively captures empirical tail behaviour in univariate settings, future research should explore conditional flow architectures and multivariate extensions to account for time-varying innovation shapes. For risk management, gains are most relevant where skewed-t baselines are used and where closer residual realism supports scenario analysis; effect sizes remain modest relative to model risk and implementation cost. Full article

This paper compares the daily return volatility by four leading international indices: JSE Top 40, FTSE 100, Nikkei 225 and S&P/ASX 200. The return series are modelled in ARMA process, where ARMA(1,3) values are taken for JSE Top 40 and S&P/ASX 200, ARMA(0,0) for FTSE 100, and ARMA(1,2) for Nikkei 225. The volatility is modelled in APARCH and GJR-GARCH (e.g., under various conditional distributions including Student-t (STD), skewed Student-t (SSTD), generalised error distribution (GED), skewed generalised error distribution (SGED), and generalised hyperbolic distribution (GHYD)). Model selection results based on information criteria indicate that the APARCH models outperform their GJR-GARCH counterparts in all cases. In particular, the ARMA(p,q)-APARCH(1,1) with SSTD is most suitable for the JSE Top 40 and the FTSE 100. The model that best describes the Nikkei 225 is an ARMA(1,2)–APARCH(1,1) model with SGED, and the S&P/ASX 200 fits an ARMA(1,3)-APARCH(1,1) model with GHYP. Among the indices, the FTSE 100 has the highest volatility persistence, while the Nikkei 225 responds more quickly to shocks. This out-of-sample forecasting test shows that ARMA(p,q)-APARCH(p,q) provides more accurate volatility predictions, especially for JSE Top 40 and S&P/ASX 200 investors. Full article

This study provides a comprehensive evaluation of six volatility forecasting models applied to twelve dominant and less dominant cryptocurrencies across multiple time horizons using high-frequency intraday data. The exponential generalized autoregressive conditional heteroskedastic (EGARCH), integrated GARCH (IGARCH), standard GARCH, GJR-GARCH, lagged realized volatility (LRE), and heterogeneous autoregressive (HAR) models are systematically compared using 5 min computed return data from September 2018 to September 2020. Our analysis encompasses three forecast horizons (1-day, 7-day, and 30-day) to assess model performance under varying temporal constraints. Through univariate Mincer–Zarnowitz regressions, encompassing tests, and out-of-sample evaluation using root mean squared error (RMSE) and quasi-likelihood loss (QLIKE) functions, we identify significant performance heterogeneity across models and cryptocurrencies. The HAR model exhibits stronger predictive accuracy at short horizons, while EGARCH exhibits relatively stronger performance at longer horizons, although overall explanatory power declines as forecast horizon increases. Importantly, no single model consistently provides optimal forecasts across all cryptocurrencies. Consistent with prior evidence suggesting model performance varies across assets. Encompassing regressions reveal that combining HAR with EGARCH specifications significantly enhances explanatory power across all temporal frames. Out-of-sample Diebold–Mariano tests indicate that HAR generates the lowest forecast errors for most cryptocurrencies, though EGARCH performs exceptionally well for high-market-capitalization assets. These findings provide regime-conditional insights into horizon- and asset-specific volatility dynamics during the pre-institutionalization phase of cryptocurrency markets. The study contributes to emerging literature by incorporating less-dominant cryptocurrencies and offering robust empirical evidence on the asymmetric and persistent volatility characteristics unique to digital asset markets. These findings should be interpreted within the context of the 2018–2020 sample period, representing a pre-institutionalized phase of cryptocurrency markets, and may not fully generalize to structurally different market regimes characterized by increased institutional participation and regulatory development. Full article

This study investigates the volatility nexus between exchange rates, interest rates, and stock market returns in South Africa, an emerging economy characterised by deep financial integration and exposure to global capital flows. Using monthly data from January 2003 to February 2025, the analysis employs a multi-layered econometric framework combining asymmetric GARCH models (EGARCH and GJR-GARCH), an Asymmetric Dynamic Conditional Correlation (ADCC-GARCH) specification, and a GARCH-MIDAS–DCC approach that decomposes volatility into long-run and short-run components while modelling time-varying cross-market dependence. The findings indicate that exchange rate volatility is the dominant and most persistent driver of financial market risk, highlighting the central role of the South African rand in transmitting global shocks to domestic markets. Equity market volatility is largely shock driven and mean reverting, with sharp increases during major crisis episodes such as the Global Financial Crisis and the COVID-19 pandemic. Dynamic correlations across markets are persistent but predominantly negative between stock returns and exchange rates, while linkages involving interest rates are weaker and more episodic. Overall, the results suggest that South Africa’s financial volatility nexus operates primarily through exchange rate-driven transmission rather than short-run contagion effects. Full article

Under the combined influences of climate change and anthropogenic activities, the variability of basin streamflow has intensified, posing substantial challenges for accurate prediction. Although Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models characterize volatility in time series, many previous studies have neglected changes in series structure, leading to inaccurate identification of the form of volatility. Building on tests for structural breaks (SBs) in time series, this study first removes the series mean using an Autoregressive Integrated Moving Average (ARIMA) model and then incorporates Markov-switching (MS) to develop a multi-state MS-GARCH model. An asymmetric MS-GARCH (MS-gjrGARCH) variant is also incorporated to describe the volatility of streamflow series with SBs. Daily streamflow data from five hydrological stations in the middle reaches of the Yellow River are used to compare the predictive performance of SB-ARIMA-MS-GARCH, SB-ARIMA-MS-gjrGARCH, ARIMA-GARCH, and ARIMA-gjrGARCH models. The results show that daily streamflow exhibits SBs, with the number and timing of breakpoints varying among stations. Standard GARCH and gjrGARCH models have limited ability to capture runoff volatility clustering, whereas MS-GARCH and MS-gjrGARCH effectively characterize volatility features within individual states. The multi-state switching structure substantially improves daily streamflow prediction accuracy compared with single-state volatility models, increasing R² by approximately 5.8% and NSE by approximately 36.3%.The proposed modeling framework offers a robust new tool for streamflow prediction in such changing environments, providing more reliable evidence for water resource management and flood risk mitigation in the Yellow River basin. Full article

This study investigates the volatility dynamics of the Bahrain All Share Index (BAX) between 2010 and 2025, a period marked by COVID-19 and regional geopolitical shocks. Using ARMA (1,1) to model returns and four GARCH-family models (ARCH, GARCH, EGARCH, GJR-GARCH) to capture volatility, we provide new evidence from a bank-based frontier market that has received limited empirical attention. The results reveal that returns are stationary and exhibit volatility clustering. Among the competing models, EGARCH (1,1) provides the best fit—exhibiting the lowest AIC and SIC values and the highest log-likelihood—revealing a significant leverage effect whereby negative shocks generate stronger volatility than positive shocks. This asymmetric volatility pattern contradicts earlier findings for Bahrain but aligns with theoretical expectations for bank-based financial systems. The findings carry implications for investors in terms of portfolio risk management, derivative pricing, and asset allocation. They also have important implications for regulators and policymakers, suggesting that counter-cyclical buffers and interest rate adjustments could be applied to stabilize the market in anticipation of negative shocks. These insights enrich the scarce literature on volatility in small frontier markets and contribute to a more nuanced understanding of the volatility dynamics in the MENA region. Full article

This study investigates the volatility of the Israeli corporate bond market, where corporate bonds are traded on a Limit Order Book (LOB) exchange with high retail trading activity. Using data from the Tel-Bond 20 and Tel-Bond 60 indices, we estimate various asymmetric GARCH models to capture the dynamics of bond returns. Our findings highlight a leverage effect, where negative shocks have a more significant impact on volatility than positive shocks, underscoring the importance of investor sentiment. The GJR model with a Student’s t-distribution best captures serial correlation, persistence of conditional volatility, and asymmetric volatility clustering. These results have significant implications for risk management, portfolio allocation, and regulatory policies, emphasizing the need for robust volatility forecasting models in transparent and active corporate bond markets. Full article