Search Results (28)

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 the dynamic interactions between Bitcoin, global financial indicators, and the Kazakhstan Stock Exchange (KASE) index within a VAR-based econometric framework, addressing a notable gap in the literature on emerging and shallow financial markets. While prior research predominantly focuses on developed economies, evidence suggests that cryptocurrency–stock market linkages are time-varying, crisis-sensitive, and often asymmetric. In this context, the present study examines both short-term causality structures and shock transmission mechanisms among KASE, Bitcoin (BTC), oil prices, the U.S. dollar index (DXY), and the VIX using monthly data for the period 2017M01–2026M04. Empirical findings indicate that, despite the absence of statistically significant Granger causality from individual global variables to KASE, the joint dynamics suggest a non-negligible, albeit indirect, interaction structure. Variance decomposition and impulse-response analyses further reveal that KASE dynamics are predominantly driven by its own shocks, reflecting the relatively segmented and internally driven nature of the market. Diagnostic tests confirm the robustness of the model, with no evidence of serial correlation or heteroskedasticity in residuals. These findings are consistent with the structural characteristics of the Kazakh financial system, including limited market depth, lower investor participation, and high sensitivity to domestic macroeconomic conditions. Unlike developed markets where stronger integration is observed, KASE appears only weakly connected to global financial and cryptocurrency markets. The study contributes to the literature by providing empirical evidence from a frontier market and highlights the importance of considering country-specific structural factors when evaluating financial integration. Policy implications emphasize the need to enhance market depth, transparency, and investor confidence to strengthen the responsiveness of KASE to global financial developments. Full article

This study investigates the determinants and predictability of stock return volatility by integrating firm-specific financial characteristics with advanced econometric and volatility modeling techniques. Using an unbalanced panel dataset comprising 1596 firms and 19,752 firm-year observations from MENA stock markets over the period 2010–2024, the analysis employs fixed-effects panel regression models, conditional volatility models, and machine learning-based forecasting approaches. Following extensive diagnostic testing, including tests for heteroskedasticity, serial correlation, cross-sectional dependence, and model specification, a two-way fixed-effects model with Driscoll–Kraay standard errors is adopted as the preferred estimation framework. The results indicate that liquidity ratio, cash ratio, sales growth, firm age, lagged volatility, and lagged returns are significant determinants of stock return volatility, whereas leverage, tangibility, board independence, firm size, Tobin’s Q, and profitability do not exhibit statistically significant effects after controlling for firm-specific and time-specific heterogeneity. The volatility analysis reveals substantial persistence in stock return volatility, with the EGARCH-t specification providing the best fit among the competing GARCH-family models according to the Akaike Information Criterion. The estimated asymmetry parameters indicate that volatility responds differently to positive and negative shocks, supporting the presence of asymmetric volatility dynamics and the suitability of asymmetric volatility models. The forecasting analysis shows that advanced machine learning and deep learning models achieve competitive predictive performance; however, differences in predictive accuracy across models are generally modest. Full article

Periods of geopolitical uncertainty have increasingly shaped the performance of global financial markets, yet the extent to which these risks influence the co-movement of asset markets in South Africa remains unclear. Although co-movement has emerged as a crucial factor for investors seeking portfolio diversification, existing studies present mixed findings, with some suggesting that geopolitical risk strengthens financial integration, defined as the extent to which markets move together in response to global shocks, while others find that it weakens these linkages by triggering market segmentation. Against this backdrop, this study examines the impact of geopolitical risk’s influence on the co-movement of South African asset markets, focusing on how shifts in global uncertainty interact with local market dynamics. Using time-series monthly data from December 2004 to January 2025, the study applies a dual-method approach. The multivariate generalised autoregressive conditional heteroskedasticity asymmetric dynamic conditional correlation (MGARCH-ADCC) model is first employed to estimate time-varying correlations across the equity, bond, and property markets. Thereafter, the autoregressive distributed lag (ARDL) model is used to assess both the short- and long-run effects of geopolitical risk on these co-movement patterns. The results indicate that geopolitical risk significantly increases co-movement between South African asset markets in both the short and long run, thereby diminishing the traditional benefits of diversification. These findings reinforce the view that market participants respond collectively to uncertainty rather than fundamentals. Overall, the study contributes to the empirical understanding of market integration under geopolitical stress and highlights the need for investors and policymakers to incorporate geopolitical risk indicators into investment and policy frameworks to strengthen market resilience. Full article

The load of the elastic tooth drum-type pepper harvester is a key parameter affecting harvesting efficiency and quality. Real-time analysis and prediction of drum load are crucial for stabilizing harvester operation and optimizing performance. Existing research focuses on either machine vision-based image analysis, which is difficult to collect in the field, or parameter-mapping methods, which suffer from time lag. This study proposes a GARCH-KPCA-ATLSTM method for load prediction, combining the generalized autoregressive conditional heteroskedasticity (GARCH) model, kernel principal component analysis (KPCA), and attention-enhanced long short-term memory (ATLSTM). EMD is first applied to denoise and reconstruct the load signal, removing mechanical vibration and other interferences. Conditional heteroskedasticity is confirmed, and the GARCH series (one symmetric and three asymmetric models) is introduced to extract fluctuation features. KPCA reduces dimensionality, removing redundant information and saving 2.91 s in computation while slightly improving accuracy. Additive attention in LSTM emphasizes critical information, enhancing learning of nonlinear relationships and further improving prediction. Comparative experiments demonstrate the model’s reliability. The method achieves RMSE = 0.911, MAE = 0.682, MBE = −0.025, MAPE = 1.147%, R² = 0.968, with a runtime of 2.023 s, confirming high accuracy and stability. This study provides a theoretical and technical foundation for real-time load prediction of pepper harvesters. 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

We propose a fully nonparametric empirical autoregressive copula framework for univariate time series, designed to capture nonlinear and asymmetric serial dependence while exactly preserving the empirical marginal distribution. The method decouples marginal behavior from temporal dependence by (i) constructing a shape-preserving empirical marginal via monotone interpolation and mapping observations to the unit interval, and (ii) estimating the lag–lead dependence through a nonparametric conditional AR(1) copula density on ${(0,1)}^2$. To ensure stable estimation near the boundaries, we employ reflection-based kernel methods that mitigate edge effects and yield well-behaved conditional densities on the unit support. Forecasts are obtained from the implied conditional predictive density: we compute point forecasts either as conditional modes (maximum a posteriori) on the copula scale or as conditional means, and then back-transform exactly using the empirical quantile function, guaranteeing marginal fidelity and support-respecting predictions. Empirically, we evaluate the approach on three CBOE volatility indices (VIX, VXD, and RVX) and benchmark it against linear ARMA models, copula-based parametric competitors, and state-space/heteroskedasticity baselines (Local level, TVP–AR, and ARMA–GARCH). The results highlight that modeling the full conditional transition density nonparametrically can deliver competitive—often best or near-best—forecast accuracy across horizons, particularly in the presence of pronounced volatility regimes and asymmetric adjustments. 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

The systematic failure of standard Value-at-Risk (VaR) models for the Tokyo Commodity Exchange (TOCOM) rubber futures contract poses significant challenges for risk management. This study addresses the issue by examining the market’s split trading sessions, which induce distinct overnight and intraday volatility regimes. We decompose daily returns into these two components and apply tailored Generalized Autoregressive Conditional Heteroskedasticity (GARCH) family models. Our empirical results, strengthened by extensive robustness checks using EGARCH, IGARCH, and GJR-GARCH specifications, reveal that intraday volatility is persistent and influenced by leverage effects, whereas overnight volatility behaves as a jump-driven process unaccounted for by conventional models. Comprehensive VaR backtesting confirms that while traditional models accurately capture intraday risk, all standard daily models—including asymmetric variants—systematically and severely underestimate overnight risk. These findings demonstrate that aggregating returns into a single daily series conflates different volatility dynamics, leading to model failures. We propose a two-tiered risk management framework that separately applies conventional models to intraday risk and jump-aware measures for overnight risk. This approach aligns risk assessment with underlying market microstructure, improving model validity and capital adequacy for TOCOM rubber futures. Full article

This study examines volatility transmission between major European indices (CAC 40, DAX, FTSE MIB, IBEX 35, EURO STOXX 50) and Tunisia’s TUNINDEX amid global crises (2008 financial crisis, COVID-19, Russo-Ukrainian war). Using GARCH(1,1) and BEKK models, the analysis reveals low correlation and weak volatility spillovers between the TUNINDEX and European markets, indicating relative decoupling. ARCH-LM tests confirm conditional heteroskedasticity, while GARCH models show persistent volatility. The BEKK model underscores marginal shock transmission, affirming the TUNINDEX’s independence. These findings suggest diversification benefits for investors but highlight local risk considerations. Practical recommendations are provided for stakeholders, with future research directions including asymmetric effects and high-frequency data analysis. Full article

There is a strong connection between the Federal Reserve’s monetary policy and the trend of international food prices. Employing the average information share model, EGARCH(Exponential Generalized Autoregressive Conditional Heteroskedasticity), and DCC-MGARCH(Dynamic Conditional Correlation-Multivariate Generalized Autoregressive Conditional Heteroskedasticity) models, this study investigates the relationship between the U.S. dollar index, international grain futures prices, and spot prices in the context of Federal Reserve monetary policy adjustments from 2000 to 2023. The findings reveal that, first, under conditions of long-run cointegration, the U.S. dollar index exerts a strong pricing influence over international grain futures, while grain futures demonstrate a significant price discovery function over spot prices. Second, both international grain futures and spot markets exhibit asymmetric volatility, with price increases being more pronounced than decreases in response to external shocks. Additionally, the U.S. dollar index has a unidirectional and inverse influence on grain futures prices, while futures and spot prices interact bidirectionally and move in the same direction. This paper contributes to understanding the impact of Federal Reserve monetary policy adjustments on international food prices and offers policy insights for countries to manage food import risks and maintain price stability. Full article

This study examines the volatility and hedging effectiveness of commodities, specifically gold and oil, on the Indian stock market, focusing on both aggregate and sectoral indices. Data have been collected from 1 January 2021 to 31 December 2024 to cover the post-COVID-19 period. Utilizing the Asymmetric Dynamic Conditional Correlation Generalized Autoregressive Conditional Heteroskedasticity (ADCC-GARCH) model, we analyze the volatility spillovers and time-varying correlations between commodity and stock market returns. The analysis of spillover connectedness reveals that both commodities exhibit limited and inconsistent hedging potential. Gold demonstrates low and stable spillovers in most sectors, indicating its diminished role as a reliable safe-haven asset in Indian markets. Oil shows relatively higher but volatile spillover effects, particularly with sectors closely tied to energy and industrial activities, reflecting its dependence on external economic and geopolitical factors. This study contributes to the literature by providing a sector-specific perspective on commodity–stock market interactions, challenging conventional assumptions of hedging efficiency of gold and oil. It also emphasizes the need to explore alternative hedging mechanisms for risk management in the post-crisis phase. Full article

Financial stability analysis requires volatility modeling, especially in emerging nations where pension fund systems are very vulnerable to macrofinancial risks. In order to examine the volatility dynamics of Romania’s private pension system, this study uses daily net asset value (NAV) data from 2012 to 2024 to evaluate four GARCH-type models: standard GARCH (sGARCH), exponential GARCH (EGARCH), Glosten–Jagannathan–Runkle GARCH (GJR-GARCH), and component GARCH (C-GARCH). The analysis includes domestic and international equity indices (BET, STOXX), government bond yields (ROMGB 10Y, ROMANI 5Y), short-term interbank rates (ROBOR ON), and exchange rate fluctuations (RON/EUR). Current findings indicate that EGARCH captures asymmetric fluctuations in pension fund performance, where positive shocks generate larger increases in volatility than negative ones, highlighting an atypical asymmetry pattern. Furthermore, the stabilizing effects of government bonds are overshadowed by stock market behavior, which becomes the primary driver of risk. Fluctuations in exchange rates further increase volatility, especially in markets vulnerable to external disturbances. The findings offer empirical evidence for the necessity of more cautious risk management approaches and highlight the importance of regulatory oversight in maintaining market confidence. The study underscores the importance of customized allocation frameworks that reduce vulnerability to disruptive events while maintaining prospects for sustained growth. This new dataset contributes to enhancing the comprehension of pension fund volatility within the context of emerging markets. These insights can assist managers and policymakers seeking to fortify retirement outcomes. Full article

This paper introduces hybrid models designed to analyze daily and weekly bitcoin return spanning the periods from 18 July 2010 to 28 December 2023 for daily data, and from 18 July 2010 to 24 December 2023 for weekly data. Firstly, the fractal and chaotic structure of the selected variables was explored. Asymmetric Cantor set, Boundary of the Dragon curve, Julia set z² −1, Boundary of the Lévy C curve, von Koch curve, and Brownian function (Wiener process) tests were applied. The R/S and Mandelbrot–Wallis tests confirmed long-term dependence and fractionality. The largest Lyapunov test, the Rosenstein, Collins and DeLuca, and Kantz methods of Lyapunov exponents, and the HCT and Shannon entropy tests tracked by the Kolmogorov–Sinai (KS) complexity test determined the evidence of chaos, entropy, and complexity. The BDS test of independence test approved nonlinearity, and the TeraesvirtaNW and WhiteNW tests, the Tsay test for nonlinearity, the LR test for threshold nonlinearity, and White’s test and Engle test confirmed nonlinearity and heteroskedasticity, in addition to fractionality and chaos. In the second stage, the standard ARFIMA method was applied, and its results were compared to the LieNLS and LieOLS methods. The results showed that, under conditions of chaos, entropy, and complexity, the ARFIMA method did not yield successful results. Both baseline models, LieNLS and LieOLS, are enhanced by integrating them with deep learning methods. The models, LieLSTMOLS and LieLSTMNLS, leverage manifold-based approaches, opting for matrix representations over traditional differential operator representations of Lie algebras were employed. The parameters and coefficients obtained from LieNLS and LieOLS, and the LieLSTMOLS and LieLSTMNLS methods were compared. And the forecasting capabilities of these hybrid models, particularly LieLSTMOLS and LieLSTMNLS, were compared with those of the main models. The in-sample and out-of-sample analyses demonstrated that the LieLSTMOLS and LieLSTMNLS methods outperform the others in terms of MAE and RMSE, thereby offering a more reliable means of assessing the selected data. Our study underscores the importance of employing the LieLSTM method for analyzing the dynamics of bitcoin. Our findings have significant implications for investors, traders, and policymakers. Full article

Metaverse (MV) technology introduces new tools for users each day. MV companies have a significant share in the total stock markets today, and their size is increasing. However, MV technologies are questioned as to whether they contribute to environmental pollution with their increasing energy consumption (EC). This study explores complex nonlinear contagion with tail dependence and causality between MV stocks, EC, and environmental pollution proxied with carbon dioxide emissions (CO₂) with a decade-long daily dataset covering 18 May 2012–16 March 2023. The Mandelbrot–Wallis and Lo’s rescaled range (R/S) tests confirm long-term dependence and fractionality, and the largest Lyapunov exponents, Shannon and Havrda, Charvât, and Tsallis (HCT) entropy tests followed by the Kolmogorov–Sinai (KS) complexity measure confirm chaos, entropy, and complexity. The Brock, Dechert, and Scheinkman (BDS) test of independence test confirms nonlinearity, and White‘s test of heteroskedasticity of nonlinear forms and Engle’s autoregressive conditional heteroskedasticity test confirm heteroskedasticity, in addition to fractionality and chaos. In modeling, the marginal distributions are modeled with Markov-Switching Generalized Autoregressive Conditional Heteroskedasticity Copula (MS-GARCH–Copula) processes with two regimes for low and high volatility and asymmetric tail dependence between MV, EC, and CO₂ in all regimes. The findings indicate relatively higher contagion with larger copula parameters in high-volatility regimes. Nonlinear causality is modeled under regime-switching heteroskedasticity, and the results indicate unidirectional causality from MV to EC, from MV to CO_2, and from EC to CO₂, in addition to bidirectional causality among MV and EC, which amplifies the effects on air pollution. The findings of this paper offer vital insights into the MV, EC, and CO₂ nexus under chaos, fractionality, and nonlinearity. Important policy recommendations are generated. Full article