Recently, Indian economy has experienced strong Foreign investment flows through Foreign Direct Investment(FDI) and Foreign Portfolio Investment (FPI). It's long term trend highlighted economy has received $748.78 billion through FDI since 2014-2025 whereas FPI has been boosted by equity market gains with total FPI asset under custody hitting $858 billion. A healthy and vibrant industrial sectors of capital markets is important for development of a nation. In the present scenario, sectors of Foreign investment in Indian economy for instance Automotive, Pharmaceuticals, Information Technology (IT), Textiles, Construction, power, equity segment and assets under custody (AUC) have attracted attention of investors to invest in these Industries particularly. This paper attempted to analyse some of sectors and their impact on Industrial Development in India by foreign investors. The present study is based on quantitative data and used secondary data of annual time series. Data has been collected from the report of Reserve Bank of India, Department for Promotion of Industry and Internal Trade (DPIIT),world Bank report etc. To study the impact methods are practised such as comparative sectorial analysis, Autoregressive Distributed Lag (ARDL) and Garch model has been used to estimate volatility spillovers of FPI to sectoral output. The results indicated strong and positive long-run relationship with capital intensive, technology-based sectors hence leading to stable output growth and value addition. On the contrary, the FPI inflows showed a strong but volatile connection between FPI inflows and construction and power industries, which is highly vulnerable to market sentiment. However, it was observed from study that the investment activities in industrial sectors of FDI and FPI have had significant impact on Indian economy.

This study investigates the relationship between press freedom and bank default risk across countries, with particular attention to the role of institutional quality, financial development, and information transmission mechanisms. Using an unbalanced panel of 128 countries over the period 2000–2022, the paper applies dynamic panel data techniques to examine how press freedom affects banking stability, measured by the banking Z-score. To account for cross-country heterogeneity, countries are grouped by income level, geographic region, and resource dependence. In addition, a panel Blinder–Oaxaca decomposition is employed to identify the factors driving differences in average bank default risk across country groups, while a Threshold ARCH (TARCH) model is used to assess asymmetric responses of bank risk to positive and negative news. The results show that press freedom alone is not a consistent predictor of bank default risk across countries. Instead, its impact depends on the broader informational and institutional environment. In countries with higher education levels and greater internet penetration, increased press freedom is associated with higher bank default risk, indicating that more informed and digitally connected populations may react more strongly to financial news, amplifying herding behavior and bank fragility. Evidence from the TARCH model further suggests that bank default risk responds asymmetrically to news shocks, with negative news exerting a stronger effect than positive news. Overall, the findings underscore the importance of institutional context when evaluating the role of press freedom in financial stability.

Conditional heteroskedasticity models are commonly used for modelling financial time series data which are characterized by extreme and/or skewed observations. These data features might not be properly captured by the most commonly adopted distribution. In this paper, a mixture model for financial time series characterized by conditional heteroskedasticity model is developed, introducing the Finite Mixture of Scale Mixture of Skew Normal of Generalized Autoregressive Conditional Heteroskedastic ( FM m -SMSN-GARCH ) model. The SMSN distributions allow for the lightly/heavily-tailed, symmetric, and asymmetric distributions providing greater flexibility to handle outliers and complex data. The proposed model has several desirable features, such as the development of a convenient hierarchical representation of the FM m -SMSN family that makes it possible to construct a likelihood function to derive the maximum likelihood estimates via an EM–type algorithm. A comprehensive simulation study and a real-data application demonstrate the superior performance of the proposed method.

Regional financial integration in East Africa remains shallow, yet contagion risks persist due to market fragility and illiquidity. Using daily data from 2014 to 2025 from the Nairobi Securities Exchange (NSE), Dar es Salaam Stock Exchange (DSE), Rwanda Stock Exchange (RSE), and Uganda Securities Exchange (USE), this study examines volatility spillovers, dynamic connectedness, and contagion through autoregressive moving average – generalised autoregressive conditional heteroscedasticity (ARMA–GARCH) diagnostics, asymmetric dynamic conditional correlation (ADCC–GARCH) correlations, and the Diebold–Yilmaz framework. The results show weak spillovers and limited connectedness in tranquil periods, reflecting persistent segmentation. However, systemic stress triggers abnormal surges in correlations and connectedness, consistent with contagion as a temporary amplification of cross-market linkages. The NSE emerges as the dominant transmitter, driven by liquidity and cross-listings, while the USE acts as a passive absorber. The RSE and DSE alternate between marginal transmitters and receivers depending on conditions. These findings support the Adaptive Market and Financial Instability Hypotheses, underscoring the need for harmonised regulation, liquidity reforms, and adaptive risk management to bolster resilience.

A hybrid decision support framework for monetary policy management: Integrating triple exponential smoothing with GARCH models for Indonesian inflation forecasting

The research article presents an overall comparative study of multivariate GARCH M-GARCH in portfolio risk management, where three prevailing specifications VEC, CCC and DCC models are considered. We take daily closing prices of four major assets of the year 2018 through to 2023; S&P 500, NASDAQ-100, gold futures, and US Treasury Bonds, to estimate conditional variances, covariances, and dynamic correlations using maximum likelihood estimation. The descriptive statistics indicate that volatility is highly concentrated in clustering and time varying across assets with NASDAQ having the highest volatility (2.08) and significant negative skewness that shows non-normal returns. Comparison on models based on information criteria indicates that the Dynamic Conditional Correlation (DCC) specification has better performance with less computation need, fewer 8 parameters as compared to 21 (VEC) and greater log-likelihood with high improvement (164.67 units). Adequate model specification is shown through diagnostic testing using Ljung-Box test and ARCH-LM tests. Empirical results indicate that the volatility persistence (alpha + - 0 = 0.98) and the dynamics of high correlation (beta = 0.9321) are high which indicates long-memory properties and mean-reverting behavior which does not support constant correlation assumptions.

ABSTRACT We present the MS-Beta- t -QVAR (Markov-switching, MS; quasi-vector autoregressive, QVAR) model for financial returns, which jointly models the interacting scale and shape parameters of the t distribution. By allowing both parameters to evolve through a bivariate score-driven filter that endogenously switches regimes, this model effectively captures the changes in scale and shape dynamics that characterize volatility in emerging financial markets. We use daily NIFTY 50 log-return data from July 1990 to April 2025. The model identifies economically significant high-volatility and low-volatility periods. We compare the in-sample fit and out-of-sample volatility forecasting accuracy of the MS-Beta- t -QVAR model with those of the MS- t -GARCH (generalized autoregressive conditional heteroscedasticity), MS-Beta- t -EGARCH (exponential GARCH) and their single-regime versions. Our findings indicate that the statistical and forecasting performance of the MS-Beta- t -QVAR model is superior to that of the MS- t -GARCH, MS-Beta- t -EGARCH and their single-regime counterparts. These results underscore the importance of modelling regime-dependent interactions between the scale and shape parameters for effective investor risk management and macro-prudential oversight.

Because it is a crucial indicator of investment risk and can signal potential price swings, share volatility is vital. Larger volatility suggests a larger chance of both significant gains and large losses. Because investors utilise it to find trading opportunities and match their assets with their risk tolerance, it is essential for making well-informed decisions, pricing alternatives, and building portfolios. The primary purpose of the article. Forecasting and assessing the volatility of stocks in the securities market of the Republic of Kazakhstan. Research methodology. The article systematically analysed and synthesised scientific information. Analysing various methods in the research of foreign scientists, a generalised autoregressive heteroskedasticity model was used, which assumes that the current variability of the dispersion is influenced by both previous changes in indicators and prior estimates of the dispersion (GARCH model). Research features / value. This article attempts to assess the riskiness of stocks in the securities market of the Republic of Kazakhstan by reviewing existing theories and empirical studies. Research results. A comparison of the risks associated with HSBK, KZTK, and KZTO stocks reveals that an investor should focus primarily on a stock's risk. To do this, you need to identify the stock's high- and low-volatility periods, as well as the distribution of daily price fluctuations. GARCH model results indicate that KZTK stock has a higher risk than other stocks. Empirical research has shown that these financial instruments alternate between periods of high and low volatility. A financial instrument's risk will be overestimated during a period of low volatility by the first data points from an exceptionally high volatility period.

A well-known traditional GARCH model assumes normal innovations which do not adequately capture sudden variations typically caused by economic shocks or disturbances. This has necessitated the need to develop non-linear, distributional and robust models. In this study, a new set of GARCH models with smooth transition non-linearities and novel innovation distributions are developed to improve the modeling and forecasting of stock returns volatilities in the Nigeria /US stock markets’ Daily data on Heating Oil, Crude Oil, and Gasoline regular spot prices (Naira/US per Dollar) from 1985 to 2025 were obtained from the U.S. Energy Information Administration (EIA) website (https://www.eia.gov/dnav/pet/pet_pri_spt_s1_d.htm). This study was carried out using copula-based regime switching GARCH Generalized Error distribution (GED) model and a hidden Markov model. The copula switching GARCH (CoS GARCH) framework showed that the spot prices of crude oil, heating oil and gasoline demonstrated distinct patterns of volatility clustering and distributions with heavy and notable interdependence among different regimes. The estimated transition probability matrix indicated that the Markov chain associated with the volatility states displayed significant persistence. The equations for the conditional means indicated that returns were marginally different across the regimes, which aligns with the established observation that energy price returns have small means compared with their variances. The findings of the study therefore established the presence of heavy tails, clustering of volatility, structural changes, and significant interdependence in energy markets.

The paper analyzes the volatility trends of the Saudi Arabian Tadawul All Share Index (TASI) and the S&P 500 index, focusing on the COVID-19 pandemic as a key market shock. The analysis incorporates daily stock return data covering the period from January 2015 to May 2025. The volatility of emerging and developed markets is examined through EGARCH and GARCH approaches to study characteristics such as volatility clustering and asymmetry. The effect of the pandemic is directly embedded by introducing COVID-19 dummy variables into the models. Empirical findings suggest that both indices are characterized by volatility clustering, and the EGARCH model is more appropriate than the GARCH model for estimating asymmetric volatility, particularly during crisis periods. Additionally, the COVID-19 dummy variable is statistically significant in the EGARCH model, as opposed to the GARCH model. The results support the leverage effect, indicating that negative shocks have a more significant impact on market volatility than positive ones. The S&P 500 showed a faster recovery after the COVID-19 crisis, whereas TASI was slower in mean reversion, indicating structural and behavioral divergence between the markets. This comparative study contributes to the literature by providing a clear picture of volatility dynamics in diverse financial contexts and highlighting the superiority of EGARCH models during crisis periods. The findings offer guidance to policymakers aiming to improve market stability and to investors seeking diversification into both developing and mature markets.

ABSTRACT Spurious behaviours in regression analysis with independent random walks or even with stationary series are well known. However, how their spuriousity is affected by heteroscedastic errors or by nonlinearity in series has not been discussed in the literature. Using a Monte Carlo analysis, this study investigates the effect of autoregressive conditional heteroscedasticity (ARCH) on spurious regression, and it finds that only ARCH in variable models can neutralize most of spuriousity, an outcome that will have implications for unit root and cointegration analysis and it also finds evidence of autocorrelated errors, while the Cochrane-Orcutt procedure helps to resolve these issues.

ABSTRACT This article presents a novel extension of the GARCH model incorporating weighted liquidity, modeled by fractional Brownian motion. The existence of a stationary solution is proven, and the higher‐order moments are calculated to illustrate the statistical properties of the model. Analysis of the auto‐correlation function of the squared process confirms the long‐term memory characteristic of the model. Numerical simulations are employed to validate the theoretical findings, demonstrating the significance of the model in the financial market.

ABSTRACT This study investigates the impact of inflation uncertainty on corporate financing decisions during the unprecedented post-2021 European inflation surge. Using a panel dataset of 892 non-financial firms across 19 developed European countries from 2007 to 2023, we use the GARCH (1,1) model to measure inflation uncertainty. Applying fixed-effects and system GMM estimators, our empirical analysis reveals a robust negative relationship between inflation uncertainty and corporate leverage. We identify specific economic channels that drive this deleveraging behaviour. First, higher inflation uncertainty worsens information asymmetry, leading creditors to demand higher risk premiums or limit credit, consistent with agency theory. Second, short-term debt is significantly more sensitive to inflation risks than long-term debt, supporting a supply-side constraint channel where creditors shorten maturity to mitigate agency risks. Third, our dynamic analysis suggests that the costs of financial distress outweigh the transaction costs of rebalancing; therefore, firms tend to rapidly adjust their leverages to the optimal capital structure. Finally, we show that robust market institutions significantly mitigate adverse financing constraints related to inflation risks. Our findings indicate that inflation uncertainty is a significant determinant of corporate financial policy through distress avoidance and credit supply channels.

This study investigates the frequency-based structure of Turkey's business cycles using quarterly real GDP growth data from 1961 to 2024 and the Hodrick-Prescott (HP) filter. This study tested the hypothesis that successive cycle lengths converge toward the golden ratio (1.618) or its inverse (0.618). Methodologically, the series was normalized using a GARCH(1,1) model, dominant frequencies were identified via Fourier transformation, and cycle lengths were classified using a Gaussian mixture model before being projected via harmonic regression. Validation using the Harding and Pagan (2002) Concordance Index and phase synchronization analysis confirmed a high degree of alignment between the model and real growth data. The results indicate that short- and medium-term cycles cluster around the inverse of the golden ratio (0.618), suggesting that Turkish economic fluctuations are not random but are governed by regular structural rhythms that are aligned with historical turning points.

The integration of sustainability factors into investment decisions has transformed modern finance, with investors increasingly seeking to align their portfolios with environmental and societal values. The critical question remains as to whether the sustainability factor is priced in emerging markets. This study aims to provide a comprehensive analysis of the risk-adjusted return performance of three sustainability indexes of the emerging Indian market: NIFTY environmental, social and governance index (N100ESG), S&P BSE carbon-based thematic index (CARBONEX) and S&P BSE GREENEX (GREENEX) in comparison to the broad-based NSE 100 index (NIFTY100). The sample period for the analysis spans from January 2015 to August 2024. We have used risk-adjusted measures to evaluate the performance of sustainability indices. Additionally, we have analyzed downside risk, market-timing ability and volatility persistence using various generalized autoregressive conditional heteroskedasticity (GARCH)-type models. The findings indicate that sustainable investments offer competitive returns with better downside protection, especially for long-term investors. Among the indices, N100ESG demonstrated superior overall performance, while GREENEX stood out for risk–return resilience. However, reliance on market-cap criteria may dilute ESG purity. A more nuanced regulatory framework is essential to enhance the effectiveness of sustainable investing in India.

Abstract This paper investigates the daily exchange rate volatility of the Swedish krona (SEK) against the USD, EUR, GBP, and NOK over the period 2010–2023. Using asymmetric power ARCH (APARCH) models, the analysis uncovers significant differences in volatility dynamics across currency pairs and subperiods. A negative asymmetric return–volatility relationship is identified for SEK/EUR, indicating stronger reactions to negative shocks, while an inverted asymmetry is found for SEK/NOK—a pattern rarely documented in prior studies. No significant asymmetry is detected for SEK/USD or SEK/GBP. To address the limitations of conventional parametric models in small, open economies, a distribution-free support vector regression (SVR) approach with a wavelet kernel is integrated within the APARCH framework. In this study, the SVR-APARCH model demonstrates superior forecasting performance compared with standard APARCH models estimated via maximum likelihood estimation. Furthermore, it is shown to be generally more suitable for volatility forecasting than the hybrid ANN-APARCH and boosting-APARCH models. The results underscore the model’s enhanced capacity to capture the complex and nonlinear features of exchange rate volatility. The study contributes to the literature by providing robust evidence of asymmetric volatility patterns in SEK exchange rates and by introducing an effective hybrid modeling approach for improved volatility forecasting.

Purpose This study analyzes volatility dynamics and regional financial integration in European and Latin American equity markets under heightened global uncertainty and the growing relevance of sustainable finance. It aims to assess volatility persistence, asymmetric responses to negative information, and the role of intraregional integration in shock transmission and financial stability. Design/methodology/approach Daily equity index returns from representative European and Latin American markets over 2010–2025 are analyzed using asymmetric GARCH-type models (EGARCH and GJR-GARCH) with skewed innovations. Volatility persistence is measured through model parameters and half-life indicators, while financial integration is examined using Dynamic Conditional Correlation (DCC-GARCH) models. Robustness is evaluated through structural stability tests and pre- and post-COVID-19 comparisons. Findings European markets exhibit high volatility persistence but short half-lives (approximately 4–6 days), indicating faster shock absorption. Latin American markets display longer half-lives (around 8–12 days), reflecting more persistent volatility. Asymmetric effects are stronger and more systematic in Europe, while Latin America shows weaker and more heterogeneous responses. Intraregional correlations are extremely high in Europe, limiting diversification, whereas Latin America remains moderately and unevenly integrated. No evidence of structural breaks is found. Originality/value The study offers a unified long-horizon comparative framework combining asymmetric GARCH models, half-life measures, dynamic correlations, and stability diagnostics. It provides robust evidence on structural differences between developed and emerging markets, with implications for investors and policymakers in financial stability and sustainable finance.

The primary focus of this study is to examine how shocks and volatility are transmitted across sector indices in the Indian stock market. This study employs a dynamic conditional correlation generalized autoregressive conditional heteroscedasticity (DCC-GARCH) model, utilizing daily data from five prominent sectoral indices of the National Stock Exchange (NSE) in India, from 1 January 2016 to 31 May 2024. The study shows that sectoral volatility responds very differently across pre-COVID, COVID, post-COVID and geopolitical-crisis periods, with pro-cyclic sectors displaying sharper shock sensitivity during the pandemic and defensive sectors showing stronger stability under geopolitical stress. Consumer durables and financial services consistently provide the strongest hedging benefits during COVID and post-COVID periods, while IT-linked pairs exhibit weak hedging relationships throughout. The geopolitical shock generates volatility but does not compress sector movements as strongly as the pandemic, resulting in shallower and less persistent spillovers. Dynamic hedge ratios and portfolio weights reveal that IT becomes more relevant only in the post-COVID phase, but it does not function as a strong hedge during crisis-driven volatility. Crisis conditions tend to compress diversification opportunities by increasing correlations and connectedness, requiring more careful portfolio rebalancing. These findings offer new insights into how sector-specific behaviours and hedging performance evolve under varying macro-financial conditions, contributing to adaptive risk-management and portfolio-optimization strategies.

The present study aims to investigate the complex relationship between the oil price volatility and inflation in the economy of Iraq, focusing on the empirical evidence. The research hypothesis states that in the case of Iraq as an oil-dependent country, high oil price volatility is strongly associated with the significant increase in the inflation rate. Quantitative research is the methodology of inquiry, relying on the secondary data from the World Bank and the Central Bank of Iraq. The study applies multiple sophisticated econometric techniques, such as Regression Analysis, Vector Autoregression, Cointegration, and Error Correction Model, along with Generalized Autoregressive Conditional Heteroscedasticity models. The results reveal a high, statistically significant association between the oil price volatility and inflation rate fluctuations. In particular, the GARCH model results demonstrate how oil price variance also influences the variance of the inflation rate. The study argues that well-developed fiscal policies along with economic diversification are not only beneficial but essential to ameliorating the oil. The practical implications are important, as they refer to the strong need for a solid fiscal stabilization fund and serious efforts for economic diversification to withstand the oil market shocks occurrence. Further research should focus on the specific fiscal policies, explore the intimately related macroeconomic indicators, and extend the same analysis to the peer countries Keywords: Oil Price, Volatility, Inflation, Iraqi Economy, Economic Impact

A GARCH model with two volatility components and two driving factors