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I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.

This paper examined the volatility models for exchange rate return, including Random Walk model, AR model, GARCH model and extensive GARCH model, with Normal and Student-t distribution assumption as well as nonparametric specification test of these models. We fit these models to Bangladesh foreign exchange rate index from January 1999 to December 31, 2012. The return series of Bangladesh foreign exchange rate are leptokurtic, significant skewness, deviation from normality as well as the returns series are volatility clustering as well. We found that student t distribution into GARCH model improves the better performance to forecast the volatility for Bangladesh foreign exchange market. The traditional likelihood comparison showed that the importance of GARCH model in modeling of Bangladesh foreign market, but the modern nonparametric specification test found that RW, AR and the model with GARCH effect are still grossly mis-specified. All these imply that there is still a long way before we reach the adequate specification for Bangladesh exchange rate dynamics.

Several empirical studies have proven that emerging countries are attractive destinations for Foreign Institutional Investors (FIIs) because of high expected returns, weak market efficiency and high growth that make them attractive destination for diversification of funds. But higher expected returns come coupled with high risk arising from political and economic instability. This study aims to compare the linear (symmetric) and non-linear (asymmetric) Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models in forecasting the volatility of top five major emerging countries among E7, that is, China, India, Indonesia, Brazil and Mexico.

The volatility of financial markets of five major emerging countries has been empirically investigated for a period of two decades from January 2000 to December 2019 using univariate volatility models including GARCH 1, 1, Exponential Generalized Autoregressive Conditional Heteroscedasticity (E-GARCH 1, 1) and Threshold Generalized Autoregressive Conditional Heteroscedasticity (T-GARCH-1, 1) models. Further, to examine time-varying volatility, the distinctions of structural break have been captured in view of the global financial crisis of 2008. Thus, the period under the study has been segregated into pre- and post-crisis, that is, January 2001–December 2008 and January 2009–December 2019, respectively.

The findings indicate that GARCH (1, 1) model is superior to non-linear GARCH models for forecasting volatility because the effect of leverage is insignificant. China has been considered as most volatile, whereas India is volatile but positively skewed and Indonesia is the least volatile country. The results can help investors in better international diversification of their portfolio and identifying best suitable hedging opportunities.

This study can help investors to construct a more risk-adjusted returns international portfolio. Further, it adds to the scant literature available on the inconclusive debate on the choice of linear versus non-linear models to forecast market volatility.

Earlier studies related to univariate volatility models are mostly applications of the models. Only few studies have considered the robustness while applying the models. However, none of the studies to the best of the authors’ searches have considered these models for identifying the diversification opportunity among the emerging countries. Hence, this study is able to derive diversification and hedging opportunities by applying wide ranges of the statistical applications and models, that is, descriptive, correlations and univariate volatility models. It makes the study more rigorous and unique compared to the previous literature.

The current paper aims to fill a gap in the literature by analyzing the nature of volatility on the Karachi Stock Exchange (KSE) 100 index of the KSE, and develop an understanding as to which model is most suitable for measuring volatility among those used. The study contributes significantly to the literature as, compared with the limited previous studies of Pakistan undertaken in the past, it covers three types of data (i.e. daily, weekly and monthly) for the whole period from the introduction of the KSE 100 index on November 2, 1991 to December 31, 2013. In addition, to analyze the impact of global financial crises upon volatility, the data have been divided into pre-crisis (1991-2007) and post-crisis (2008-2013) periods.

This study has used an advanced set of volatility models such as autoregressive conditional heteroskedasticity [ARCH (1)], generalized autoregressive conditional heteroskedasticity [GARCH (1, 1)], GARCH in mean [GARCH-M (1, 1)], exponential GARCH [E-GARCH (1, 1)], threshold GARCH [T-GARCH (1, 1)], power GARCH [P-GARCH (1, 1)] and also a simple exponentially weighted moving average (EWMA) model.

The results reveal that daily, weekly and monthly return series show non-normal distribution, stationarity and volatility clustering. However, the heteroskedasticity is absent only in the monthly returns making only the EWMA model usable to measure the volatility level in the monthly series. The P-GARCH (1, 1) model proved to be a better model for modeling volatility in the case of daily returns, while the GARCH (1, 1) model proved to be the most appropriate for weekly data based on the Schwarz information criterion (SIC) and log likelihood (LL) functionality. The study shows high persistence of volatility, a mean reverting process and an absence of a risk premium in the KSE market with an insignificant leverage effect only in the case of weekly returns. However, a significant leverage effect is reported regarding the daily series of the KSE 100 index. In addition, to analyze the impact of global financial crises upon volatility, the findings show that the subperiods demonstrated a slightly low volatility and the global economic crisis did not cause a rise in volatility levels.

Previously, the literature about volatility modeling in Pakistan’s markets has been limited to a few models of relatively small sample size. The current thesis has attempted to overcome these limitations and used diverse models for three types of data series (daily, weekly and monthly). In addition, the Pakistani economy has been beset by turmoil throughout its history, experiencing a range of shocks from the mild to the extreme. This paper has measured the impact of those shocks upon the volatility levels of the KSE.

This study aims to forecast daily value-at-risk (VaR) for international stock indices by using the conditional extreme value theory (EVT) with the Realized GARCH (RGARCH) model. The predictive ability of this Realized GARCH-EVT (RG-EVT) model is compared with those of the standalone GARCH models and the conditional EVT specifications with standard GARCH models.

The authors use daily data on returns and realized volatilities for 13 international stock indices for the period from 1 January 2003 to 8 October 2014. One-step-ahead VaR forecasts are generated using six forecasting models: GARCH, EGARCH, RGARCH, GARCH-EVT, EGARCH-EVT and RG-EVT. The EVT models are implemented using the two-stage conditional EVT framework of McNeil and Frey (2000). The forecasting performance is evaluated using multiple statistical tests to ensure the robustness of the results.

The authors find that regardless of the choice of the GARCH model, the two-stage conditional EVT approach provides significantly better out-of-sample performance than the standalone GARCH model. The standalone RGARCH model does not perform better than the GARCH and EGARCH models. However, using the RGARCH model in the first stage of the conditional EVT approach leads to a significant improvement in the VaR forecasting performance. Overall, among the six forecasting models, the RG-EVT model provides the best forecasts of daily VaR.

To the best of the authors’ knowledge, this is the earliest implementation of the RGARCH model within the conditional EVT framework. Additionally, the authors use a data set with a reasonably long sample period (around 11 years) in the context of high-frequency data-based forecasting studies. More significantly, the data set has a cross-sectional dimension that is rarely considered in the existing VaR forecasting literature. Therefore, the findings are likely to be widely applicable and are robust to the data snooping bias.

We aim to clarify the effect of economic uncertainty on Chinese stock market fluctuations. We extend the understanding of the asymmetric connectedness between economic uncertainty and stock market risk and provide different characteristics of spillovers from economic uncertainty to both upside and downside risk. Furthermore, we aim to provide the different impact patterns of stock market volatility following several exogenous shocks.

We construct a Chinese economic uncertainty index using a Factor-Augmented Variable Auto-Regressive Stochastic Volatility (FAVAR-SV) model for high-dimensional data. We then examine the asymmetric impact of realized volatility and economic uncertainty on the long-term volatility components of the stock market through the asymmetric Generalized Autoregressive Conditional Heteroskedasticity-Mixed Data Sampling (GARCH-MIDAS) model.

Negative news, including negative return-related volatility and higher economic uncertainty, has a greater impact on the long-term volatility components than positive news. During the financial crisis of 2008, economic uncertainty and realized volatility had a significant impact on long-term volatility components but did not constitute long-term volatility components during the 2015 A-share stock market crash and the 2020 COVID-19 pandemic. The two-factor asymmetric GARCH-MIDAS model outperformed the other two models in terms of explanatory power, fitting ability and out-of-sample forecasting ability for the long-term volatility component.

Many GARCH series models can also combine the GARCH series model with the MIDAS method, including but not limited to Exponential GARCH (EGARCH) and Threshold GARCH (TGARCH). These diverse models may exhibit distinct reactions to economic uncertainty. Consequently, further research should be undertaken to juxtapose alternative models for assessing the stock market response.

Our conclusions have important implications for stakeholders, including policymakers, market regulators and investors, to promote market stability. Understanding the asymmetric shock arising from economic uncertainty on volatility enables market participants to assess the potential repercussions of negative news, engage in timely and effective volatility prediction, implement risk management strategies and offer a reference for financial regulators to preemptively address and mitigate systemic financial risks.

First, in the face of domestic and international uncertainties and challenges, policymakers must increase communication with the market and improve policy transparency to effectively guide market expectations. Second, stock market authorities should improve the basic regulatory system of the capital market and optimize investor structure. Third, investors should gradually shift to long-term value investment concepts and jointly promote market stability.

This study offers a novel perspective on incorporating a Chinese economic uncertainty index constructed by a high-dimensional FAVAR-SV model into the asymmetric GARCH-MIDAS model.

Investors aim for returns when investing in stocks, making return volatility a crucial concern. This study compares symmetric and asymmetric GARCH models to forecast volatility in emerging nations like the G4 countries. Accurate volatility forecasting is vital for investors to make well-informed investment decisions, forming the core purpose of this study.

From January 1993 to May 2021, the study spans four periods, focusing on the global economic crisis of 2008, the Russian crisis of 2015 and the COVID-19 pandemic. Standard generalized autoregressive conditional heteroscedasticity (GARCH), exponential GARCH (E-GARCH) and Glosten-Jagannathan-Runkle GARCH models were employed to analyse the data. Robustness was assessed using the Akaike information criterion, Schwarz information criterion and maximum log-likelihood criteria.

The study's findings show that the E-GARCH model is the best model for forecasting volatility in emerging nations. This is because the E-GARCH model is able to capture the asymmetric effects of positive and negative shocks on volatility.

This unique study compares symmetric and asymmetric GARCH models for forecasting volatility in emerging nations, a novel approach not explored in prior research. The insights gained can aid investors in constructing more effective risk-adjusted international portfolios, offering a better understanding of stock market volatility to inform strategic investment decisions.

One important characteristic of cryptocurrencies has been their high and erratic volatility. To represent this complicated behavior, recent studies have emphasized the use of autoregressive models frequently concluding that generalized autoregressive conditional heteroskedasticity (GARCH) models are the most adequate to overcome the limitations of conventional standard deviation estimates. Some studies have expanded this approach including jumps into the modeling. Following this line of research, and extending previous research, our study analyzes the volatility of Bitcoin employing and comparing some symmetric and asymmetric GARCH model extensions (threshold ARCH (TARCH), exponential GARCH (EGARCH), asymmetric power ARCH (APARCH), component GARCH (CGARCH), and asymmetric component GARCH (ACGARCH)), under two distributions (normal and generalized error). Additionally, because linear GARCH models can produce biased results if the series exhibit structural changes, once the conditional volatility has been modeled, we identify the best fitting GARCH model applying a Markov switching model to test whether Bitcoin volatility evolves according to two different regimes: high volatility and low volatility. The period of study includes daily series from July 16, 2010 (the earliest date available) to January 24, 2019. Findings reveal that EGARCH model under generalized error distribution provides the best fit to model Bitcoin conditional volatility. According to the Markov switching autoregressive (MS-AR) Bitcoin’s conditional volatility displays two regimes: high volatility and low volatility.

In this chapter, we outline the statistical consequences of neglecting structural breaks and regime switches in autoregressive and GARCH models and propose two strategies to approach the problem. The first strategy is to identify regimes of constant unconditional volatility using a change point detector and estimate a separate GARCH model on the resulting segments. The second approach is to use a multiple-regime GARCH model, such as the Flexible Coefficient GARCH (FCGARCH) specification, where the regime-switches are governed by an observable variable. We apply both alternatives to an array of financial time series and compare their forecast performance.

We examine the role of structural breaks in forecasting stock return volatility. We begin by testing for structural breaks in the unconditional variance of daily returns for the S&P 500 market index and ten sectoral stock indices for 9/12/1989–1/19/2006 using an iterative cumulative sum of squares procedure. We find evidence of multiple variance breaks in almost all of the return series, indicating that structural breaks are an empirically relevant feature of return volatility. We then undertake an out-of-sample forecasting exercise to analyze how instabilities in unconditional variance affect the forecasting performance of asymmetric volatility models, focusing on procedures that employ a variety of estimation window sizes designed to accommodate potential structural breaks. The exercise demonstrates that structural breaks present important challenges to forecasting stock return volatility. We find that averaging across volatility forecasts generated by individual forecasting models estimated using different window sizes performs well in many cases and appears to offer a useful approach to forecasting stock return volatility in the presence of structural breaks.