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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.

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.

A univariate GARCH(p,q) process is quickly transformed to a univariate autoregressive moving-average process in squares of an underlying variable. For positive integer m, eigenvalue restrictions have been proposed as necessary and sufficient restrictions for existence of a unique mth moment of the output of a univariate GARCH process or, equivalently, the 2mth moment of the underlying variable. However, proofs in the literature that an eigenvalue restriction is necessary and sufficient for existence of unique 4th or higher even moments of the underlying variable, are either incorrect, incomplete, or unnecessarily long. Thus, the paper contains a short and general proof that an eigenvalue restriction is necessary and sufficient for existence of a unique 4th moment of the underlying variable of a univariate GARCH process. The paper also derives an expression for computing the 4th moment in terms of the GARCH parameters, which immediately implies a necessary and sufficient inequality restriction for existence of the 4th moment. Because the inequality restriction is easily computed in a finite number of basic arithmetic operations on the GARCH parameters and does not require computing eigenvalues, it provides an easy means for computing “by hand” the 4th moment and for checking its existence for low-dimensional GARCH processes. Finally, the paper illustrates the computations with some GARCH(1,1) processes reported in the literature.

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.

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 study aims to implement a novel approach of using the Realized generalized autoregressive conditional heteroskedasticity (GARCH) model within the conditional extreme value theory (EVT) framework to generate quantile forecasts. The Realized GARCH-EVT models are estimated with different realized volatility measures. The forecasting ability of the Realized GARCH-EVT models is compared with that of the standard GARCH-EVT models.

One-step-ahead forecasts of Value-at-Risk (VaR) and expected shortfall (ES) for five European stock indices, using different two-stage GARCH-EVT models, are generated. The forecasting ability of the standard GARCH-EVT model and the asymmetric exponential GARCH (EGARCH)-EVT model is compared with that of the Realized GARCH-EVT model. Additionally, five realized volatility measures are used to test whether the choice of realized volatility measure affects the forecasting performance of the Realized GARCH-EVT model.

In terms of the out-of-sample comparisons, the Realized GARCH-EVT models generally outperform the standard GARCH-EVT and EGARCH-EVT models. However, the choice of the realized estimator does not affect the forecasting ability of the Realized GARCH-EVT model.

It is one of the earliest implementations of the two-stage Realized GARCH-EVT model for generating quantile forecasts. To the best of the authors’ knowledge, this is the first study that compares the performance of different realized estimators within Realized GARCH-EVT framework. In the context of high-frequency data-based forecasting studies, a sample period of around 11 years is reasonably large. More importantly, the data set has a cross-sectional dimension with multiple European stock indices, whereas most of the earlier studies are based on the US market.

Financial returns are often modeled as stationary time series with innovations having heteroscedastic conditional variances. This paper seeks to derive the kurtosis of stationary processes with GARCH errors. The problem of hypothesis testing for stationary ARMA(p, q) processes with GARCH errors is studied. Forecasting of ARMA(p, q) processes with GARCH errors is also discussed in some detail.

Estimating‐function methodology was the principal method used for the research. The results were also illustrated using examples and simulation studies. Volatility modeling is the subject of the paper.

The kurtosis of stationary processes with GARCH errors is derived in terms of the model parameters (ψ), Ψ‐weights, and the kurtosis of the innovation process. Hypothesis testing for stationary ARMA(p, q) processes with GARCH errors based on the estimating‐function approach is shown to be superior to the least‐squares approach. The fourth moment of the l‐steps‐ahead forecast error is related to the model parameters and the kurtosis of the innovation process.

This paper will be of value to econometricians and to anyone with an interest in the statistical properties of volatility modeling.

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.