• Communications for Statistical Applications and Methods
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• v.21 no.4
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• pp.327-334
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• 2014

Various modified GARCH(1, 1) models have been found adequate in many applications. We are interested in their continuous time versions and limiting properties. We first define a stochastic integral that includes useful continuous time versions of modified GARCH(1, 1) processes and give sufficient conditions under which the process is exponentially ergodic and ${\beta}$-mixing. The central limit theorem for the process is also obtained.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1033-1043
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• 2011

In this paper, we use a nested family of models of Generalized Autoregressive Conditional Heteroscedasticity(GARCH) to verify asymmetric conditional heteroscedasticity in the KOSPI and Won-Dollar exchange rate. This study starts from an investigation of whether time series data have asymmetric features not explained by standard GARCH models. First, we use kernel density plot to show the non-normality and asymmetry in data as well as to capture asymmetric conditional heteroscedasticity. Later, we use three representative asymmetric heteroscedastic models, EGARCH(Exponential Garch), GJR-GARCH(Glosten, Jagannathan and Runkle), APARCH(Asymmetric Power Arch) that are improved from standard GARCH models to give a better explanation of asymmetry. Thereby we highlight the fact that volatility tends to respond asymmetrically according to positive and/or negative values of past changes referred to as the leverage effect. Furthermore, it is verified that how the direction of asymmetry is different depending on characteristics of time series data. For the KOSPI and Korean won-US dollar exchange rate, asymmetric heteroscedastic model analysis successfully reveal the leverage effect. We obtained predictive values of conditional volatility and its prediction standard errors by using moving block bootstrap.

• Asian Journal of Business Environment
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• v.11 no.4
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• pp.17-29
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• 2021

Purpose: The aim of this study is to explore the dynamic linkage between conditional stock market volatility and macroeconomic uncertainty of Bangladesh. Research design, data, and methodology: This study uses monthly data covering the time period from January 2005 to December 2018. A comprehensive set of macroeconomic variables, namely industrial production index (IP), consumer price index (CPI), broad money supply (M2), 91-day treasury bill rate (TB), treasury bond yield (GB), exchange rate (EX), inflow of foreign remittance (RT) and stock market index of DSEX are used for analysis. Symmetric and asymmetric univariate GARCH family of models and multivariate VAR model, along with block exogeneity and impulse response functions, are implemented on conditional volatility series to discover the possible interactions and causal relations between macroeconomic forces and stock return. Results: The analysis of the study exhibits time-varying volatility and volatility persistence in all the variables of interest. Moreover, the asymmetric effect is found significant in the stock return and most of the growth series of macroeconomic fundamentals. Results from the multivariate VAR model indicate that only short-term interest rate significantly influence the stock market volatility, while conditional stock return volatility is significant in explaining the volatility of industrial production, inflation, and treasury bill rate. Conclusion: The findings suggest an increasing interdependence between the money market and equity market as well as the macroeconomic fundamentals of Bangladesh.

• The Journal of Asian Finance, Economics and Business
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• v.9 no.10
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• pp.1-13
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• 2022

This paper empirically explores the predicting ability of the newly proposed smooth transition (ST) time-varying combining forecast methods. The proposed method allows the "weight" of combining forecasts to change gradually over time through its unique feature of transition variables. Stock market returns from 7 countries were applied to Ad Hoc models, the well-known Generalized Autoregressive Conditional Heteroskedasticity (GARCH) family models, and the Smooth Transition Exponential Smoothing (STES) models. Of the individual models, GJRGARCH and STES-E&AE emerged as the best models and thereby were chosen for constructing the combined forecast models where a total of nine ST combining methods were developed. The robustness of the ST combining forecasts is also validated by the Diebold-Mariano (DM) test. The post-sample forecasting performance shows that ST combining forecast methods outperformed all the individual models and fixed weight combining models. This study contributes in two ways: 1) the ST combining methods statistically outperformed all the individual forecast methods and the existing traditional combining methods using simple averaging and Bates & Granger method. 2) trading volume as a transition variable in ST methods was superior to other individual models as well as the ST models with single sign or size of past shocks as transition variables.