A Comparison of GARCH Models for Volatility Estimation of Returns on Securities in Resource Group of Thai Stock Market

Abstract

The objectives of this study are to estimate volatility of returns on securities in ResourceGroup of Thai Stock Market using basic specifications of ARCH/GARCH/EGARCH model, and to measure skewness and kurtosis of the error term distribution from models selection.A test of ARCH Effect is performed in order to examine whether all data fitt with the ARCH family, and then ARCH (1, 1), GARCH (1,1) and EGARCH (1,1) are developed. A conditional variance equation from ARCH (1,1) is 2 0 1 1 2 t = + t− σ α α ε , and fromGARCH (1,1) is in a form 2 1 1 2 0 1 1 2 σ t = α +α at− + β σ t− and for EGARCH (1,1) is 1 1 1 2 1 1 2 ln( ) ln( ) − − − − = + − + + t t t t t t σ ε γ σ ε σ ω β σ α . The Akaike Criterion (AIC) and Schwarz criterion (SC) statisticsare used in model selection for non-nested alternatives-smaller values of the AIC and SC are preferred. For testing normality, a test statistic is Jarque-Bera and if the residual are normally distributed, the histogram should be bell-shaped and the Jarque-Bera statistic should not be significant, and if the null hypothesis is rejected, then innovation would be introduced through student’s t distribution. After all these steps, skewness and kurtosis are calculated in the study. Results of the study showed that 6 out of 30 securities data fitted with ARCH (1,1) model with insignificance statistical results which indicated that there must be a reconsideration of applying higher order of ARCHinstead of ARCH (1,1) model. There were 5 securities fitted with GARCH (1,1) model, with the same pattern, i.e., lower value for the coefficient of the ARCH term and higher value for the GARCH term which lead to a high fluctuations in GARCH. This finding indicated that the asset return was expectedly large in either the upward or the downward direction, and the estimation results indicated that GARCH (1,1) is appropriated to explain volatility cluster and estimate value of risk on security return. There were 19 securities that data esimation indicated that EGARCH (1,1) model was an appropriate form of variance equation, and showed that all volatility estimation were about 50% or about at moderated level. The skewness and Kurtosis of all residuals distributions showed that all skewness values were greater than zero (skewed to the right) and all Kurtosis values were greater than 3 (Leptokurtic distribution). This means that for each security, the daily price was concentrated on the left side of the mean value, and there were some extreme values to the right side. For the kurtosis, the distribution had a thicker tail which meaned that there was a high probability that the set of data would gain such extreme values