MODELING VOLATILITY PERSISTENCE OF STOCK MARKET MONTHLY RETURNS VOLATILITY USING GARCH MODELS UNDER DIFFERENT DISTRIBUTIONS

Abstract

This papers aims to uncover stylized facts of monthly stock market
returns and identify adequate GARCH model with appropriate
distribution density that captures conditional variance in monthly
stock market returns. We obtain monthly close values of Bombay
Stock Exchange’s (BSE) Sensex over the period January 1991 to
December 2019 (348 monthly observations). To model the
conditional variance, volatility clustering, asymmetry, and leverage
effect we apply four conventional GARCH models under three
different distribution densities. We use two information criterions to
choose best fit model. Results reveal positive Skewness, weaker
excess kurtosis, no autocorrelations in relative returns and log
returns. On the other side presence of autocorrelation in squared log
returns indicates volatility clustering. All the four GARCH models
have better information criterion values under Gaussian distribution
compared to t-distribution and Generalized Error Distribution.
Furthermore, results indicate that conventional GARCH model is
adequate to measure the conditional volatility. GJR-GARCH model
under Gaussian distribution exhibit leverage effect but statistically
not significant at any standard significance levels. Other asymmetric
models do not exhibit leverage effect. Among the 12 models modeled
in present paper, GARCH model has superior information criterion
values, log likelihood value, and lowest standard error values for all
the coefficients in the model.