Modelling and forecasting stock market volatility using GARCH models

Abstract

This study empirically models and forecasts stock market volatility in Nigeria using the GARCH family of econometric models applied to twenty five years of monthly Nigerian Exchange Group All-Share Index data spanning January 2000 to December 2024. The work is motivated by the substantial structural shocks introduced by the 2023 macroeconomic policy reforms, specifically the removal of petroleum fuel subsidies and the unification of the foreign exchange windows, which fundamentally altered the volatility dynamics of the Nigerian equity market. Five model specifications were estimated: GARCH (1,1) with normal and Student-t innovations, EGARCH (1,1) with normal innovations, and GJR-GARCH (1,1) with normal and Student-t innovations. Prior to estimation, comprehensive diagnostic tests confirmed that the return series exhibits the canonical stylised facts of financial time series, namely significant excess kurtosis of 5.04, non-normality with a Jarque-Bera statistic of 317.67, stationarity of the log returns with an Augmented Dickey-Fuller statistic of negative 4.32, and strong conditional heteroskedasticity with an ARCH-LM statistic of 33.84. The GJR-GARCH model confirmed a statistically and economically significant leverage effect, with negative shocks raising conditional variance roughly two and a half times more than positive shocks of equal magnitude. On information criteria the GARCH (1,1) with Student-t innovations was preferred, while the GJR-GARCH with Student-t innovations produced the most accurate out-of-sample forecasts on the mean absolute error criterion. The study recommends the adoption of asymmetric specifications with fat-tailed innovations for risk management in the Nigerian market.