A HYBRID APPROACH TO FORECASTING STOCK INDICESUSING THE ARMA–GARCH AND ARMA–EGARCH MODELS:EVIDENCE FROM THE NIGERIAN STOCK EXCHANGE

Abstract

 The modeling of stock indices on the Nigerian Stock Exchange
(NSE) has been carried out using Gaussian-related distributions even when the observed data are not normal. It is necessary to incorporate distributions that are non-normal. Therefore, this study examined the application of classical and hybrid econometric models to forecast the daily movements of the Nigerian Stock Exchange Index (NSE30). Five competing models were evaluated: the Autoregressive Integrated Moving Average (ARIMA), the Generalized Autoregressive Conditional Heteroskedasticity (GARCH), the Exponential GARCH (EGARCH), and two hybrid extensions that combine mean and variance equations, namely ARIMA–GARCHandARIMA–EGARCH.Preliminary time–series diagnostics, including stationarity, normality, autocorrelation, and heteroskedasticity tests, revealed that the log–return series is stationary, non normally distributed, and characterised by conditional volatility clustering.
The ARIMA(1,1,2) model, identified through the Akaike Information Crite
rion, served as the baseline specification for subsequent volatility modelling. Empirical analysis indicates that incorporating volatility dynamics substantially enhances forecasting performance. The EGARCH(1,1) model captures leverage effects in the NSE 30 series by giving greater weight to negative shocks,
while the symmetric GARCH(1,1) model explains volatility persistence. When combined with ARIMA, both hybrid models deliver the most accurate forecasts, with identical lowest error values, and the DieboldMariano test confirms their clear superiority over the standalone ARIMA model.