Modeling and Comparison of the Nigerian All Share Index Using ARIMA and Hybrid ARIMA-GARCH Models

Abstract

In this Paper, the performance of the Autoregressive Integrated Moving Average (ARIMA) and hybrid Autoregressive Integrated Moving Average Generalized Autoregressive Conditional Heteroscedastic (ARIMA-GARCH) models was compared using daily data (Five working days) of the Nigeria stock exchange data stream. There are 4610 share price index between the 14^th January 2005 and 14^th September 2023. An attempt was made to make the share price index data stationary. The ARIMA model's residuals and squared residuals were subjected to the Box-Ljung, Box-Pierce, and McLeod-Li tests. These tests demonstrated that the ARIMA model's residuals possessed a conditional variance, or volatility. The volatility was then modeled using the GARCH model. The fitted ARIMA model was obtained using the Box-Jenkins technique, and the hybrid ARIMA-GARCH model was utilized to capture the sequences' volatilities. The results indicates that in terms of the lowermost Akaike information criteria (AIC) and Mean absolute error (MAE), the best ARIMA out of the ARIMA models verified was ARIMA (2, 1, 2). The comparison of ARIMA (2, 1, 2) with hybrid (ARIMA-GARCH) in terms of the uppermost maximum likelihood (ML), lowermost AIC and MAE indicates that the hybrid model is the best. Therefore, the study recommends that the Nigerian financial markets should replace the application of ARIMA only with ARIMA-GARCH in modelling Nigeria all share price index data.