A Study of Nigeria Monthly Stock Price Index Using ARTFIMA-FIGARCH Hybrid Model

Abstract

Long memory is a phenomenon in time series analysis that is exhibited by a slow decay of the autocorrelation function. It has been observed that the presence of long memory in both mean and volatility can complicate model fitting and compromise forecasting reliability. Meanwhile, the Autoregressive Tempered Fractional Integrated Moving Average (ARTFIMA) as a tempered fractionally differenced long memory mean model and the Fractionally Integrated Generalized Autoregressive Conditional Heteroscedasticity (FIGARCH), which is a long memory variance model, could not independently and effectively address the challenges of time series data that displayed long memory in mean and volatility. To tackle this challenge, we introduce a hybrid model called the ARTFIMA-FIGARCH by combining ARTFIMA and FIGARCH models using the transformation method under the assumption that the residuals of the ARTFIMA model are non-normal, serially correlated, and heteroscedastic. To evaluate the effectiveness of this model, we employed the Nigerian Monthly Stock Price Index as well as simulated data sets as a testing ground and compared its performance against existing models like ARFIMA, ARTFIMA, and ARFIMA-FIGARCH. The selection of the most suitable model was determined using the Akaike Information Criterion (AIC) and model performance was assessed through various forecast accuracy measures. Our findings demonstrated that ARTFIMA (0,1.06,1)-FIGARCH (1,0.15,1) emerged as the best candidate of the new model and outperformed ARFIMA (1,1.06,0)-FIGARCH (1,0.15,1). Based on the findings of this study, it is concluded that ARTFIMA-FIGARCH is considered to be the most suitable model for studying the mean and volatility of the Nigerian monthly stock price index.