Long Memory and Volatility Models in Forecasting Exchange Rate of Nigerian Naira to United State Dollar

Abstract

Financial time series such as stock prices, inflation rates, interest rates, and exchange rates are known to exhibit upward and downward trend and often possesses long memory and volatility behavior. These behaviors are crucial in the analysis, modeling and forecasting of time series data. Unfortunately, many analysts don’t take into consideration the consequences of long memory and volatility while modeling financial time series data. Therefore, this paper intends to examine the effect of long memory and volatility in forecasting Exchange Rate of Nigerian Naira-United State Dollar. The data used for this study is obtained from Central Bank of Nigeria’s website for the period of January 2002 to Feb 2020. Observations from time series and Autocorrelation function (ACF) plot shows that the data was not stationary. This was confirmed by the Augmented Dickey Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) unit root tests on the datasets. Fractional differencing was used to transform the series and ARFIMA(1,d,1) and ARFIMA(1,d,2) models were selected using AIC criterion. However, the residuals of these models were found to be serially correlated and heteroscedastic. These problems led to combining ARFIMA with GARCH model in order to adequately study long memory and volatility simultaneously. Therefore ARFIMA models were combined with GARCH(1,1) to form ARFIMA(1,d,1)-GARCH(1,1) and ARFIMA(1,d,2)- GARCH(1,1). The results of the forecast performance indicate that the best model is ARFIMA(1,d,2)– GARCH(1,1).