**ABSTRACT**

This paper investigates the presence of long memory both in mean and volatility of Naira per Dollar exchange rate series, using models of autoregressive fractionally integrated moving average (ARFIMA), generalized autoregressive conditional heteroscedastic (GARCH) and fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) origins. Long memory tests are carried out both for the returns and volatility series. The ARFIMA model with error following either GARCH or FIGARCH process were fitted to the exchange rate data and the results of GPH estimator indicate the existence of long memory in both the conditional mean and volatility. At the end, the forecasting performance of the fitted models were carried out in terms of RMSE and the residuals are also examined to check adequacy of the fitted models. ARFIMA-GARCH model demonstrates a better performance.

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