European Journal of Scientific Research ISSN 1450-216X Vol.32 No.2 (2009), pp.167-176 © EuroJournals Publishing, Inc. 2009 http://www.eurojournals.com/ejsr.htm Measuring Forecast Performance of ARMA and ARFIMA Models: An Application to US Dollar/UK Pound Foreign Exchange Rate Olanrewaju. I. Shittu Department of Statistics, University of Ibadan Nigeria E-mail: oi.shittu@mail.ui.edu.ng Olaoluwa Simon Yaya Department of Statistics, University of Ibadan Nigeria Abstract The classical approach to modelling economic series is to apply the Box – Jenkins approach of ARMA or ARIMA depending on whether the series is stationary or non- stationary. If such series exhibits long memory property, forecast values based on ARIMA model may not be reliable. This studies therefore focused on measuring forecast performance of ARIMA(p,d,q) and ARFIMA (p,d,q) models for stationary type series that exhibit Long memory properties. The UK Pound/US Dollar exchange rate data were analysed by OX 5.1 package using the Root mean Square forecast Error (RMSFE) and Mean Absolute Percentage Forecast Error (MAPFE) as measurement criteria. The ARFIMA model was found to be better than ARMA model as indicated by model diagnostic tools. The estimated forecast values from ARFIMA model is more realistic and closely reflect the current economic reality in the two countries as indicated by the forecast evaluation tools. The results are in agreement with Kwiatkowski et.al.(1992) and Boutahar, M. (2008). Keywords: Fractional integration, Nonlinearity, Long memory, Exchange rate, Forecasting. 1. Introduction Let a process { } , 1,..., t X t T = be a stochastic process generated by zero mean ARIMA process as ( ) ( ) t t BX B ε Φ =Θ where ( ) 1 1 ... p p B B B φ φ Φ =− − − , ( ) 1 1 ... p p B B B θ θ Θ =− − − are polynomials in B; ( ) 1,..., i i p φ = and ( ) 1,..., i i q θ = are the autoregressive and moving average parameters respectively and t ε is a white noise series with variance 2 ε σ . If { } , 1,..., t X t T = is an integrated series ( ) I d for , we term such series a ‘short range’ dependence process which can be modelled using the Autoregressive Integrated Moving Average (ARIMA(p,d,q)) Box and Jenkins (1960). However, if d is not an integer i.e 1 d < , we term the series ‘long range’ dependence process or fractionally integrated series of order d a . The overall pattern of the fractionally integrated series is characterized by