A Model for Daily Exchange Rates of the Naira and the XOF by Seasonal ARIMA Methods

The daily exchange rates of the Nigerian Naira (NGN) and West African CFA franc (XOF) from Thursday, 14th March, 2013 to Saturday, 23rd November 2013 are being modeled by Seasonal Autoregressive Integrated Moving Average (SARIMA) methods. This realization of the time series, referred to as NXOF, is a generally decreasing one, reflecting the relative depreciation of the Naira within the period of interest. As expected the Augmented Dickey Fuller (ADF) Tests adjudge it to be non-stationary. There is indication that NXOF is seasonal of period 7 days, there being a tendency for weekly maximums around Mondays and minimums around Sundays. A seasonal (i.e. 7-day) differencing produces a series SDNXOF with an overall horizontal trend. A non-seasonal differencing of SDNXOF yields a series DSDNXOF with an overall horizontal trend. Both SDNXOF and DSDNXOF are adjudged stationary by the ADF test. By the autocorrelation functions of SDNXOF and DSDNXOF two SARIMA models are suggestive: the (1, 0, 5)x(0, 1, 0)7 and the (0, 1, 1)x(0, 1, 1)7. Residual analysis of the models reveals that the latter is the more adequate model.