Monthly XAF-USD Exchange Rates Modeling by SARIMA Techniques

The monthly exchange rates between the Central African Franc (XAF) and the US Dollar (USD) are herein modeled by SARIMA techniques. The realization from January 1997 to March 2013 (referred to as XDER herein) is analyzed in this work. The time plot of XDER in Figure 1 shows an overall upward secular trend with no obvious regular seasonal component. As expected, XDER is shown to be non-stationary by the Augmented Dickey Fuller (ADF) test. Seasonal (i.e. 12-monthly) differencing of XDER yields the series SDXDER which shows an overall horizontal trend, yet with no definite seasonal movement (See figure 2). The ADF test certifies SDXDER as stationary. Its correlogram in Figure 4 suggests an ARMA(1, 5) model fit. A non-seasonal differencing of SDXDER yields the series DSDXDER which exhibits an overall horizontal trend. No seasonal component is discernible from the visual inspection of its time plot of Figure 3. However its correlogram in Figure 5 has a significant negative spike at lag 12 and comparable spikes at lags 11 and 13, an indication of a 12 monthly seasonality and the presence of a seasonal moving average component of order one. Moreover this is the autocorrelation structure of a (0, 1, 1)x(0, 1, 1)12 SARIMA model. Hence the two models, (1, 0, 5)x(0, 1, 0)12 and (0, 1, 1)x(0, 1, 1)12 , are proposed and fitted. The latter has been shown to be the more adequate.