The Fitting of a SARIMA model to Monthly Naira-Euro Exchange Rates

Abstract

The time plot of the series NEER shows an overall positive trend with a peak in early 2010 after a deep depression in late 2008. No seasonality is discernible by this visual inspection. Seasonal (i.e. 12-month) differencing yields SDNEER which exhibits an overall slightly positive trend and a high peak in late 2009. Still the visual inspection of the time plot in Figure 2 hardly makes any seasonality obvious. A non-seasonal differencing of SDNEER yields DSDNEER with an overall horizontal trend. Though the time plot in Figure 3 does not give an impression of any regular seasonality, the correlogram of Figure 4 reveals seasonality of period 12 months. Besides there is indication that the product of two moving average components both of order one is involved: one component is seasonal and the other non-seasonal. In addition to that a significant spike of the partial autocorrelation function at lag 12 suggests the involvement of a seasonal  autoregressive component of order one. Therefore a (0, 1, 1)x(1, 1, 1)₁₂ SARIMA model is proposed and fitted. It has been shown to be adequate

Keywords: : Naira-Euro Exchange Rates, SARIMA models, Nigeria