European Journal of Statistics and Probability (EJSP)

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Additive Sarima Modelling of Monthly Nigerian Naira – Cfa Franc Exchange Rates


This paper is on SARIMA modelling of monthly Naira-CFA Franc exchange rates. The time plot of the realisation from January 2004 to June 2013 in Figure 1 shows an overall upward secular trend with no clear seasonality. The time plot of the seasonal (i.e. 12-monthly) differences in Figure 2 shows an overall horizontal trend with no definite seasonality. The time plot of further non-seasonal differences in Figure 3 shows a horizontal trend and still no clear seasonality. The autocorrelation function of the resultant series of Figure 4 has a significant negative spike at lag 12 indicating a 12-monthly seasonality and the involvement of a seasonal moving average component of order one. Its partial autocorrelation function has a significant spike at lag 12 suggesting the inclusion of a seasonal autoregressive component of order one. Using the duality relationship between autoregressive and moving average models, it is argued that this autoregressive component of high order (i.e. of order 12) be replaced by a moving average component of (low) order one. Hence an additive SARIMA model with significant lags 1 and 12 is proposed and fitted. The model is shown to be adequate

Keywords: Additive SARIMA models, CFA Franc, Foreign exchange rates, Naira

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