Modelling of Daily Nigerian Naira - British Pound Exchange Rates Using SARIMA Methods

Aims: To fit a time series model to daily Naira-Pound exchange rate series.
Study Design: Seasonal Autoregressive Integrated Moving Average Model.
Place and Duration of Study: Department of Mathematics/Computer Science, Rivers State University of Science and Technology, Nigeria, from December 2012 to March 2013.
Methodology: The correlogram of a non-seasonal difference of the 7-point difference of the data was plotted. On the basis of that plot, a seasonal autoregressive integrated moving average (0, 1, 1)x(0, 1, 1)7model was proposed and fitted. This model was compared with a suggestive ARIMA model with a view to establishing SARIMA supremacy.
Results: Seasonality of order 7 is evident from the analysis of the differences of the seasonal differences of the original series. All three moving average parameters (i.e. for lags 1, 7 and 8) of the SARIMA model are highly significant, their P-values being 0.0005, 0.0000 and 0.0001 respectively. The model agrees very closely with the observed data. Up to 51% of variations in the data set are explained by the model. The residuals are observed not to be correlated with each other. On the other hand only 8% of the variability in the data set is accounted for by the ARIMA(1, 1, 1) model.
Conclusion: The SARIMA model more adequately represents the data set.