Modelling Nigeria External Reserves Using Duality of Autoregressive and Moving Average Models

This research work was focused on modeling Nigeria's external reserves using the duality of autoregressive and moving average models. The suggested ARIMA models based on ACF and PACF were ARIMA (1, 2, 1), and ARIMA (2, 2, 1), from which the dual form of the model was derived. The error variances of the models and the dual were derived. The estimates of the model parameters were obtained for the computation of the error variances. Amongst the original models, ARIMA (1, 2, 1) has the least error variance. In comparison between the error variances of the original ARIMA models and the dual forms, the original models perform better than the dual for as its reaches its breaking point of 0.7 of which it becomes non dualized model. This places the original model of the ARIMA (1,2,1) at a higher comparative advantage than the dual form of ARIMA model. This research underscores the need for duality in the ARIMA model for comparison when modeling economic and financial time series.