An Autoregressive Process with Fourier Terms for Seasonal-Periodic Time Series Datasets

Abstract

A healthy economy depends on rapid economic growth, but this can be seriously hampered by an unstable inflation rate. Consequently, the purpose of this study is to model and forecast Nigeria's yearly inflation rate by taking cognisance of the variation the series exhibited. The methods used are descriptive statistics, Fourier Autoregressive (FAR), Autoregressive Integrated Moving Average (ARIMA) and Seasonal-ARIMA processes. Descriptive statistics outcomes of the series indicated that the mean is 15.85 with a standard deviation of 15.03. The time plot showed the inflation rate series is nonstationary and exhibited seasonal and cyclical variations. The series is stationary during the initial difference, as demonstrated by applying the Augmented Dickey-Fuller test. The tentative FAR, ARIMA and SARIMA models were determined using autocorrelation and partial autocorrelation functions. The models estimated were chosen based on Akaike and Schwarz information criteria values. The adequacy of FAR(1), ARIMA(1,1,2) and SARIMA models were determined based on Autocorrelation and partial autocorrelation function residual plots. The out-sample FAR(1) model forecast captured and exhibited the seasonality and periodicity present in the Nigerian yearly inflation rate series, which are not attained in the other models. Based on the forecast evaluation metrics obtained for the models, FAR(1) is the better model since its forecast evaluation metrics are lower. Conclusively, FAR(1) is the better model for forecasting the Nigerian inflation rate when the variation exhibited by series is considered.