Time series model building with Fourier autoregressive model

Abstract

This paper presents time series model building using Fourier autoregressive models. This model is capable of modelling and forecasting time series data that exhibit periodic and seasonal movements. From the implementation of the model, FAR(1), FAR(2) and FAR(3) models were chosen based on the periodic autocorrelation function (PeACF) and periodic partial autocorrelation function. The coefficients of the tentative modelwere estimated using a discrete Fourier transform estimation method. The FAR(1) model was chosen as the optimal model based on the smallest value of periodic Akaike and Bayesian information criteria, and the residuals of the fitted models were diagnosed to be white noise using the periodic residual autocorrelation function. The out-sample forecasts were obtained for the Nigerian monthly rainfall series from January 2018 to December 2019 using the FAR(1) and SARIMA(1,1,1)x(1,1,1)₁₂ models. The results exhibited a continuous periodic and seasonal movement but the periodic movement in the forecasted rainfall series was better with FAR(1) because its values showed a close reflection of the original series. The values of the forecast evaluation for both models showed that the forecast was consistent and accurate but the FAR(1) model forecast was more accurate since its forecast evaluation values were relatively lower. Hence, the Fourier autoregressive model is adequate and suitable for modelling and forecasting periodicity and seasonality in Nigerian rainfall time series data and any part of the world with rainfall series that are mostly characterised with periodic variation.