Trend-Fourier Time Series Regression Model for Secular-Cyclical Datasets

Abstract

The study proposed a Trend-Fourier Regression (TFR) model to handle time series datasets with simultaneous trend and cyclical variations. The model steps involve identification, estimation, diagnosis and forecasting. The Nigerian monthly Crude Oil Price (NMCOP) was used to implement the model and NMCOP was identified as trend-cyclical. The model estimation using Ordinary Least Squares method indicates that an increase in time will result in changes in NMCOP. Durbin-Watson statistics, histogram and autocorrelation function of residual plots were used to diagnose and specify the model to be stable. The coefficient of determination (R^2) indicates that over 80% of dependent variable variations were explained, with an adjusted (R^2) indicating a predictive ability exceeding 80%. The model efficiency was confirmed through out-sample and forecast evaluations, revealing superiority due to its smaller MAE, RMSE, and MAPE values, indicating minimal error. Conclusively, the TFR model is suitable for datasets that exhibit trend-cyclical variations simultaneously.