A Ridge-Penalised Fourier Autoregressive Framework for High-Dimensional Periodic Time Series Dataset

Time series associated with the seasonal climate are highly persistent with strong periodic behaviour making reliable statistical forecasting a challenge. Integrated autoregressive models on a conventional framework may fail to represent multifrequency seasonality. Fourier Autoregressive (FAR) models offer flexibility but may experience instability when the model complexity escalates in nature. The objective of this study is to improve forecast and parameter stability in the Fourier autoregressive framework by consideration of ridge penalisation. Using Nigeria's data on monthly rainfall and relative humidity from 2014 to 2024, the study creates and estimates classical FAR and ridge-penalised FAR models. Results from the ADF and KPSS tests on stationary indicate both series become stationary after first differencing. The identification of the model is done on the basis of information criteria and periodic correlation analysis. The out-of-sample Root Mean Square Error and Mean Absolute Percentage Error is used to evaluate the forecast performance. Fourier-based models help achieve far superior results than conventional ARIMA specifications, according to the empirical results. reduces RMSE from 90.94 based on to 73.72 when applied for rainfall, but ridge-penalised FAR further improves performance with lowest RMSE of 73.31. Further, MAPE goes down to 197.09 from 515.34. Similar improvements occur for relative humidity. The RMSE declines from 9.68 under to 6.60 for , and further to 6.34 for . Diagnostic findings validate well-mannered residuals with no remaining serial dependence. The research concludes that ridge penalisation improves the generalisation potential of Fourier autoregressive models, thereby resulting in a robust and reliable framework for seasonal climatic time series forecasting with strong periodic structures.