Bayesian Analysis of Seasonal and Periodic Time Series: Evidence from Nigerian Monthly Rainfall, 1981–2024

Abstract

Monthly rainfall in Nigeria exhibits pronounced annual seasonality, season-dependent variability, and changes in temporal dependence that may not be adequately represented by a single fixed-parameter model. This study presents a Bayesian modelling framework for monthly rainfall records from 37 Nigerian Meteorological Agency stations spanning January 1981 to December 2024, a 44-year period comprising 528 monthly values per station. The framework combines Whittle-likelihood spectral estimation, B-spline modelling of the log-spectral density, Bayesian structural time series (BSTS) decomposition, periodic autoregression, locally stationary spectral analysis, and reversible-jump Markov chain Monte Carlo for structural-break detection. Predictive distributions from complementary specifications are combined through Bayesian model averaging (BMA). Reported validation results for 2022–2024 indicate that BMA reduces root mean squared error relative to SARIMA by 8.3% at a 12-month horizon and 15.0% at a 24-month horizon. BMA has the lowest reported mean absolute percentage error at both horizons and the lowest 24-month RMSE; however, BSTS has the lowest 12-month RMSE. Structural-break summaries identify modal break locations within 1987–1989 at 22 stations and within 2001–2004 at 19 stations. These findings support the use of complementary seasonal models, particularly for longer-horizon prediction, rather than establishing uniform superiority of model averaging. Interpretation remains conditional on the reported evaluation design, and further documentation of forecast origins, model weights, zero-rainfall treatment, and posterior diagnostics is required for independent verification.