Bayesian Structural Time Series Modelling of Monthly Petroleum Product Sales in Plateau State, Nigeria

Monthly petroleum-product sales can vary with seasonal activity, market conditions, and distribution constraints. This study examines reported monthly sales volumes of Premium Motor Spirit (PMS) and Automotive Gas Oil (AGO) at plateau state petroleum-products distribution depot in Nigeria, using 72 observations for each product from January 2020 to December 2025. Exploratory plots, seasonal-trend decomposition, and Bayesian structural time-series (BSTS) summaries were assessed alongside alternative structural and autoregressive specifications. The basic BSTS summaries reported coefficients of determination of 0.6976 for PMS and 0.3821 for AGO. Posterior medians for the tabulated autoregressive coefficients were -0.1437 for PMS and -0.4899 for AGO, although both 95% credible intervals included zero. Model-comparison summaries varied across specification groups, and identical reported AR(1) and AR(2) outputs did not establish an independent advantage for the higher-order model. Ljung-Box results for the autoregressive specifications showed residual serial dependence at 12 and 24 months (PMS: p = 0.022 and 0.0005; AGO: p = 0.0020 and 0.0002). The analyses describe substantial temporal variation in depot sales and illustrate the interpretation of Bayesian structural-model output. Persistent residual dependence, limited seasonal replication, differences among model-summary blocks, and the absence of held-out predictive evaluation restrict conclusions about forecast performance and operational usefulness.