A Generalized Bayesian Structural Time Series Framework for Forecasting Seasonal Data with Sparse Observations

This study proposes a Generalized Bayesian Structural Time Series (GBSTS) framework for forecasting seasonal time series with sparse observations. Rather than introducing new state-space components, the proposed framework systematically integrates alternative trend and seasonal specifications with multiple missing-data reconstruction strategies within a unified Bayesian state-space formulation. This integration enables the joint assessment of structural model specification and missing-data treatment under varying sample sizes, seasonal structures, and levels of data sparsity. Forecasting performance is evaluated through a Monte Carlo simulation study considering different seasonal mechanisms, missing-data rates of 10%, 30%, and 50%, and a fixed 12-month forecasting horizon. An empirical analysis of monthly temperature and relative humidity series is additionally conducted to assess the practical applicability of the proposed framework. The results show that the GBSTS with a local linear trend and trigonometric seasonal component achieved the best overall forecasting performance among the models considered, demonstrating robust predictive accuracy across varying data conditions and levels of sparsity. Among the imputation methods examined, Kalman smoothing and seasonal split generally yielded comparable forecasting performance across different data conditions and levels of sparsity. Overall, the findings indicate that integrating flexible structural specifications and missing-data reconstruction within the GBSTS framework provides an effective and interpretable Bayesian approach for forecasting seasonal time series with sparse observations.