Paper Title
Bayesian Models for Spatial Time Series Data Applied to Rubber Yields in Southern Provinces of Thailand

The objectives of this research are to propose a Bayesian model for spatial time series analysis, to apply the proposed model to forecast a monthly rubber yield in Southern provinces of Thailand, and to compare the performance of the proposed model with the classical Holt-Winters Additive Exponential smoothing. The proposed model is a linear mixed model (LMM) with spatial effects which follow a conditional autoregressive model (CAR). Dummy variables are used for seasonal effects. A Bayesian method is used for parameter estimation. The estimated monthly yields are used for the monthly rubber yield forecasting. The dependent variables are the rubber yields in each month of each province. The data are secondary data at a provincial level. The factors considered are spatial effects, heterogeneity effects, and seasonal effects. The results show that the factors influencing on the amount of rubber yields are, spatial, heterogeneity, and seasonal effects. The proposed model is proper and forecast accurately. Using the mean absolute error (MAE), the proposed model has a better performance compared to the classical Holt-Winters Additive Exponential smoothing in both model fitting and model validating. The proposed model should be the first consideration for spatial time series forecasting. Keywords- Rubber yield forecasting, Rubber yields in southern provinces of Thailand, Spatial time series data, Spatial effects, Seasonal effects, Heterogeneity effects