The objectives of this research are to propose a linear mixed model (LMM) for spatial time series with a seasonal component to apply the proposed model to monthly rubber yields in southern provinces of Thailand to forecast rubber yields in southern provinces of Thailand and to compare the performance of the proposed model to the Holt-Winters Additive Exponential smoothing model (Holt-Winters ES) and the seasonal autoregressive integrated moving average model (SARIMA). The proposed model is a linear mixed model (LMM) with spatial effects following a conditional autoregressive model (CAR model). Seasonal dummy variables and Fourier terms are two methods used to account for the seasonal effects. A Bayesian method is used for parameter estimation. The estimated monthly yields are used to forecast the monthly rubber yields. The dependent variables are the monthly rubber yields in each province. The effects considered are spatial effects heterogeneity effects and seasonal effects. The data are secondary data at a provincial level. The results show that the effects influencing on the amount of rubber yields are spatial heterogeneity and seasonal effects. The proposed model with sesonal dummy variables is the most appropriate model copared to the LMM with Fourier sesonal effects Holt-Withers ES and SARIMA. The mean absolute errors (MAE) are smallest in both model fitting and model validating parts. The proposed model with sesaonal dummy variables should be the first consideration for forecasting spatial time series with a seasonal component.

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 yield 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.