The objectives of this research were to propose a model with some functions including CAR spatial effects and to select a proper model for predicting rince and rubber yields in southern provices of Thailand. A linear mixed model (LMM) with spatial effects and dummy varables and Fourier seasonal effects was proposed. Bayesian estimation was used and the estimated rice and rubber yields were used for prediction. The dependent variables were rice and rubber yields in southern provinces of Thailand. Factors considered were rain temperature soil fertilizer soil organic matter trend and also sesonal effects. The results show that rain temperature soil fertilizer soil organic matter trend and sesonal effects influence on rice and rubber yields. The proposed model with Fourier seasonal term is the most appropriate comparing to the model with dummy variable for season effects and the Holt-Winters model. Therefore the proposed model with Fourier sesaonal term should be the first consideration for prediction.

The objectives of this research were to create a model for time sereries data prices and yields of natural rubber to be more accurate prediction and to compare the proposed model with the classical time series models such as the Holt-Winters Additive Exponential smoothing model (Holt-Winters ES) and the seasonal autoregressive integrated moving average model (SARIMA). The proposed model was a linear mixed model (LMM) consisting with trend autoregression outliers and sesonal terms. Dummy varialbles and Fourier seasonal effects were studied. Bayesian estimation was used and the estimated prices and yields were used for prediction. The results show that the proposed model with a Fouries seasonal effect is the most appropriated comparing with the dummy seasonal effect the Holt-Winters ES and the SARIMA having the least mean absolute values (MAE) both fiting and validating parts. The proposed model with sesaonal dummy variables should be the first consideration for forecasting spatial time series with a seasonal component.