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.

This research aims to apply the principle of stochastic process for modeling. The parameters are estimated using Bayesian methods. The monthly average real price of paddy rice 15% and yield of paddy rice in Thailand were studied. The price and the yield of paddy rice which are time series data consisting of four components autocorrelation an exponential cumulative distribution function for trend outliers and two different types of seasons: the dummy seasons and Fourier function seasons. Writing algorithms programming in OpenBUGS and evaluating the performance of models from simulation programming in R were conducted. After that Bayesian methods with dummy seasons and Fourier function season were compared using RMSE MSE and MAE as the criteria. The results show that the Bayesian model with an exponential cumulative distribution function for trend and dummy seasons give the lowest RMSE MSE and MAE for both model fitting and model validating.