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.

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.

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 objective of this research is to use a stochastic process for building a model using Bayesian parameter estimation. The model is applied to the of crash prices and future prices of rice in Thailand for 120 moths including monthly closing average price of white rice 5% non-glutinous paddy 15% and Hom Mali non-glutinous paddy 105. The data are time series data containing autocorrelation trend seasonality and outliers. The algorithms are turned into codes in OpenBugs and the performance of the model is evaluated using simulation in R. The model with a Weibull cumulative distribution function trend the model with an exponential cumulative distribution function trend and the exponential smoothing model are compared. The root mean squared error (RMSE) mean absolute percentage error (MAPE) and mean absolute error (MAE) are used as the criteria. The results show that the model with the model with an exponential cumulative distribution function trend gives smallest RMSE MAPE and MAE for the crash prices of non-glutinous paddy 15% and Hom Mali non-glutinous paddy 105 for both model fitting part and model validation part. The model with a Weibull cumulative distribution function trend gives the smallest RMSE MAPE and MAE for the closing average price of white rice 5% for both model fitting part and model validation part.