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.

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.

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.

The objective of this research is to select a proper cumulative function for trend in an analysis of simultaneous multiple time series data with autocorrelation trend and outliers using a Bayesian method. The proposed model is applied to fluctuate stock price data in the stock exchange of Thailand. The data consist of the closing prices of 5 stocks. The algorithms are written in OpenBUGS and the performance of the model is evaluated via a simulation study in R. The cumulative distribution functions considered here are a Weibull cumulative distribution function and an exponential cumulative distribution. They are compared using RMSE MAPE and MAE as criteria. The research found that an exponential cumulative function for trends gives smaller values of the three criteria in both model fitting and model validation for the4 stocks EA NWR and KTB. However a Weibull cumulative distribution function gives smaller values of three criteria for the PTT in both model fitting and model validation.