The objectives of this research are to propose a model for estimating and detecting rice yields in Thailand to investigate the factors related to the rice yields to find the trend and to construct the maps of rice yields in Thailand. A linear mixed model (LMM) including the spatial effects which follow the conditional autoregressive model (CAR) and the time effects which follow the first-order linear autoregressive (AR(1)) model is proposed. The estimated rice yields are used to construct the rice yield maps in Thailand. The dependent variables are the rice yield in each month of each province. The factors considered are rainfall average temperatures and regions. The results indicate that the factors enfluencing the rice yields are rainfall average temperatures and regions (North Northeast South East West Central region is a refrence region). The trend also effects the rice yields. The rice yeilds maps are easy for readers to identify which areas have high or low yields and easy to compare the yields among areas by looking at their different colors.

The objectives of this research are to propose a linear mixed model including spatial effects to present the distribution of air pollution of each gas being Sulphur dioxide (SO2) Nitrogen dioxide (NO2) Carbon monoxide (CO) and Ozone (O3) and particulate matter (PM10) and to investigate the factors related to those air pollution in each area of Bangkok Metropolitan Region. The spatial effects are assumed to be a conditional autoregressive (CAR) model. The dependent variables are the amount of SO2 NO2 CO O3 and PM10 in each area and the independents considered are Industrial area business area and suburb area. The results indicate that the factors influencing the amount of air pollution ranking from most to least are industrial area suburb area and business area respectively.

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.