The objectives of this research are to propose an efficient and proper model that fits the cassava and rubber yields data. A generalized estimating equation (GEE) and a linear mixed model (LMM) with spatial correlation following the conditional autoregressive model (CAR) were adopted. The dependent variables are the cassava and rubber yields collected each month in every province of Thailand. The factors considered are rainfall averaged temperatures and regions. The results from GEE and LMM show that the factors influencing on the cassava and rubber yields are rainfall averaged temperature and region. Both GEE and LMM fit the correlated data. The GEE is used to explain the influence of factors on the yields in all provinces while the LMM is used to explain the influence of factors on the yields in each province.

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.