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 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.

This research is the comparative study of three forecasting methods on SET 100 index. These methods are Simple Exponential Smoothing method Holts method and Box-Jenkins method. Two sets of data were used in this study. The first one used as a training set was collected from January 2 2008 to September 30 2011. The other one used as a testing set was collected from October 3 2011 to October 14 2011. We propose that the most appropriate forecasting method is the one which give the lowest MAE MSE MAPE and diagnostic checking. The results show that Holt’s method displays the lowest MAE MSE and MAPE. The next one is Box-Jenkins method while the Simple Exponential Smoothing method exhibits the highest value of all three indicators. However the model from Box-Jenkins method is the only one way that reveals no residual autocorrelation. This leads to the conclusion that the appropriate models for forecasting of SET 100 Index is ARIMA (213).

The objective of this study is to compare three forecasting methods on three agricultural products consisting of fresh whole chicken (include bone no entrails) red meat pork hip section and Jasmine rice. These methods are Simple Exponential Smoothing method Holt’s method and Winter’s method. Data are colleced for a period of 60 months from January 2007 to December 2011. The most suitable forecasting method are the one that shows no residual autocorrelation and gives the lowest MSE MAPE. The results show that Simple Exponential Smoothing method is the most suitable method on three agricultural products due to this method reveals no residual autocorrelation and displays the lowest MSE MAPE.

The objective of this research is to construct the appropriate forecasting model for the export quantity of concentrated latex by the three time series analysis methods which are Box-Jenkins method Winters’ multiplicative exponential smoothing method and combined forecasting method. Time series data from the website of Office of Agricultural Economics during January 1998 to February 2014 (194 values) are used and divided into two series. The first 182 values from January 1998 until February 2013 for the models prediction and the last 12 values from March 2013 until February 2014 for comparison the performance of forecasting models via the criterion of the lowest root mean squared error and the criterion of the highest correlation coefficient between existing values and forecasted values. Research findings indicated that for all forecasting methods that have been studied the most powerful method is the combined forecasting and the forecasting model is where and represent the single forecasts at time t from Box-Jenkins method and Winters’ multiplicative exponential smoothing method respectively.