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 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.

This research aimed to design and construct a forecasting support system on demand of fresh durian of Thailand by applying 2 mathematical models which were Time Series model and Artificial Neural Network model in order to find an accurate model of forecasting support system on demand of durian yield to forecast durian yield quantity of Thailand in advance and use the forecast results to plan and determine quantity of fresh durian and durian product conforming with domestic consumption and export in order not to be over demand and cheap durian sold price. The forecast models were applied with Time Series model by using Moving Average Weighted Moving Average Single Exponential Smoothing and Holt’s Linear Exponential Smoothing techniques and Back Propagation of Artificial Neural Network model which used 4 input variables relating to durian yield. All of the forecast models were used to forecast total durian yield quantity in 26 provinces of durian cultivated area all around Thailand. Durian yield quantity data used was from 1996 to 2008. After that the forecast results were used to find the errors of MAE MSE RMSE and MAPE. Then the errors of each forecast model were compared. The forecast model which had the least error was the most accurate forecast model. The research result is following. Back Propagation with 4-8-1 structure of Artificial Neural Network model had the least error so that it was the most accurate forecast model to forecast fresh durian yield quantity in advance.