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.

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.