Bayesian Model for Time Series with Trend, Autoregression and Outliers

We propose the Bayesian forecasting model that can detect trend, autoregression, and outliers in the time series data. We use cumulative Weibull distribution function for trend, binary selection for outliers, and autoregression for related time series data. Gibbs sampling algorithm which is one of MCMC methods is used for parameter estimation. The proposed models are applied to the vegetable price time series data in Thailand. According to the RMSE, MAPE, and MAE criteria for the model comparison, the proposed model provides the best results compared to the exponential smoothing and SARIMA models.