Abstract
Bayesian methods furnish an attractive approach to time series data analysis. This article proposes the forecasting models that can detect trend, seasonality, auto regression and outliers in time series data related to some covariates. Cumulative Weibull distribution functions for trend, dummy variables for seasonality, binary selections for outliers and latent autoregression for autocorrelated time series data are used for the data analysis. The Gibbs sampling, a Markov Chain Monte Carlo (MCMC) algorithm, is used for the parameter estimation. The proposed models are applied to vegetable price time series data in Thailand. According to the RMSE, MAPE and MAE criteria for model comparisons, the proposed models provide the best results compared to the exponential smoothing models, SARIMA models and the Bayesian models with trend, auto regression and outliers.
Highlights
Several classical methods have been designed to handle those components
Cumulative Weibull distribution functions for trend, dummy variables for seasonality, binary selections for outliers and latent autoregression for autocorrelated time series data are used for the data analysis
According to the Root Mean Squared Error (RMSE), Mean Absolute Percent Error (MAPE) and Mean Absolute Error (MAE) criteria for model comparisons, the proposed models provide the best results compared to the exponential smoothing models, SARIMA models and the Bayesian models with trend, auto regression and outliers
Summary
Several classical methods have been designed to handle those components. The Holt-Winters exponentialTime series data are observations obtained through repeated measurements over time. Time series data can be decomposed into three main components: trend which is a long term direction, seasonality which is systematic and calendar related movements and irregularity which is unsystematic and short term fluctuations. The seasonal ARIMA denoted as SARIMA is a generalization and extension of the regular ARIMA It is used for time series where a pattern repeates seasonally over time The presence of those components could mislead the time series analysis procedure resulting in the wrong conclusion
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