Determining the Order of a Moving Average Model of Time Series Using Reversible Jump MCMC: A Comparison between Laplacian and Gaussian Noises

Abstract

Moving average (MA) is a time series model often used for pattern forecasting and recognition. It contains a noise that is often assumed to have a Gaussian distribution. However, in various applications, noise often does not have this distribution. This paper suggests using Laplacian noise in the MA model, instead. The comparison of Gaussian and Laplacian noises was also investigated to ascertain the right noise for the model. Moreover, the Bayesian method was used to estimate the parameters, such as the order and coefficient of the model, as well as noise variance. The posterior distribution has a complex form because the parameters are concerened with the combination of spaces of different dimensions. Therefore, to overcome this problem, the Markov Chain Monte Carlo (MCMC) reversible jump algorithm is adopted. A simulation study was conducted to evaluate its performance. After it has worked properly, it was applied to model human heart rate data. The results showed that the MCMC algorithm can estimate the parameters of the MA model. This was developed using Laplace distributed noise. Moreover, when compared with the Gaussian, the Laplacian noise resulted in a higher order model and produced a smaller variance.