DATA MODELING WITH AUTOREGRESSIVE BASED ON REVERSIBLE JUMP MCMC SIMULATION: COMPARING GAUSSIAN AND LAPLACIAN NOISE
Keywords:Autoregressive processes, Bayes methods, Gaussian noise, Laplacian noise, Monte Carlo methods
The autoregressive model (AR) is one of the stochastic models in the time series that is used for forecasting. The AR model is affected by noise which has a distribution. The accuracy in choosing the noise distribution has an impact on the fit of the AR model to the data. This paper presents an AR model in which the noise has a Laplace distribution. And also, the Laplacian AR model is compared with the Gaussian AR model. The Bayesian approach was adopted to estimate the AR model parameters. The Binomial distribution was chosen as the prior distribution for the older model, the uniform distribution was chosen as the prior distribution for the AR model coefficients. The Bayesian estimator for the AR model parameters is calculated based on the posterior distribution with the help of the reversible jump algorithm Markov Chain Monte Carlo (MCMC). The results in this paper indicate that the reversible jump MCMC algorithm is categorized as valid in estimating the parameters of the AR model. Based on a simulation study, this paper shows that the Laplacian AR model can be used as an alternative to approximate an AR model that contains non-Gaussian noise. To support this finding, the research can be studied further from a theoretical point of view. With the help of the reversible jump MCMC algorithm, the Bayesian estimator for the AR model parameters is computed based on the posterior distribution. According to the findings of this paper, the reversible jump MCMC algorithm is suitable for estimating the parameters of the AR model. This research illustrates that the Laplacian AR model can be utilized as an alternative to approximate an AR model with non-Gaussian noise, based on a simulation analysis. The findings can be investigated further from a theoretical standpoint to support this finding.