# International Journal of Computational Intelligence Systems

Volume 13, Issue 1, 2020, Pages 310 - 317

# Hierarchical Bayesian Choice of Laplacian ARMA Models Based on Reversible Jump MCMC Computation

Authors
Suparman*
Department of Mathematics Education, Universitas Ahmad Dahlan, Yogyakarta, Indonesia
Corresponding Author
Suparman
Received 19 December 2019, Accepted 20 February 2020, Available Online 18 March 2020.
DOI
10.2991/ijcis.d.200310.006How to use a DOI?
Keywords
ARMA time series; Hierarchical Bayesian; Laplacian noise; Reversible jump MCMC
Abstract

An autoregressive moving average (ARMA) is a time series model that is applied in everyday life for pattern recognition and forecasting. The ARMA model contains a noise which is assumed to have a specific distribution. The noise is often considered to have a Gaussian distribution. However in applications, the noise is sometimes found that does not have a Gaussian distribution. The first objective is to develop the ARMA model in which noise has a Laplacian distribution. The second objective is to estimate the parameters of the ARMA model. The ARMA model parameters include ARMA model orders, ARMA model coefficients, and noise variance. The parameter estimation of the ARMA model is carried out in the Bayesian framework. In the Bayesian framework, the ARMA model parameters are treated as a variable that has a prior distribution. The prior distribution for the ARMA model parameters is combined with the likelihood function for the data to get the posterior distribution for the parameter. The posterior distribution for parameters has a complex form so that the Bayes estimator cannot be determined analytically. The reversible jump Markov chain Monte Carlo (MCMC) algorithm was adopted to determine the Bayes estimator. The first result, the ARMA model can be developed by assuming Laplacian distribution noise. The second result, the performance of the algorithm was tested using simulation studies. The simulation shows that the reversible jump MCMC algorithm can estimate the parameters of the ARMA model correctly.

Open Access

Journal
International Journal of Computational Intelligence Systems
Volume-Issue
13 - 1
Pages
310 - 317
Publication Date
2020/03/18
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
10.2991/ijcis.d.200310.006How to use a DOI?
Open Access

TY  - JOUR
AU  - Suparman
PY  - 2020
DA  - 2020/03/18
TI  - Hierarchical Bayesian Choice of Laplacian ARMA Models Based on Reversible Jump MCMC Computation
JO  - International Journal of Computational Intelligence Systems
SP  - 310
EP  - 317
VL  - 13
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.200310.006
DO  - 10.2991/ijcis.d.200310.006
ID  - 2020
ER  -