Testing a linear ARMA Model against threshold-ARMA models

a Bayesian approach

Rubing Liang, Qiang Xia, Jiazhu Pan, Jinshan Liu

Research output: Contribution to journalArticle

1 Citation (Scopus)
43 Downloads (Pure)

Abstract

We introduce a Bayesian approach to test linear autoregressive moving-average (ARMA) models against threshold autoregressive moving-average (TARMA) models. Firstly, the marginal posterior densities of all parameters, including the threshold and delay, of a TARMA model are obtained by using Gibbs sampler with Metropolis-Hastings algorithm. Secondly, reversible-jump Markov chain Monte Carlo (RJMCMC) method is adopted to calculate the posterior probabilities for ARMA and TARMA models: Posterior evidence in favor of TARMA models indicates threshold nonlinearity. Finally, based on RJMCMC scheme and Akaike information criterion (AIC) or Bayesian information criterion (BIC), the procedure for modeling TARMA models is exploited. Simulation experiments and a real data example show that our method works well for distinguishing a ARMA from a TARMA model and for building TARMA models.
Original languageEnglish
Pages (from-to)1302-1317
Number of pages16
JournalCommunications in Statistics - Simulation and Computation
Volume46
Issue number2
Early online date25 Mar 2015
DOIs
Publication statusPublished - 28 Feb 2017

Fingerprint

Autoregressive Moving Average Model
Bayesian Approach
Testing
Reversible Jump Markov Chain Monte Carlo
Autoregressive Moving Average
Markov processes
Metropolis-Hastings Algorithm
Bayesian Information Criterion
Akaike Information Criterion
Gibbs Sampler
Markov Chain Monte Carlo Methods
Posterior Probability
Simulation Experiment
Monte Carlo methods
Nonlinearity
Calculate

Keywords

  • Bayesian interference
  • ARMA models
  • Gibbs sampler
  • Metropolis-Hastings algorithm
  • RJMCMC methods
  • AIC
  • BIC
  • TARMA models

Cite this

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title = "Testing a linear ARMA Model against threshold-ARMA models: a Bayesian approach",
abstract = "We introduce a Bayesian approach to test linear autoregressive moving-average (ARMA) models against threshold autoregressive moving-average (TARMA) models. Firstly, the marginal posterior densities of all parameters, including the threshold and delay, of a TARMA model are obtained by using Gibbs sampler with Metropolis-Hastings algorithm. Secondly, reversible-jump Markov chain Monte Carlo (RJMCMC) method is adopted to calculate the posterior probabilities for ARMA and TARMA models: Posterior evidence in favor of TARMA models indicates threshold nonlinearity. Finally, based on RJMCMC scheme and Akaike information criterion (AIC) or Bayesian information criterion (BIC), the procedure for modeling TARMA models is exploited. Simulation experiments and a real data example show that our method works well for distinguishing a ARMA from a TARMA model and for building TARMA models.",
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Testing a linear ARMA Model against threshold-ARMA models : a Bayesian approach. / Liang, Rubing; Xia, Qiang; Pan, Jiazhu; Liu, Jinshan.

In: Communications in Statistics - Simulation and Computation, Vol. 46, No. 2, 28.02.2017, p. 1302-1317.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Testing a linear ARMA Model against threshold-ARMA models

T2 - a Bayesian approach

AU - Liang, Rubing

AU - Xia, Qiang

AU - Pan, Jiazhu

AU - Liu, Jinshan

N1 - This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Statistics - Simulation and Computation on 25/03/2015, available online: http://www.tandfonline.com/10.1080/03610918.2014.1002616

PY - 2017/2/28

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N2 - We introduce a Bayesian approach to test linear autoregressive moving-average (ARMA) models against threshold autoregressive moving-average (TARMA) models. Firstly, the marginal posterior densities of all parameters, including the threshold and delay, of a TARMA model are obtained by using Gibbs sampler with Metropolis-Hastings algorithm. Secondly, reversible-jump Markov chain Monte Carlo (RJMCMC) method is adopted to calculate the posterior probabilities for ARMA and TARMA models: Posterior evidence in favor of TARMA models indicates threshold nonlinearity. Finally, based on RJMCMC scheme and Akaike information criterion (AIC) or Bayesian information criterion (BIC), the procedure for modeling TARMA models is exploited. Simulation experiments and a real data example show that our method works well for distinguishing a ARMA from a TARMA model and for building TARMA models.

AB - We introduce a Bayesian approach to test linear autoregressive moving-average (ARMA) models against threshold autoregressive moving-average (TARMA) models. Firstly, the marginal posterior densities of all parameters, including the threshold and delay, of a TARMA model are obtained by using Gibbs sampler with Metropolis-Hastings algorithm. Secondly, reversible-jump Markov chain Monte Carlo (RJMCMC) method is adopted to calculate the posterior probabilities for ARMA and TARMA models: Posterior evidence in favor of TARMA models indicates threshold nonlinearity. Finally, based on RJMCMC scheme and Akaike information criterion (AIC) or Bayesian information criterion (BIC), the procedure for modeling TARMA models is exploited. Simulation experiments and a real data example show that our method works well for distinguishing a ARMA from a TARMA model and for building TARMA models.

KW - Bayesian interference

KW - ARMA models

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KW - Metropolis-Hastings algorithm

KW - RJMCMC methods

KW - AIC

KW - BIC

KW - TARMA models

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JO - Communications in Statistics - Simulation and Computation

JF - Communications in Statistics - Simulation and Computation

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