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A Bayesian nonlinearity test for threshold moving average models
Author(s) -
Xia Qiang,
Pan Jiazhu,
Zhang Zhiqiang,
Liu Jinshan
Publication year - 2010
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2010.00667.x
Subject(s) - mathematics , markov chain monte carlo , gibbs sampling , posterior probability , threshold model , bayesian probability , reversible jump markov chain monte carlo , statistics , metropolis–hastings algorithm , jump , nonlinear system , monte carlo method , markov chain , algorithm , statistical physics , physics , quantum mechanics
We propose a Bayesian test for nonlinearity of threshold moving average (TMA) models. First, we obtain the marginal posterior densities of all parameters, including the threshold and delay, of the TMA model using Gibbs sampler with the Metropolis–Hastings algorithm. And then, we adopt reversible‐jump Markov chain Monte Carlo methods to calculate the posterior probabilities for MA and TMA models. Posterior evidence in favour of the TMA model indicates threshold nonlinearity. Simulation experiments and a real example show that our method works very well in distinguishing MA and TMA models.