Bayes inference in regression models with ARMA\((p,q)\) errors. (English) Zbl 0807.62065
Summary: We develop practical and exact methods of analyzing \(\text{ARMA} (p,q)\) regression error models in a Bayesian framework by using the Gibbs sampling and Metropolis-Hastings algorithms [W. K. Hastings, Biometrika 57, 97-109 (1970; Zbl 0219.65008)] and we prove that the kernel of the proposed Markov chain sampler converges to the true density. The procedures can be applied to pure ARMA time series models and to determine features of the likelihood function by choosing appropriate diffuse priors.
Our results are unconditional on the initial observations. We also show how the algorithm can be further simplified for the important special cases of stationary \(\text{AR}(p)\) and invertible \(\text{MA} (q)\) models. Recursive transformations developed in this paper to diagonalize the covariance matrix of the errors should prove useful in frequentist estimation. Examples with simulated and actual economic data are presented.
Our results are unconditional on the initial observations. We also show how the algorithm can be further simplified for the important special cases of stationary \(\text{AR}(p)\) and invertible \(\text{MA} (q)\) models. Recursive transformations developed in this paper to diagonalize the covariance matrix of the errors should prove useful in frequentist estimation. Examples with simulated and actual economic data are presented.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62F15 | Bayesian inference |
Keywords:
data augmentation; full conditional distributions; ARMA(p,q) regression error models; stationary AR(p); invertible MA(q) models; recursive transformations; Gibbs sampling; Metropolis-Hastings algorithms; Markov chain sampler; ARMA time series; likelihood function; diffuse priors; frequentist estimationCitations:
Zbl 0219.65008Software:
AS 154References:
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