Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-07T06:29:13.117Z Has data issue: false hasContentIssue false
  • English
  • Français

Bayesian Inference of Trend and Difference-Stationarity

Published online by Cambridge University Press:  11 February 2009

Robert E. McCulloch  and
Ruey S. Tsay
Robert E. McCulloch
Affiliation:
University of Chicago
Ruey S. Tsay
Affiliation:
University of Chicago
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes a general Bayesian framework for distinguishing between trend- and difference-stationarity. Usually, in model selection, we assume that all of the data were generated by one of the models under consideration. In studying time series, however, we may be concerned that the process is changing over time, so that the preferred model changes over time as well. To handle this possibility, we compute the posterior probabilities of the competing models for each observation. This way we can see if different segments of the series behave differently with respect to the competing models. The proposed method is a generalization of the usual odds ratio for model discrimination in Bayesian inference. In application, we employ the Gibbs sampler to overcome the computational difficulty. The procedure is illustrated by a real example.

Type
Articles
Information
Econometric Theory , Volume 10 , Issue 3-4 , August 1994 , pp. 596 - 608
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCE

1.Albert, J. & Chib, S.. Bayesian inference of autoregressive time series with mean and variance subject to Markov jumps. Journal of Business and Economic Statistics 11 (1993): 1–15.CrossRefGoogle Scholar
2.Carlin, B., Gelfand, A. & Smith, A.F.M.. Hierarchical Bayesian analysis of change point problems. Applied Statistics 41 (1992): 389–405.CrossRefGoogle Scholar
3.DeJong, D.N., Nankervis, J.C., Savin, N.E. & Whiteman, C.H.. Integration versus trend stationarity in time series. Econometrica 60 (1992): 423–433.CrossRefGoogle Scholar
4.Dickey, D.A. & Fuller, W.A.. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74 (1979): 427–431.Google Scholar
5.Fuller, W.A.Introduction to Statistical Time Series. New York: Wiley, 1976.Google Scholar
6.Gelfand, A.E., Hills, S.E., Racine-Poon, A. & Smith, A.F.M.. Illustration of Bayesian inference in normal data models using Gibbs sampling. Journal of the American Statistical Association 85 (1990): 972–985.CrossRefGoogle Scholar
7.Geman, S. & Geman, D.. Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transaction on Pattern Analysis and Machine Intelligence 6 (1984): 721–741.CrossRefGoogle ScholarPubMed
8.Hamilton, J.D.A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57 (1989): 357–384.CrossRefGoogle Scholar
9.Hamilton, J.D.Analysis of time series subject to changes in regime. Journal of Economics 45 (1990): 39–70.CrossRefGoogle Scholar
10.McCulloch, R.E. & Tsay, R.S.. Statistical inference of macroeconomic time series via Markov switching models. Technical report, University of Chicago, 1992.Google Scholar
11.Perron, P.Testing for a unit root with a changing mean. Journal of Business and Economic Statistics 8 (1990): 153–162.CrossRefGoogle Scholar
12.Phillips, P.C.B.Time series regression with unit roots. Econometrica 55 (1987): 277–302.CrossRefGoogle Scholar
13.Phillips, P.C.B.Bayes methods for trending multiple time series with an empirical application to the US economyPaper presented at the Joint Statistical Meetings in BostonMA1992.Google Scholar
14.Phillips, P.C.B. & Ploberger, W.. Posterior odds testing for a unit root with data-based model selection. Econometric Theory 10 (1994): 774–808.CrossRefGoogle Scholar
15.Tierney, L.Markov chains for exploring posterior distributions. Annals of Statistics, forthcoming.Google Scholar
16.Tsay, R.S.Testing for non-invertible models with applications. Journal of Business and Economics Statistics 11 (1993): 225–233.Google Scholar