### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 596-608 |

Number of pages | 13 |

Journal | Econometric Theory |

Volume | 10 |

Issue number | 3-4 |

DOIs | |

State | Published - 1994 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Social Sciences (miscellaneous)
- Economics and Econometrics

### Cite this

*Econometric Theory*,

*10*(3-4), 596-608. https://doi.org/10.1017/S0266466600008689

**Bayesian inference of trend and difference-stationarity.** / McCulloch, Robert; Tsay, Ruey S.

Research output: Contribution to journal › Article

*Econometric Theory*, vol. 10, no. 3-4, pp. 596-608. https://doi.org/10.1017/S0266466600008689

}

TY - JOUR

T1 - Bayesian inference of trend and difference-stationarity

AU - McCulloch, Robert

AU - Tsay, Ruey S.

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21844527319&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844527319&partnerID=8YFLogxK

U2 - 10.1017/S0266466600008689

DO - 10.1017/S0266466600008689

M3 - Article

AN - SCOPUS:21844527319

VL - 10

SP - 596

EP - 608

JO - Econometric Theory

JF - Econometric Theory

SN - 0266-4666

IS - 3-4

ER -