Multiple time series models with stochastic regressors are considered and primary attention is given to vector autoregressions (VAR's) with trending mechanisms that may be stochastic, deterministic or both. In a Bayesian framework, the data density in such a system implies the existence of a time series "Bayes model" and "Bayes measure" of the data. These are predictive models and measures for the next period observation given the historical trajectory to the present. Issues of model selection, hypothesis testing and forecast evaluation are all studied within the context of these models and the measures are used to develop selection criteria, test statistics and encompassing tests within the compass of the same statistical methodology. Of particular interest in applications are lag order and trend degree, causal effects, the presence and number of unit roots in the system, and for integrated series the presence of cointegration and the rank of the cointegration space, which can be interpreted as an order selection problem. In data where there is evidence of mildly explosive behavior we also wish to allow for the presence of co-motion among variables even though they are individually not modelled as integrated series. The paper develops a statistical framework for addressing these features of trending multiple time series and reports an extended empirical application of the methodology to a model of the US economy that sets out to explain the behavior of and to forecast interest rates, unemployment, money stock, prices and income. The performance of a data-based, evolving "Bayes model" of these series is evaluated against some rival fixed format VAR's, VAR's with Minnesota priors (BVARM's) and univariate models. The empirical results show that fixed format VAR's and BVARM's all perform poorly in forecasting exercises in comparison with evolving "Bayes models" that explicitly adapt in form as new data becomes available.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Sims, Christopher A, 1980.
"Macroeconomics and Reality,"
Econometrica,
Econometric Society, vol. 48(1), pages 1-48, January.
[Downloadable!] (restricted)
Toda, Hiro Y & Phillips, Peter C B, 1993.
"Vector Autoregressions and Causality,"
Econometrica,
Econometric Society, vol. 61(6), pages 1367-93, November.
[Downloadable!] (restricted)
Other versions:
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)