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An Empirical Bayesian Approach to Cointegrating Rank Selection and Test of the Present Value Model for Stock Prices

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Modelling and Prediction Honoring Seymour Geisser

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Abstract

This paper provides an empirical Bayesian approach to the problem of jointly estimating the lag order and the cointegrating rank of a partially non-stationary reduced rank regression. The method employed is a variant of the Posterior Information Criterion (PIC) of Phillips and Ploberger (1994, 1995) and is similar to the asymptotic predictive odds version of the PIC criterion given in Phillips (1994). Here, we use a proper (Gaussian) prior whose hyperparameters are estimated from an initial subsample of the data. The form of the prior is suggested by the asymptotic posterior distribution of the parameters of the model, and, hence, the criterion can be interpreted as an approximate predictive odds ratio in the case where the sample size is large. Applying this procedure to the extended Campbell-Shiller data set for stock prices and dividends, we find the present value model for stock prices to be inconsistent with the data.

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Author information

Authors and Affiliations

  1. Department of Economics, University of Maryland, Maryland, College Park, 20742, USA

    John C. Chao

  2. Cowles Foundation for Research in Economics, Yale University, P.O. Box 208281, New Haven, Connecticut, 06520-8281, USA

    Peter C. B. Phillips

Authors
  1. John C. Chao
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  2. Peter C. B. Phillips
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Editor information

Editors and Affiliations

  1. Institute of Statistics, National Chiao Tung University, 1001 Ta-Hseuh Road, Hsichu, Taiwan R.O.C

    Jack C. Lee

  2. Department of Statistics, University of California, Davis, 95616, Davis, CA, USA

    Wesley O. Johnson

  3. Graduate School of Business, University of Chicago, 1101 East 58th Street, 60637, Chicago, IL, USA

    Arnold Zellner

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© 1996 Springer Science+Business Media New York

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Chao, J.C., Phillips, P.C.B. (1996). An Empirical Bayesian Approach to Cointegrating Rank Selection and Test of the Present Value Model for Stock Prices. In: Lee, J.C., Johnson, W.O., Zellner, A. (eds) Modelling and Prediction Honoring Seymour Geisser. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2414-3_21

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  • DOI: https://doi.org/10.1007/978-1-4612-2414-3_21

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7529-9

  • Online ISBN: 978-1-4612-2414-3

  • eBook Packages: Springer Book Archive

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