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Model selection in partially nonstationary vector autoregressive processes with reduced rank structure

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  • Chao, John C.
  • Phillips, Peter C. B.

Abstract

The current practice for determining the number of cointegrating vectors, or the cointegrating rank, in a vector autoregression (VAR) requires the investigator to perform a sequence of cointegration tests. However, as was shown in Johansen (1992), this type of sequential procedure does not lead to consistent estimation of the cointegrating rank. Moreover, these methods take as given the correct specification of the lag order of the VAR, though in actual applications the true lag length is rarely known, Simulation studies by Toda and Phillips (1994) and Chao (1993), on the other hand, have shown that test performance of these procedures can be adversely affected by lag misspecification. This paper addresses these issues by extending the analysis of Phillips and Ploberger (1996) on the Posterior Information Criterion (PIC) to a partially nonstationary vector autoregressive process with reduced rank structure. This extension allows lag length and cointegrating rank to be jointly selected by the criterion, and it leads to the consistent estimation of both. In addition, we also evaluate the finite sample performance of PIC relative to existing model selection procedures, BIC and AIC, through a Monte Carlo study. Results here show PIC to perform at least as well and sometimes better than the other two methods in all the cases examined.
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Suggested Citation

  • Chao, John C. & Phillips, Peter C. B., 1999. "Model selection in partially nonstationary vector autoregressive processes with reduced rank structure," Journal of Econometrics, Elsevier, vol. 91(2), pages 227-271, August.
  • Handle: RePEc:eee:econom:v:91:y:1999:i:2:p:227-271
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    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    2. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-1393, November.
    3. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
    4. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    5. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, pages 283-306.
    6. Johansen, Soren, 1992. "Determination of Cointegration Rank in the Presence of a Linear Trend," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, pages 383-397.
    7. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
    8. John F. Geweke, 1994. "Bayesian comparison of econometric models," Working Papers 532, Federal Reserve Bank of Minneapolis.
    9. Peter C.B. Phillips, 1992. "Bayes Methods for Trending Multiple Time Series with an Empirical Application to the US Economy," Cowles Foundation Discussion Papers 1025, Cowles Foundation for Research in Economics, Yale University.
    10. Peter C.B. Phillips, 1995. "Automated Forecasts of Asia-Pacific Economic Activity," Cowles Foundation Discussion Papers 1103, Cowles Foundation for Research in Economics, Yale University.
    11. Phillips, Peter C.B. & Ploberger, Werner, 1994. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Econometric Theory, Cambridge University Press, pages 774-808.
    12. Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
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    15. repec:cup:etheor:v:10:y:1994:i:3-4:p:764-73 is not listed on IDEAS
    16. Chao, John C. & Phillips, Peter C. B., 1999. "Model selection in partially nonstationary vector autoregressive processes with reduced rank structure," Journal of Econometrics, Elsevier, pages 227-271.
    17. repec:cup:etheor:v:10:y:1994:i:3-4:p:774-808 is not listed on IDEAS
    18. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    19. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
    20. Phillips, Peter C. B., 1998. "Impulse response and forecast error variance asymptotics in nonstationary VARs," Journal of Econometrics, Elsevier, pages 21-56.
    21. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
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    23. Jae-Young Kim, 1998. "Large Sample Properties of Posterior Densities, Bayesian Information Criterion and the Likelihood Principle in Nonstationary Time Series Models," Econometrica, Econometric Society, vol. 66(2), pages 359-380, March.
    24. Kim, Jae-Young, 1994. "Bayesian Asymptotic Theory in a Time Series Model with a Possible Nonstationary Process," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 764-773, August.
    25. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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