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Model Selection in Partially Nonstationary Vector Autoregressive Processes with Reduced Rank Structure

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Author Info
John C. Chao (University of Maryland)
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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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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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1155.

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Length: 47 pages
Date of creation: Jul 1997
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Publication status: Published in Journal of Econometrics, 91, 1999
Handle: RePEc:cwl:cwldpp:1155

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Cointegrating rank; information criterion; order selection; PIC; reduced rank regression; vector autoregression;

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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.:

  1. Phillips, Peter C.B. & Ploberger, Werner, 1994. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 774-808, August. [Downloadable!]
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  2. repec:cup:etheor:v:10:y:1994:i:3-4:p:764-73 is not listed on IDEAS
  3. 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:
  4. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November. [Downloadable!] (restricted)
  5. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation, Yale University, revised Feb 1987. [Downloadable!]
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  6. repec:cup:etheor:v:10:y:1994:i:3-4:p:774-808 is not listed on IDEAS
  7. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March. [Downloadable!] (restricted)
  8. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December. [Downloadable!] (restricted)
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  9. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July. [Downloadable!] (restricted)
  10. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation, Yale University. [Downloadable!]
  11. Johansen, S., 1991. "Determination of Cointegration Rank in the Presence of a Linear Trend," Papers 76a, Helsinki - Department of Economics.
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  12. 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. [Downloadable!] (restricted)
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  13. John F. Geweke, 1994. "Bayesian comparison of econometric models," Working Papers 532, Federal Reserve Bank of Minneapolis.
  14. 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, Yale University. [Downloadable!]
  15. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November. [Downloadable!] (restricted)
  16. 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. [Downloadable!]
  17. 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. [Downloadable!] (restricted)
  18. Phillips, Peter C. B., 1995. "Bayesian prediction a response," Journal of Econometrics, Elsevier, vol. 69(1), pages 351-365, September. [Downloadable!] (restricted)
  19. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)
Full references

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.)

  1. George Athanasopoulos & Osmani T. de C. Guillén & João V. Issler & Farshid Vahid, 2009. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Monash Econometrics and Business Statistics Working Papers 2/09, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
    Other versions:
  2. Alfred A. Haug & Pierre L. Siklos, 2002. "The Term Spread International Evidence of Non-Linear Adjustment," Working Papers 2002_08, York University, Department of Economics, revised Jul 2004. [Downloadable!]
  3. Peter C.B. Phillips, 1994. "Nonstationary Time Series and Cointegration: Recent Books and Themes for the Future," Cowles Foundation Discussion Papers 1081, Cowles Foundation, Yale University. [Downloadable!]
  4. Alfred A. Haug & Julie Tam, 2001. "A Closer Look at Long Run Money Demand," Working Papers 2002_09, York University, Department of Economics, revised Sep 2002. [Downloadable!]
  5. Neri, Marcelo Cortes & Soares, Wagner Lopes, 2008. "Turismo sustentável e alivio a pobreza: avaliação de impacto," Economics Working Papers (Ensaios Economicos da EPGE) 689, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
  6. Dietmar Maringer & Peter Winker, 2004. "Optimal Lag Structure Selection in VEC-Models," Computing in Economics and Finance 2004 155, Society for Computational Economics. [Downloadable!]
  7. Aaron F. Schiff & Peter C.B. Phillips, 2000. "Forecasting New Zealand's Real GDP," Cowles Foundation Discussion Papers 1278, Cowles Foundation, Yale University. [Downloadable!]
  8. Kelvin Balcombe, 2005. "Model Selection Using Information Criteria and Genetic Algorithms," Computational Economics, Springer, vol. 25(3), pages 207-228, June. [Downloadable!] (restricted)
  9. Zhongjun Qu & Pierre Perron, 2006. "A Modified Information Criterion for Cointegration Tests based on a VAR Approximation," Boston University - Department of Economics - Working Papers Series WP2006-011, Boston University - Department of Economics. [Downloadable!]
    Other versions:
  10. Mau-Ting Lin, 2004. "Measuring the effect of money: test, estimation and identification," Money Macro and Finance (MMF) Research Group Conference 2003 53, Money Macro and Finance Research Group. [Downloadable!]
  11. Badi H. Baltagi & Zijun Wang, 2006. "Testing for Cointegrating Rank via Model Selection: Evidence from 165 Data Sets," Center for Policy Research Working Papers 83, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
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  12. Peter C.B. Phillips, 1995. "Impulse Response and Forecast Error Variance Asymptotics in Nonstationary VAR's," Cowles Foundation Discussion Papers 1102, Cowles Foundation, Yale University. [Downloadable!]
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  13. Hagerman, Amy & Jin, Yanhong, 2009. "The Buzz In The Pits: Livestock Futures' Response To A Rumor Of Foreign Animal Disease," 2009 Annual Meeting, July 26-28, 2009, Milwaukee, Wisconsin 49493, Agricultural and Applied Economics Association. [Downloadable!]
  14. Peter C.B. Phillips, 2003. "Laws and Limits of Econometrics," Cowles Foundation Discussion Papers 1397, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  15. Mototsugu Shintani, 2000. "A Simple Cointegrating Rank Test Without Vector Autoregression," Working Papers 0044, Department of Economics, Vanderbilt University. [Downloadable!]
    Other versions:
  16. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
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