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A Modified Information Criterion for Cointegration Tests based on a VAR Approximation

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Author Info
Zhongjun Qu () (Department of Economics, University of Illinois at Urbana-Champaign)
Pierre Perron () (Department of Economics, Boston University)

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Abstract

We consider Johansen’s (1988, 1991) cointegration tests when a Vector AutoRegressive (VAR) process of order k is used to approximate a more general linear process with an infinite VAR representation. In this case, and in particular when a moving average component is present, traditional methods to select the lag order, such as Akaike’s (AIC) or the Bayesian information criteria, lead to too parsimonious a model, with the implication that the cointegration tests suffer from substantial size distortions in finite samples. We extend the analysis of Ng and Perron (2001) to derive a Modified Akaike’s Information Criterion (MAIC) in this multivariate setting. The idea is to use the information specified by the null hypothesis as it relates to restrictions on the parameters of the model to keep an extra term in the penalty function of the AIC. This MAIC takes a very simple form for which this extra term is simply the likelihood ratio test for testing the null hypothesis of r against more than r cointegrating vectors. We provide theoretical analyses of its validity and of the fact that cointegration tests constructed from a VAR whose lag order is selected using the MAIC have the same limit distribution as when the order is finite and known. We also provide theoretical and simulation analyses to show how the MAIC leads to VAR approximations that yield tests with drastically improved size properties with little loss of power.

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Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2006-011.

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Length: 50pages
Date of creation: Feb 2006
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Handle: RePEc:bos:wpaper:wp2006-011

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  1. Serena Ng & Pierre Perron, 2005. "A Note on the Selection of Time Series Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(1), pages 115-134, 02. [Downloadable!] (restricted)
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  2. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  3. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November. [Downloadable!] (restricted)
  4. 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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  5. Kuersteiner, Guido M., 2005. "Automatic Inference For Infinite Order Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 21(01), pages 85-115, February. [Downloadable!]
  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. Perron, Pierre & Campbell, John Y, 1993. "A Note on Johansen's Cointegration Procedure When Trends Are Present," Empirical Economics, Springer, vol. 18(4), pages 777-89.
  9. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May. [Downloadable!] (restricted)
  10. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July. [Downloadable!] (restricted)
  11. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor and Francis Journals, vol. 21(4), pages 431-447. [Downloadable!] (restricted)
  12. Perron, Pierre & Ng, Serena, 1996. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Review of Economic Studies, Blackwell Publishing, vol. 63(3), pages 435-63, July. [Downloadable!] (restricted)
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  13. Cheung, Yin-Wong & Lai, Kon S, 1993. "Finite-Sample Sizes of Johansen's Likelihood Ration Tests for Conintegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(3), pages 313-28, August.
  14. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November. [Downloadable!] (restricted)
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  15. Lutkepohl, Helmut & Saikkonen, Pentti, 1997. "Impulse response analysis in infinite order cointegrated vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 127-157, November. [Downloadable!] (restricted)
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  16. Nabeya, Seiji & Perron, Pierre, 1994. "Local asymptotic distribution related to the AR(1) model with dependent errors," Journal of Econometrics, Elsevier, vol. 62(2), pages 229-264, June. [Downloadable!] (restricted)
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  17. Cavanaugh, Joseph E., 1997. "Unifying the derivations for the Akaike and corrected Akaike information criteria," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 201-208, April. [Downloadable!] (restricted)
  18. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February. [Downloadable!]
  19. 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. [Downloadable!] (restricted)
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  20. 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)
  21. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June. [Downloadable!] (restricted)
  22. repec:cup:etheor:v:8:y:1992:i:1:p:1-27 is not listed on IDEAS
  23. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254. [Downloadable!] (restricted)
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