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Semiparametric Cointegrating Rank Selection

Some convenient limit properties of usual information criteria are given for cointegrating rank selection. Allowing for a nonparametric short memory component and using a reduced rank regression with only a single lag, standard information criteria are shown to be weakly consistent in the choice of cointegrating rank provided the penalty coefficient C_n -> infinity and C_n/n -> 0 as n -> infinity. The limit distribution of the AIC criterion, which is inconsistent, is also obtained. The analysis provides a general limit theory for semiparametric reduced rank regression under weakly dependent errors. The method does not require the specification of a full model, is convenient for practical implementation in empirical work, and is sympathetic with semiparametric estimation approaches to cointegration analysis. Some simulations results on finite sample performance of the criterion are reported.

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File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1658.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1658.

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Length: 23 pages
Date of creation: May 2008
Date of revision:
Publication status: Published in Econometrics Journal (2009), 12: S83-S104
Handle: RePEc:cwl:cwldpp:1658
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Web page: http://cowles.econ.yale.edu/

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

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  1. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  2. 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.
  3. Peter C.B. Phillips, 2008. "Unit Root Model Selection," Cowles Foundation Discussion Papers 1653, Cowles Foundation for Research in Economics, Yale University.
  4. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation for Research in Economics, Yale University.
  5. Bent Nielsen, 2001. "Order determination in general vector autoregressions," Economics Papers 2001-W10, Economics Group, Nuffield College, University of Oxford.
  6. Wang, Zijun & Bessler, David A., 2005. "A Monte Carlo Study On The Selection Of Cointegrating Rank Using Information Criteria," Econometric Theory, Cambridge University Press, vol. 21(03), pages 593-620, June.
  7. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  8. John C. Chao & Peter C.B. Phillips, 1997. "Model Selection in Partially Nonstationary Vector Autoregressive Processes with Reduced Rank Structure," Cowles Foundation Discussion Papers 1155, Cowles Foundation for Research in Economics, Yale University.
  9. Kapetanios, George, 2004. "The Asymptotic Distribution Of The Cointegration Rank Estimator Under The Akaike Information Criterion," Econometric Theory, Cambridge University Press, vol. 20(04), pages 735-742, August.
  10. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, 07.
  11. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
  12. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  13. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
  14. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
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