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Semiparametric Cointegrating Rank Selection

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Abstract

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

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Keywords: Cointegrating rank; Consistency; Information criteria; Model selection; Nonparametric; Short memory; Unit roots;

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  1. 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.
  2. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, Econometric Society, vol. 66(6), pages 1299-1326, November.
  3. Jushan Bai & Serena Ng, 2001. "A Panic Attack on Unit Roots and Cointegration," Economics Working Paper Archive 469, The Johns Hopkins University,Department of Economics.
  4. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  5. 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.
  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. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1023-78, September.
  8. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, Econometric Society, vol. 64(4), pages 763-812, July.
  9. Bent Nielsen, 2001. "Order determination in general vector autoregressions," Economics Papers 2001-W10, Economics Group, Nuffield College, University of Oxford.
  10. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198774501, October.
  11. Peter C.B. Phillips, 2008. "Unit Root Model Selection," Cowles Foundation Discussion Papers 1653, Cowles Foundation for Research in Economics, Yale University.
  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 & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, Econometric Society, vol. 64(2), pages 381-412, March.
  14. 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.
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Cited by:
  1. J. Isaac Miller & Ronald Ratti, 2008. "Crude Oil and Stock Markets: Stability, Instability, and Bubbles," Working Papers, Department of Economics, University of Missouri 0810, Department of Economics, University of Missouri, revised 20 Jan 2009.
  2. Igor Masten & Massimiliano Marcellino & Anindya Banerjeey, 2009. "Forecasting with Factor-augmented Error Correction Models," RSCAS Working Papers 2009/32, European University Institute.
  3. Seong, Byeongchan, 2013. "Semiparametric selection of seasonal cointegrating ranks using information criteria," Economics Letters, Elsevier, vol. 120(3), pages 592-595.
  4. Zhipeng Liao & Peter C.B. Phillips, 2012. "Automated Estimation of Vector Error Correction Models," Cowles Foundation Discussion Papers 1873, Cowles Foundation for Research in Economics, Yale University.
  5. Peter C.B. Phillips & Zhipeng Liao, 2012. "Series Estimation of Stochastic Processes: Recent Developments and Econometric Applications," Cowles Foundation Discussion Papers 1871, Cowles Foundation for Research in Economics, Yale University.
  6. Xu Cheng & Peter C. B. Phillips, 2009. "Cointegrating Rank Selection in Models with Time-Varying Variance," Cowles Foundation Discussion Papers 1688, Cowles Foundation for Research in Economics, Yale University.
  7. Anindya Banerjee & Massimiliano Marcellino & Igor Masten, 2010. "Forecasting with Factor-augmented Error Correction," Discussion Papers, Department of Economics, University of Birmingham 09-06r, Department of Economics, University of Birmingham.
  8. Peter C.B. Phillips & Ji Hyung Lee, 2012. "VARs with Mixed Roots Near Unity," Cowles Foundation Discussion Papers 1845, Cowles Foundation for Research in Economics, Yale University.

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