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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.

Suggested Citation

  • Xu Cheng & Peter C.B. Phillips, 2008. "Semiparametric Cointegrating Rank Selection," Cowles Foundation Discussion Papers 1658, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1658
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    References listed on IDEAS

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    1. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    2. Peter C.B. Phillips, 2008. "Unit Root Model Selection," Cowles Foundation Discussion Papers 1653, Cowles Foundation for Research in Economics, Yale University.
    3. Giuseppe Cavaliere, 2005. "Unit Root Tests under Time-Varying Variances," Econometric Reviews, Taylor & Francis Journals, vol. 23(3), pages 259-292.
    4. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    5. 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.
    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(3), 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. 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.
    9. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    10. 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.
    11. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    12. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
    13. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, 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(4), pages 735-742, August.
    15. Bent Nielsen, 2001. "Order determination in general vector autoregressions," Economics Papers 2001-W10, Economics Group, Nuffield College, University of Oxford.
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    Cited by:

    1. Tu, Yundong & Yi, Yanping, 2017. "Forecasting cointegrated nonstationary time series with time-varying variance," Journal of Econometrics, Elsevier, vol. 196(1), pages 83-98.
    2. Beare, Brendan K. & Seo, Won-Ki, 2020. "Representation Of I(1) And I(2) Autoregressive Hilbertian Processes," Econometric Theory, Cambridge University Press, vol. 36(5), pages 773-802, October.
    3. Liao, Zhipeng & Phillips, Peter C. B., 2015. "Automated Estimation Of Vector Error Correction Models," Econometric Theory, Cambridge University Press, vol. 31(3), pages 581-646, June.
    4. Cheng, Xu & Phillips, Peter C.B., 2012. "Cointegrating rank selection in models with time-varying variance," Journal of Econometrics, Elsevier, vol. 169(2), pages 155-165.
    5. Banerjee, Anindya & Marcellino, Massimiliano & Masten, Igor, 2014. "Forecasting with factor-augmented error correction models," International Journal of Forecasting, Elsevier, vol. 30(3), pages 589-612.
    6. Peter C. B. Phillips & Ji Hyung Lee, 2015. "Limit Theory for VARs with Mixed Roots Near Unity," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 1035-1056, December.
    7. Seong, Byeongchan, 2013. "Semiparametric selection of seasonal cointegrating ranks using information criteria," Economics Letters, Elsevier, vol. 120(3), pages 592-595.
    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.
    9. Anindya Banerjee & Massimiliano Marcellino & Igor Masten, 2016. "An Overview of the Factor-augmented Error-Correction Model," Advances in Econometrics, in: Eric Hillebrand & Siem Jan Koopman (ed.), Dynamic Factor Models, volume 35, pages 3-41, Emerald Publishing Ltd.
    10. Sabzikar, Farzad & Wang, Qiying & Phillips, Peter C.B., 2020. "Asymptotic theory for near integrated processes driven by tempered linear processes," Journal of Econometrics, Elsevier, vol. 216(1), pages 192-202.
    11. Miller, J. Isaac & Ratti, Ronald A., 2009. "Crude oil and stock markets: Stability, instability, and bubbles," Energy Economics, Elsevier, vol. 31(4), pages 559-568, July.
    12. Li, Degui & Phillips, Peter C.B. & Gao, Jiti, 2020. "Kernel-based Inference in Time-Varying Coefficient Cointegrating Regression," Journal of Econometrics, Elsevier, vol. 215(2), pages 607-632.
    13. Marçal, Emerson Fernandes & Zimmermann, Beatrice Aline & Mendonça, Diogo de Prince & Merlin, Giovanni Tondin, 2015. "Addressing important econometric issues on how to construct theoretical based exchange rate misalignment estimates," Textos para discussão 401, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    14. 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.
    15. Anindya Banerjee & Massimiliano Marcellino & Igor Masten, 2010. "Forecasting with Factor-augmented Error Correction," Discussion Papers 09-06r, Department of Economics, University of Birmingham.
    16. Lenard Lieb & Stephan Smeekes, 2017. "Inference for Impulse Responses under Model Uncertainty," Papers 1709.09583, arXiv.org, revised Oct 2019.

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    More about this item

    Keywords

    Cointegrating rank; Consistency; Information criteria; Model selection; Nonparametric; Short memory; Unit roots;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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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