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Cointegrating Rank Selection in Models with Time-Varying Variance

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Author Info
Xu Cheng (Dept. of Economics, Yale University)
Peter C. B. Phillips () (Cowles Foundation, Yale University)

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Abstract

Reduced rank regression (RRR) models with time varying heterogeneity are considered. Standard information criteria for selecting cointegrating rank are shown to be weakly consistent in semiparametric RRR models in which the errors have general nonparametric short memory components and shifting volatility provided the penalty coefficient C_{n}-> infinity and C_{n}/n -> 0 as n -> infinity. The AIC criterion is inconsistent and its limit distribution is given. The results extend those in Cheng and Phillips (2008) and are useful in empirical work where structural breaks or time evolution in the error variances is present. An empirical application to exchange rate data is provided.

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File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1688.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1688.

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Length: 27 pages
Date of creation: Jan 2009
Date of revision:
Handle: RePEc:cwl:cwldpp:1688

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Related research
Keywords: Cointegrating rank; Consistency; Heterogeneity; Information criteria; Model selection; Nonparametric; Time varying variances; Unit roots;

Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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  1. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  2. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December. [Downloadable!] (restricted)
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  3. Phillips, Peter C. B. & McFarland, James W., 1997. "Forward exchange market unbiasedness: the case of the Australian dollar since 1984," Journal of International Money and Finance, Elsevier, vol. 16(6), pages 885-907, December. [Downloadable!] (restricted)
    Other versions:
  4. Diebold, Francis X & Gardeazabal, Javier & Yilmaz, Kamil, 1994. " On Cointegration and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 727-35, June. [Downloadable!] (restricted)
    Other versions:
  5. Peter C.B. Phillips, 2008. "Unit Root Model Selection," Cowles Foundation Discussion Papers 1653, Cowles Foundation, Yale University. [Downloadable!]
  6. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July. [Downloadable!] (restricted)
  7. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March. [Downloadable!] (restricted)
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  8. Peter C. B. Phillips & Ke-Li Xu, 2006. "Inference in Autoregression under Heteroskedasticity," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(2), pages 289-308, 03. [Downloadable!] (restricted)
  9. Mark W. Watson, 1999. "Explaining the increased variability in long-term interest rates," Economic Quarterly, Federal Reserve Bank of Richmond, issue Fall, pages 71-96. [Downloadable!]
  10. Baillie, Richard T & Bollerslev, Tim, 1989. " Common Stochastic Trends in a System of Exchange Rates," Journal of Finance, American Finance Association, vol. 44(1), pages 167-81, March. [Downloadable!] (restricted)
  11. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January. [Downloadable!] (restricted)
  12. Nielsen M.O., 2004. "Optimal Residual-Based Tests for Fractional Cointegration and Exchange Rate Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 331-345, July. [Downloadable!] (restricted)
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  13. Uwe Hassler & Francesc Marmol & Carlos Velasco, 2002. "Residual Log-Periodogram Inference for Long-Run Relationships," Darmstadt Discussion Papers in Economics 115, Institut für Volkswirtschaftslehre (Department of Economics), Technische Universität Darmstadt (Darmstadt University of Technology). [Downloadable!]
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  14. Xu Cheng & Peter C.B. Phillips, 2008. "Semiparametric Cointegrating Rank Selection," Cowles Foundation Discussion Papers 1658, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  15. Baillie, Richard T & Bollerslev, Tim, 1994. " Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-45, June. [Downloadable!] (restricted)
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  16. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-78, September. [Downloadable!] (restricted)
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  17. Hamori, Shigeyuki & Tokihisa, Akira, 1997. "Testing for a unit root in the presence of a variance shift1," Economics Letters, Elsevier, vol. 57(3), pages 245-253, December. [Downloadable!] (restricted)
  18. 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. [Downloadable!] (restricted)
  19. 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)
  20. 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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