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Extreme canonical correlations and high-dimensional cointegration analysis

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  • Onatski, Alexei
  • Wang, Chen

Abstract

We prove that the extreme squared sample canonical correlations between a random walk and its own innovations almost surely converge to the upper and lower boundaries of the support of the Wachter distribution when the sample size and the dimensionality go to infinity proportionally. This result is used to derive previously unknown analytic expressions for the Bartlett-type correction coefficients for Johansen’s trace and maximum eigenvalue tests in a high-dimensional VAR(1). An analysis of cointegration among a large number of log exchange rates illustrates the usefulness of our theoretical results.

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  • Onatski, Alexei & Wang, Chen, 2019. "Extreme canonical correlations and high-dimensional cointegration analysis," Journal of Econometrics, Elsevier, vol. 212(1), pages 307-322.
    • Handle: RePEc:eee:econom:v:212:y:2019:i:1:p:307-322
    DOI: 10.1016/j.jeconom.2019.04.032
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    1. MacKinnon, James G & Haug, Alfred A & Michelis, Leo, 1999. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 563-577, Sept.-Oct.
    2. George C. Davis, 2003. "The Generalized Composite Commodity Theorem: Stronger Support in the Presence of Data Limitations," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 476-480, May.
    3. Lewbel, Arthur, 1996. "Aggregation without Separability: A Generalized Composite Commodity Theorem," American Economic Review, American Economic Association, vol. 86(3), pages 524-543, June.
    4. Anindya Banerjee & Massimiliano Marcellino & Igor Masten, 2017. "Structural FECM: Cointegration in large‐scale structural FAVAR models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1069-1086, September.
    5. Anindya Banerjee & Massimiliano Marcellino & Chiara Osbat, 2004. "Some cautions on the use of panel methods for integrated series of macroeconomic data," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 322-340, December.
    6. Rolf Larsson, 1998. "Bartlett Corrections for Unit Root Test Statistics," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(4), pages 425-438, July.
    7. GONZALO, Jesus & PITARAKIS, Jean-Yves, 1994. "Comovements in Large Systems," LIDAM Discussion Papers CORE 1994065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Charles Engel & Nelson C. Mark & Kenneth D. West, 2015. "Factor Model Forecasts of Exchange Rates," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 32-55, February.
    9. Pedroni, Peter L. & Vogelsang, Timothy J. & Wagner, Martin & Westerlund, Joakim, 2015. "Nonparametric rank tests for non-stationary panels," Journal of Econometrics, Elsevier, vol. 185(2), pages 378-391.
    10. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    11. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, Decembrie.
    12. Alexei Onatski & Chen Wang, 2018. "Alternative Asymptotics for Cointegration Tests in Large VARs," Econometrica, Econometric Society, vol. 86(4), pages 1465-1478, July.
    13. 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.
    14. Jensen, J. L. & Wood, Andrew T. A., 1997. "On the non-existence of a Bartlett correction for unit root tests," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 181-187, September.
    15. Soren Johansen, 2002. "A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model," Econometrica, Econometric Society, vol. 70(5), pages 1929-1961, September.
    16. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
    17. Diebold, Francis X & Gardeazabal, Javier & Yilmaz, Kamil, 1994. "On Cointegration and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 727-735, June.
    18. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    19. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    20. Ho, Mun S & Sorensen, Bent E, 1996. "Finding Cointegration Rank in High Dimensional Systems Using the Johansen Test: An Illustration Using Data Based Monte Carlo Simulations," The Review of Economics and Statistics, MIT Press, vol. 78(4), pages 726-732, November.
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    Cited by:

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    3. Gonzalo, Jesús & Pitarakis, Jean-Yves, 2021. "Spurious relationships in high-dimensional systems with strong or mild persistence," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1480-1497.
    4. Feng, Zongbao & Chen, Weiya & Liu, Yang & Chen, Hongyu & Skibniewski, Mirosław J., 2023. "Long-term equilibrium relationship analysis and energy-saving measures of metro energy consumption and its influencing factors based on cointegration theory and an ARDL model," Energy, Elsevier, vol. 263(PD).
    5. Anna Bykhovskaya & Vadim Gorin, 2022. "Asymptotics of Cointegration Tests for High-Dimensional VAR($k$)," Papers 2202.07150, arXiv.org, revised Nov 2023.
    6. Anna Bykhovskaya & Vadim Gorin, 2020. "Cointegration in large VARs," Papers 2006.14179, arXiv.org, revised Dec 2021.

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    More about this item

    Keywords

    High-dimensional cointegration; Extreme canonical correlations; Trace statistic; Maximum eigenvalue statistic; Bartlett correction;
    All these keywords.

    JEL classification:

    • 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
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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