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Identifying Cointegration by Eigenanalysis

Author

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  • Rongmao Zhang
  • Peter Robinson
  • Qiwei Yao

Abstract

We propose a new and easy-to-use method for identifying cointegrated components of nonstationary time series, consisting of an eigenanalysis for a certain nonnegative definite matrix. Our setting is model-free, and we allow the integer-valued integration orders of the observable series to be unknown, and to possibly differ. Consistency of estimates of the cointegration space and cointegration rank is established both when the dimension of the observable time series is fixed as sample size increases, and when it diverges slowly. The proposed methodology is also extended and justified in a fractional setting. A Monte Carlo study of finite-sample performance, and a small empirical illustration, are reported. Supplementary materials for this article are available online.

Suggested Citation

  • Rongmao Zhang & Peter Robinson & Qiwei Yao, 2019. "Identifying Cointegration by Eigenanalysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 916-927, April.
    • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:526:p:916-927
    DOI: 10.1080/01621459.2018.1458620
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    Cited by:

    1. Gianluca Cubadda & Marco Mazzali, 2024. "The vector error correction index model: representation, estimation and identification," The Econometrics Journal, Royal Economic Society, vol. 27(1), pages 126-150.
    2. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "A comparison of semiparametric tests for fractional cointegration," Statistical Papers, Springer, vol. 62(4), pages 1997-2030, August.
    3. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    4. Gianluca Cubadda & Alain Hecq, 2022. "Dimension Reduction for High‐Dimensional Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1123-1152, October.
    5. Alain Hecq & Luca Margaritella & Stephan Smeekes, 2023. "Inference in Non-stationary High-Dimensional VARs," Papers 2302.01434, arXiv.org, revised Sep 2023.
    6. Fan, Rui & Lee, Ji Hyung & Shin, Youngki, 2023. "Predictive quantile regression with mixed roots and increasing dimensions: The ALQR approach," Journal of Econometrics, Elsevier, vol. 237(2).
    7. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," LSE Research Online Documents on Economics 103830, London School of Economics and Political Science, LSE Library.
    8. Ziwei Mei & Zhentao Shi, 2022. "On LASSO for High Dimensional Predictive Regression," Papers 2212.07052, arXiv.org, revised Jan 2024.
    9. Morten {O}rregaard Nielsen & Won-Ki Seo & Dakyung Seong, 2023. "Inference on common trends in functional time series," Papers 2312.00590, arXiv.org, revised May 2024.
    10. Nielsen, Morten Ørregaard & Seo, Won-Ki & Seong, Dakyung, 2023. "Inference On The Dimension Of The Nonstationary Subspace In Functional Time Series," Econometric Theory, Cambridge University Press, vol. 39(3), pages 443-480, June.
    11. Gianluca Cubadda & Alain Hecq, 2020. "Dimension Reduction for High Dimensional Vector Autoregressive Models," Papers 2009.03361, arXiv.org, revised Feb 2022.
    12. Gao, Zhaoxing & Tsay, Ruey S., 2021. "Modeling high-dimensional unit-root time series," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1535-1555.
    13. Zhaoxing Gao & Ruey S. Tsay, 2020. "Modeling High-Dimensional Unit-Root Time Series," Papers 2005.03496, arXiv.org, revised Aug 2020.
    14. Saidat Fehintola Olaniran & Oyebayo Ridwan Olaniran & Jeza Allohibi & Abdulmajeed Atiah Alharbi & Mohd Tahir Ismail, 2024. "A Generalized Residual-Based Test for Fractional Cointegration in Panel Data with Fixed Effects," Mathematics, MDPI, vol. 12(8), pages 1-11, April.
    15. Mei, Ziwei & Shi, Zhentao, 2024. "On LASSO for high dimensional predictive regression," Journal of Econometrics, Elsevier, vol. 242(2).
    16. Zhan Gao & Ji Hyung Lee & Ziwei Mei & Zhentao Shi, 2024. "Econometric Inference for High Dimensional Predictive Regressions," Papers 2409.10030, arXiv.org, revised Nov 2024.
    17. Smeekes, Stephan & Wijler, Etienne, 2021. "An automated approach towards sparse single-equation cointegration modelling," Journal of Econometrics, Elsevier, vol. 221(1), pages 247-276.
    18. Patrice Abry & B. Cooper Boniece & Gustavo Didier & Herwig Wendt, 2023. "Wavelet eigenvalue regression in high dimensions," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 1-32, April.
    19. Esther Ruiz & Pilar Poncela, 2022. "Factor Extraction in Dynamic Factor Models: Kalman Filter Versus Principal Components," Foundations and Trends(R) in Econometrics, now publishers, vol. 12(2), pages 121-231, November.
    20. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    21. Massimo Franchi & Iliyan Georgiev & Paolo Paruolo, 2024. "Canonical correlation analysis of stochastic trends via functional approximation," Papers 2411.19572, arXiv.org.

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