IDEAS home Printed from https://ideas.repec.org/a/oup/emjrnl/v22y2019i2p97-116..html
   My bibliography  Save this article

Testing collinearity of vector time series

Author

Listed:
  • Tucker S McElroy
  • Agnieszka Jach

Abstract

SummaryWe investigate the collinearity of vector time series in the frequency domain, by examining the rank of the spectral density matrix at a given frequency of interest. Rank reduction corresponds to collinearity at the given frequency. When the time series is nonstationary and has been differenced to stationarity, collinearity corresponds to co-integration at a particular frequency. We examine rank through the Schur complements of the spectral density matrix, testing for rank reduction via assessing the positivity of these Schur complements, which are obtained from a nonparametric estimator of the spectral density. New asymptotic results for the test statistics are derived under the fixed bandwidth ratio paradigm; they diverge under the alternative, but under the null hypothesis of collinearity the test statistics converge to a non-standard limiting distribution. Subsampling is used to obtain the limiting null quantiles. A simulation study and an empirical illustration for 6-variate time series data are provided.

Suggested Citation

  • Tucker S McElroy & Agnieszka Jach, 2019. "Testing collinearity of vector time series," The Econometrics Journal, Royal Economic Society, vol. 22(2), pages 97-116.
    • Handle: RePEc:oup:emjrnl:v:22:y:2019:i:2:p:97-116.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/ectj/uty002
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. McElroy, Tucker S. & Politis, Dimitris N., 2014. "Spectral density and spectral distribution inference for long memory time series via fixed-b asymptotics," Journal of Econometrics, Elsevier, vol. 182(1), pages 211-225.
    2. Fabio Busetti, 2006. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 419-438.
    3. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(2), pages 176-199, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. McElroy, Tucker S. & Jach, Agnieszka, 2023. "Identification of the differencing operator of a non-stationary time series via testing for zeroes in the spectral density," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    2. Tucker S. McElroy & Anindya Roy, 2022. "Model identification via total Frobenius norm of multivariate spectra," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 473-495, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fabio Busetti, 2006. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 419-438.
    2. González-Rivera, Gloria & Rodríguez Caballero, Carlos Vladimir, 2023. "Modelling intervals of minimum/maximum temperatures in the Iberian Peninsula," DES - Working Papers. Statistics and Econometrics. WS 37968, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Sauro Mocetti, 2012. "Educational choices and the selection process: before and after compulsory schooling," Education Economics, Taylor & Francis Journals, vol. 20(2), pages 189-209, February.
    4. Tommaso Proietti & Alessandra Luati, 2013. "Maximum likelihood estimation of time series models: the Kalman filter and beyond," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 15, pages 334-362, Edward Elgar Publishing.
    5. Hans Christian Kongsted, 2002. "Testing the Nominal-to-Real Transformation," Discussion Papers 02-06, University of Copenhagen. Department of Economics.
    6. repec:spo:wpecon:info:hdl:2441/2130 is not listed on IDEAS
    7. Pelagatti, Matteo M. & Sen, Pranab K., 2013. "Rank tests for short memory stationarity," Journal of Econometrics, Elsevier, vol. 172(1), pages 90-105.
    8. Giorgio Canarella & Rangan Gupta & Stephen M. Miller & Stephen K. Pollard, 2019. "Unemployment rate hysteresis and the great recession: exploring the metropolitan evidence," Empirical Economics, Springer, vol. 56(1), pages 61-79, January.
    9. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    10. Jukka Nyblom & Andrew Harvey, 2001. "Testing against smooth stochastic trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 415-429.
    11. Lorenzo Lucchese & Mikko Pakkanen & Almut Veraart, 2022. "The Short-Term Predictability of Returns in Order Book Markets: a Deep Learning Perspective," Papers 2211.13777, arXiv.org, revised Oct 2023.
    12. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    13. Qihui Chen & Zheng Fang, 2018. "Improved Inference on the Rank of a Matrix," Papers 1812.02337, arXiv.org, revised Mar 2019.
    14. Paul Beaudry & Franck Portier, 2006. "Stock Prices, News, and Economic Fluctuations," American Economic Review, American Economic Association, vol. 96(4), pages 1293-1307, September.
    15. Fabio Busetti & Silvestro di Sanzo, 2011. "Bootstrap LR tests of stationarity, common trends and cointegration," Temi di discussione (Economic working papers) 799, Bank of Italy, Economic Research and International Relations Area.
    16. Chen, Xiaoshan & MacDonald, Ronald, 2015. "Measuring the dollar–euro permanent equilibrium exchange rate using the unobserved components model," Journal of International Money and Finance, Elsevier, vol. 53(C), pages 20-35.
    17. Tucker McElroy & Michael W. McCracken, 2017. "Multistep ahead forecasting of vector time series," Econometric Reviews, Taylor & Francis Journals, vol. 36(5), pages 495-513, May.
    18. Sven Schreiber, 2012. "Estimating the natural rate of unemployment in euro-area countries with co-integrated systems," Applied Economics, Taylor & Francis Journals, vol. 44(10), pages 1315-1335, April.
    19. Busettti, F. & Harvey, A., 2007. "Tests of time-invariance," Cambridge Working Papers in Economics 0657, Faculty of Economics, University of Cambridge.
    20. Shahriyar Mukhtarov & Sugra Humbatova & Natig Gadim-Oglu Hajiyev, 2021. "Is the Transition to Renewable Energy Consumption Hampered by High Oil Prices?," International Journal of Energy Economics and Policy, Econjournals, vol. 11(5), pages 377-380.
    21. Busetti, Fabio & Taylor, A. M. Robert, 2003. "Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots," Journal of Econometrics, Elsevier, vol. 117(1), pages 21-53, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:emjrnl:v:22:y:2019:i:2:p:97-116.. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Oxford University Press (email available below). General contact details of provider: https://edirc.repec.org/data/resssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.