IDEAS home Printed from https://ideas.repec.org/a/taf/jnlbes/v33y2015i4p459-473.html
   My bibliography  Save this article

Cross-Correlation Matrices for Tests of Independence and Causality Between Two Multivariate Time Series

Author

Listed:
  • Michael W. Robbins
  • Thomas J. Fisher

Abstract

An often-studied problem in time series analysis is that of testing for the independence of two (potentially multivariate) time series. Toeplitz matrices have demonstrated utility for the related setting of time series goodness-of-fit testing--ergo, herein, we extend those concepts by defining a nontrivial block Toeplitz matrix for use in the setting of independence testing. We propose test statistics based on the trace of the square of the matrix and determinant of the matrix; these statistics are connected to one another as well as known statistics previously proposed in the literature. Furthermore, the log of the determinant is argued to relate to a likelihood ratio test and is proven to be more powerful than other tests that are asymptotically equivalent under the null hypothesis. Additionally, matrix-based tests are presented for the purpose of inferring the location or direction of the causality existing between the two series. A simulation study is provided to explore the efficacy of the proposed methodology--the methods are shown to offer improvement over existing techniques, which include the famous Granger causality test. Finally, data examples involving U.S. inflation, trade volume, and exchange rates are given. Supplementary materials for this article are available online.

Suggested Citation

  • Michael W. Robbins & Thomas J. Fisher, 2015. "Cross-Correlation Matrices for Tests of Independence and Causality Between Two Multivariate Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 459-473, October.
    • Handle: RePEc:taf:jnlbes:v:33:y:2015:i:4:p:459-473
    DOI: 10.1080/07350015.2014.962699
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07350015.2014.962699
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07350015.2014.962699?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Syed Mahmud & Aman Ullah & Eray Yucel, 2004. "Testing Marshall-Lerner condition: a non-parametric approach," Applied Economics Letters, Taylor & Francis Journals, vol. 11(4), pages 231-236.
    2. Ki-Ho Kim, 1998. "US inflation and the dollar exchange rate: a vector error correction model," Applied Economics, Taylor & Francis Journals, vol. 30(5), pages 613-619.
    3. Hong, Yongmiao, 1996. "Testing for independence between two covariance stationary time series," MPRA Paper 108731, University Library of Munich, Germany.
    4. Boyd, Derick & Caporale, Gugielmo Maria & Smith, Ron, 2001. "Real Exchange Rate Effects on the Balance of Trade: Cointegration and the Marshall-Lerner Condition," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 6(3), pages 187-200, July.
    5. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    6. Tilak Abeysinghe & Tan Lin Yeok, 1998. "Exchange rate appreciation and export competitiveness. The case of Singapore," Applied Economics, Taylor & Francis Journals, vol. 30(1), pages 51-55.
    7. Thomas J. Fisher & Colin M. Gallagher, 2012. "New Weighted Portmanteau Statistics for Time Series Goodness of Fit Testing," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 777-787, June.
    8. Chafik Bouhaddioui & Roch Roy, 2006. "A Generalized Portmanteau Test For Independence Of Two Infinite‐Order Vector Autoregressive Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 505-544, July.
    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. Guochang Wang & Wai Keung Li & Ke Zhu, 2018. "New HSIC-based tests for independence between two stationary multivariate time series," Papers 1804.09866, arXiv.org.
    2. Alonso, Andrés M. & Galeano, Pedro & Peña, Daniel, 2020. "A robust procedure to build dynamic factor models with cluster structure," Journal of Econometrics, Elsevier, vol. 216(1), pages 35-52.
    3. Yi-Jing Zhang & Li-Sheng Hu, 2021. "Fault Propagation Inference Based on a Graph Neural Network for Steam Turbine Systems," Energies, MDPI, vol. 14(2), pages 1-13, January.
    4. Daniel Cirkovic & Thomas J. Fisher, 2021. "On testing for the equality of autocovariance in time series," Environmetrics, John Wiley & Sons, Ltd., vol. 32(7), November.
    5. Leong, Soon Heng & Urga, Giovanni, 2023. "A practical multivariate approach to testing volatility spillover," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    6. Chu, Ba, 2023. "A distance-based test of independence between two multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 195(C).

    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. Bertrand Candelon & Sessi Tokpavi, 2016. "A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 240-253, April.
    2. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    3. Bertrand Candelon & Sessi Tokpavi, 2016. "A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 240-253, April.
    4. Guochang Wang & Wai Keung Li & Ke Zhu, 2018. "New HSIC-based tests for independence between two stationary multivariate time series," Papers 1804.09866, arXiv.org.
    5. Muntasir Murshed & Seemran Rashid, 2020. "An Empirical Investigation of Real Exchange Rate Responses to Foreign Currency Inflows: Revisiting the Dutch Disease Phenomenon in South Asia," The Economics and Finance Letters, Conscientia Beam, vol. 7(1), pages 23-46.
    6. Soylu, Pınar Kaya & Güloğlu, Bülent, 2019. "Financial contagion and flight to quality between emerging markets and U.S. bond market," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    7. Wang, Gang-Jin & Xie, Chi & Jiang, Zhi-Qiang & Stanley, H. Eugene, 2016. "Extreme risk spillover effects in world gold markets and the global financial crisis," International Review of Economics & Finance, Elsevier, vol. 46(C), pages 55-77.
    8. Gan-Ochir Doojav, 2018. "The Effect of Real Exchange Rate on Trade Balance in a Resource-Rich Economy: The Case of Mongolia," Foreign Trade Review, , vol. 53(4), pages 211-224, November.
    9. Chu, Ba, 2023. "A distance-based test of independence between two multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    10. Hong, Yongmiao, 2001. "A test for volatility spillover with application to exchange rates," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 183-224, July.
    11. Fabio Augusto Reis Gomes & Lourenco Senne Paz, 2005. "Can real exchange rate devaluation improve the trade balance? The 1990-1998 Brazilian case," Applied Economics Letters, Taylor & Francis Journals, vol. 12(9), pages 525-528.
    12. Usama Ehsan Khan, Muhammad Umar Zahid, Afshan Uroos, Aamir Hussain Siddiqui, 2018. "Impact of Devaluation on Balance of Trade: A Context of Neighboring Countries," Journal of Finance and Economics Research, Geist Science, Iqra University, Faculty of Business Administration, vol. 3(2), pages 68-77, October.
    13. Yu Hsing, 2010. "Test of the Marshall-Lerner Condition for Eight Selected Asian Countries and Policy Implications," Global Economic Review, Taylor & Francis Journals, vol. 39(1), pages 91-98.
    14. Leong, Soon Heng & Urga, Giovanni, 2023. "A practical multivariate approach to testing volatility spillover," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    15. repec:wyi:journl:002098 is not listed on IDEAS
    16. Mayer, Alexander, 2020. "(Consistently) testing strict exogeneity against the alternative of predeterminedness in linear time-series models," Economics Letters, Elsevier, vol. 193(C).
    17. Hong, Yongmiao & Liu, Yanhui & Wang, Shouyang, 2009. "Granger causality in risk and detection of extreme risk spillover between financial markets," Journal of Econometrics, Elsevier, vol. 150(2), pages 271-287, June.
    18. Emeka Nkoro & Aham Kelvin Uko, 2016. "Exchange Rate and Inflation Volatility and Stock Prices Volatility: Evidence from Nigeria, 1986-2012," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 6(6), pages 1-4.
    19. Czujack, Corinna & Flôres Junior, Renato Galvão & Ginsburgh, Victor, 1995. "On long-run price comovements between paintings and prints," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 269, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    20. Sotirios Varelas, 2022. "Virtual Immersive Platforms as a Strategic Innovative Destination Marketing Tool in the COVID-19 Era," Sustainability, MDPI, vol. 14(19), pages 1-15, October.
    21. Loperfido, Nicola, 2010. "A note on marginal and conditional independence," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1695-1699, December.

    More about this item

    Statistics

    Access and download statistics

    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:taf:jnlbes:v:33:y:2015:i:4:p:459-473. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UBES20 .

    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.