IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v89y2004i1p148-180.html
   My bibliography  Save this article

On consistent testing for serial correlation of unknown form in vector time series models

Author

Listed:
  • Duchesne, Pierre
  • Roy, Roch

Abstract

Multivariate autoregressive models with exogenous variables (VARX) are often used in econometric applications. Many properties of the basic statistics for this class of models rely on the assumption of independent errors. Using results of Hong (Econometrica 64 (1996) 837), we propose a new test statistic for checking the hypothesis of non-correlation or independence in the Gaussian case. The test statistic is obtained by comparing the spectral density of the errors under the null hypothesis of independence with a kernel-based spectral density estimator. The asymptotic distribution of the statistic is derived under the null hypothesis. This test generalizes the portmanteau test of Hosking (J. Amer. Statist. Assoc. 75 (1980) 602). The consistency of the test is established for a general class of static regression models with autocorrelated errors. Its asymptotic slope is derived and the asymptotic relative efficiency within the class of possible kernels is also investigated. Finally, the level and power of the resulting tests are also studied by simulation.

Suggested Citation

  • Duchesne, Pierre & Roy, Roch, 2004. "On consistent testing for serial correlation of unknown form in vector time series models," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 148-180, April.
    • Handle: RePEc:eee:jmvana:v:89:y:2004:i:1:p:148-180
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00126-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-864, July.
    2. Geweke, John, 1981. "The Approximate Slopes of Econometric Tests," Econometrica, Econometric Society, vol. 49(6), pages 1427-1442, November.
    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. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    2. Poulin, Jennifer & Duchesne, Pierre, 2008. "On the power transformation of kernel-based tests for serial correlation in vector time series: Some finite sample results and a comparison with the bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4432-4457, May.
    3. Caporin Massimiliano & Paruolo Paolo, 2005. "Spatial effects in multivariate ARCH," Economics and Quantitative Methods qf0501, Department of Economics, University of Insubria.
    4. Pierre Duchesne, 2005. "Robust and powerful serial correlation tests with new robust estimates in ARX models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 49-81, January.
    5. Boubacar Mainassara, Y. & Francq, C., 2011. "Estimating structural VARMA models with uncorrelated but non-independent error terms," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 496-505, March.
    6. Alfredo García-Hiernaux, 2009. "Diagnostic checking using subspace methods," Documentos de Trabajo del ICAE 2009-03, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    7. Simos G. Meintanis & Joseph Ngatchou-Wandji & James Allison, 2018. "Testing for serial independence in vector autoregressive models," Statistical Papers, Springer, vol. 59(4), pages 1379-1410, December.
    8. Leong, Soon Heng & Urga, Giovanni, 2023. "A practical multivariate approach to testing volatility spillover," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    9. Duchesne, Pierre, 2006. "Testing for multivariate autoregressive conditional heteroskedasticity using wavelets," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2142-2163, December.

    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. Chafik Bouhaddioui & Roch Roy, 2004. "A Generalized Portmanteau Test for Independence of Two Infinite Order Vector Autoregressive Series," CIRANO Working Papers 2004s-06, CIRANO.
    2. Hong, Yongmiao, 1996. "Testing for independence between two covariance stationary time series," MPRA Paper 108731, University Library of Munich, Germany.
    3. Rhys Bidder & Ian Dew-Becker, 2016. "Long-Run Risk Is the Worst-Case Scenario," American Economic Review, American Economic Association, vol. 106(9), pages 2494-2527, September.
    4. repec:wyi:journl:002087 is not listed on IDEAS
    5. Yushu Li & Fredrik N. G. Andersson, 2021. "A simple wavelet-based test for serial correlation in panel data models," Empirical Economics, Springer, vol. 60(5), pages 2351-2363, May.
    6. Zhang, Xianyang, 2016. "White noise testing and model diagnostic checking for functional time series," Journal of Econometrics, Elsevier, vol. 194(1), pages 76-95.
    7. Hidalgo, Javier, 2009. "Goodness of fit for lattice processes," Journal of Econometrics, Elsevier, vol. 151(2), pages 113-128, August.
    8. Kuan Chung-Ming & Lee Wei-Ming, 2004. "A New Test of the Martingale Difference Hypothesis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(4), pages 1-26, December.
    9. Axel Bücher & Holger Dette & Florian Heinrichs, 2023. "A portmanteau-type test for detecting serial correlation in locally stationary functional time series," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 255-278, July.
    10. Campbell, John Y., 2001. "Why long horizons? A study of power against persistent alternatives," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 459-491, December.
    11. Sheng-Kai Chang, 2005. "The approximate slopes and the power of the GMM overidentifying restrictions test," Applied Economics Letters, Taylor & Francis Journals, vol. 12(13), pages 845-848.
    12. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, vol. 104(1), pages 1-48, August.
    13. William A. Barnett & Melvin J. Hinich & Piyu Yue, 2011. "The Exact Theoretical Rational Expectations Monetary Aggregate," World Scientific Book Chapters, in: Financial Aggregation And Index Number Theory, chapter 2, pages 53-84, World Scientific Publishing Co. Pte. Ltd..
    14. Roberto Baragona & Francesco Battaglia & Domenico Cucina, 2022. "Data-driven portmanteau tests for time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 675-698, September.
    15. White, Halbert & Hong, Yongmiao, 1999. "M-Testing Using Finite and Infinite Dimensional Parameter Estimators," University of California at San Diego, Economics Working Paper Series qt9qz123ng, Department of Economics, UC San Diego.
    16. Peñaranda, Francisco & Sentana, Enrique, 2012. "Spanning tests in return and stochastic discount factor mean–variance frontiers: A unifying approach," Journal of Econometrics, Elsevier, vol. 170(2), pages 303-324.
    17. Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution Free Goodness-of-Fit Tests for Linear Processes," STICERD - Econometrics Paper Series 482, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    18. repec:wyi:journl:002156 is not listed on IDEAS
    19. Manuel A. Dominguez & Ignacio N. Lobato, 2001. "A Consistent Test for the Martingale Difference Hypothesis," Working Papers 0101, Centro de Investigacion Economica, ITAM.
    20. Pierre Duchesne, 2005. "On the asymptotic distribution of residual autocovariances in VARX models with applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 449-473, December.
    21. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
    22. Hidalgo, Javier & Seo, Myung Hwan, 2015. "Specification Tests For Lattice Processes," Econometric Theory, Cambridge University Press, vol. 31(2), pages 294-336, April.

    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:eee:jmvana:v:89:y:2004:i:1:p:148-180. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.