IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v43y2022i6p964-1002.html

Portmanteau test for a class of multivariate asymmetric power GARCH model

Author

Listed:
  • Yacouba Boubacar Maïnassara
  • Othman Kadmiri
  • Bruno Saussereau

Abstract

We establish the asymptotic behaviour of the sum of squared residuals autocovariances and autocorrelations for the class of multi‐variate power transformed asymmetric models. We then derive a portmanteau test. We establish the asymptotic distribution of the proposed statistics. These asymptotic results are illustrated by Monte Carlo experiments. An application to a bivariate real financial data is also proposed.

Suggested Citation

  • Yacouba Boubacar Maïnassara & Othman Kadmiri & Bruno Saussereau, 2022. "Portmanteau test for a class of multivariate asymmetric power GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 964-1002, November.
    • Handle: RePEc:bla:jtsera:v:43:y:2022:i:6:p:964-1002
    DOI: 10.1111/jtsa.12646
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jtsa.12646
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jtsa.12646?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
    ---><---

    References listed on IDEAS

    as
    1. Yongning Wang & Ruey S. Tsay, 2013. "On Diagnostic Checking of Vector ARMA-GARCH Models with Gaussian and Student-t Innovations," Econometrics, MDPI, vol. 1(1), pages 1-31, April.
    2. Kroner, Kenneth F & Ng, Victor K, 1998. "Modeling Asymmetric Comovements of Asset Returns," The Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 817-844.
    3. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    4. Anne Leucht & Jens-Peter Kreiss & Michael H. Neumann, 2015. "A Model Specification Test For GARCH(1,1) Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1167-1193, December.
    5. H. Wong & W. Li, 2002. "Detecting and Diagnostic Checking Multivariate Conditional Heteroscedastic Time Series Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 45-59, March.
    6. Abdoulkarim Ilmi Amir & Yacouba Boubacar Maïnassara, 2020. "Multivariate portmanteau tests for weak multiplicative seasonal VARMA models," Statistical Papers, Springer, vol. 61(6), pages 2529-2560, December.
    7. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    8. Boubacar Maïnassara, Y. & Kadmiri, O. & Saussereau, B., 2022. "Estimation of multivariate asymmetric power GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    9. Duchesne, Pierre, 2010. "Corrigendum to: "On matricial measures of dependence in vector ARCH models with applications to diagnostic checking" [Statist. Probab. Lett. 68 (2004) 149-160]," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 910-910, May.
    10. Y. K. Tse & A. K. C. Tsui, 1999. "A Note on Diagnosing Multivariate Conditional Heteroscedasticity Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(6), pages 679-691, November.
    11. Ben, Youhong & Jiang, Feiyu, 2020. "A note on Portmanteau tests for conditional heteroscedastistic models," Economics Letters, Elsevier, vol. 192(C).
    12. Chun-Zheng Cao & Jin-Guan Lin & Li-Xing Zhu, 2010. "Heteroscedasticity and/or autocorrelation diagnostics in nonlinear models with AR(1) and symmetrical errors," Statistical Papers, Springer, vol. 51(4), pages 813-836, December.
    13. M. Dolores Jiménez-Gamero & Sangyeol Lee & Simos G. Meintanis, 2020. "Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 682-703, September.
    14. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
    15. Yacouba Boubacar Maïnassara & Bruno Saussereau, 2018. "Diagnostic Checking in Multivariate ARMA Models With Dependent Errors Using Normalized Residual Autocorrelations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1813-1827, October.
    16. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
    17. Francq, Christian & Zakoïan, Jean-Michel, 2012. "Qml Estimation Of A Class Of Multivariate Asymmetric Garch Models," Econometric Theory, Cambridge University Press, vol. 28(1), pages 179-206, February.
    18. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    19. Ke, Rui & Jia, Jing & Tan, Changchun, 2021. "A residual-based test for multivariate GARCH models using transformed quadratic residuals," Economics Letters, Elsevier, vol. 206(C).
    20. Shiqing Ling & W. K. Li, 1997. "Diagnostic checking of nonlinear multivariate time series with multivariate arch errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(5), pages 447-464, September.
    Full references (including those not matched with items on IDEAS)

    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. Annastiina Silvennoinen & Timo Teräsvirta, 2009. "Multivariate GARCH Models," Springer Books, in: Thomas Mikosch & Jens-Peter Kreiß & Richard A. Davis & Torben Gustav Andersen (ed.), Handbook of Financial Time Series, chapter 9, pages 201-229, Springer.
    2. Massimiliano Caporin & Michael McAleer, 2011. "Thresholds, news impact surfaces and dynamic asymmetric multivariate GARCH," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(2), pages 125-163, May.
    3. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    4. Boubacar Maïnassara, Y. & Kadmiri, O. & Saussereau, B., 2022. "Estimation of multivariate asymmetric power GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    5. Caporin Massimiliano & Paruolo Paolo, 2005. "Spatial effects in multivariate ARCH," Economics and Quantitative Methods qf0501, Department of Economics, University of Insubria.
    6. Yacouba Boubacar Maïnassara & Othman Kadmiri & Bruno Saussereau, 2022. "Portmanteau test for the asymmetric power GARCH model when the power is unknown," Statistical Papers, Springer, vol. 63(3), pages 755-793, June.
    7. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    8. Duchesne, Pierre, 2006. "Testing for multivariate autoregressive conditional heteroskedasticity using wavelets," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2142-2163, December.
    9. Ke, Rui & Jia, Jing & Tan, Changchun, 2021. "A residual-based test for multivariate GARCH models using transformed quadratic residuals," Economics Letters, Elsevier, vol. 206(C).
    10. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2020. "Multivariate leverage effects and realized semicovariance GARCH models," Journal of Econometrics, Elsevier, vol. 217(2), pages 411-430.
    11. Pedersen, Rasmus Søndergaard, 2016. "Targeting Estimation Of Ccc-Garch Models With Infinite Fourth Moments," Econometric Theory, Cambridge University Press, vol. 32(2), pages 498-531, April.
    12. López Cabrera, Brenda & Schulz, Franziska, 2016. "Volatility linkages between energy and agricultural commodity prices," Energy Economics, Elsevier, vol. 54(C), pages 190-203.
    13. Paul Catani & Timo Teräsvirta & Meiqun Yin, 2017. "A Lagrange multiplier test for testing the adequacy of constant conditional correlation GARCH model," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 599-621, October.
    14. Arthur Charpentier, 2015. "Prévision avec des copules en finance," Working Papers hal-01151233, HAL.
    15. Eraslan, Sercan & Ali, Faek Menla, 2017. "Financial crises and the dynamic linkages between stock and bond returns," Discussion Papers 17/2017, Deutsche Bundesbank.
    16. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    17. Christian Francq & Lajos Horváth & Jean-Michel Zakoïan, 2016. "Variance Targeting Estimation of Multivariate GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 353-382.
    18. Adams, Zeno & Füss, Roland & Glück, Thorsten, 2017. "Are correlations constant? Empirical and theoretical results on popular correlation models in finance," Journal of Banking & Finance, Elsevier, vol. 84(C), pages 9-24.
    19. Andrea Silvestrini & David Veredas, 2008. "Temporal Aggregation Of Univariate And Multivariate Time Series Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 22(3), pages 458-497, July.
    20. Zouheir Mighri & Faysal Mansouri, 2013. "Dynamic Conditional Correlation Analysis of Stock Market Contagion: Evidence from the 2007-2010 Financial Crises," International Journal of Economics and Financial Issues, Econjournals, vol. 3(3), pages 637-661.

    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:bla:jtsera:v:43:y:2022:i:6:p:964-1002. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.