IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v98y2007i7p1321-1336.html
   My bibliography  Save this article

Weak convergence of non-stationary multivariate marked processes with applications to martingale testing

Author

Listed:
  • Escanciano, J. Carlos

Abstract

This paper establishes the weak convergence of a class of marked empirical processes of possibly non-stationary and/or non-ergodic multivariate time series sequences under martingale conditions. The assumptions involved are similar to those in Brown's martingale central limit theorem. In particular, no mixing conditions are imposed. As an application, we propose a test statistic for the martingale hypothesis and we derive its asymptotic null distribution. Finally, a Monte Carlo study shows that the asymptotic results provide good approximations for small and moderate sample sizes. An application to the S&P 500 is also considered.

Suggested Citation

  • Escanciano, J. Carlos, 2007. "Weak convergence of non-stationary multivariate marked processes with applications to martingale testing," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1321-1336, August.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:7:p:1321-1336
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(07)00041-3
    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. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
    2. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September.
    3. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    4. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    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. Wang, Qiying & Wu, Dongsheng & Zhu, Ke, 2018. "Model checks for nonlinear cointegrating regression," Journal of Econometrics, Elsevier, vol. 207(2), pages 261-284.
    2. Juan Carlos Escanciano & Zaichao Du, 2015. "Backtesting Expected Shortfall: Accounting for Tail Risk," CAEPR Working Papers 2015-001, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    3. Ferger, Dietmar, 2009. "Argmax-stable marked empirical processes," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1203-1206, May.
    4. Zaichao Du, 2016. "Nonparametric bootstrap tests for independence of generalized errors," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 55-83, February.
    5. Yoichi Nishiyama, 2009. "Goodness‐of‐fit test for a nonlinear time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 674-681, November.
    6. Zaichao Du & Juan Carlos Escanciano, 2017. "Backtesting Expected Shortfall: Accounting for Tail Risk," Management Science, INFORMS, vol. 63(4), pages 940-958, April.
    7. Peter C. B. Phillips & Sainan Jin, 2014. "Testing the Martingale Hypothesis," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 537-554, October.
    8. Zaichao Du & Juan Carlos Escanciano, 2015. "A Nonparametric Distribution-Free Test for Serial Independence of Errors," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 1011-1034, December.
    9. Xuexin WANG, 2021. "Generalized Spectral Tests for High Dimensional Multivariate Martingale Difference Hypotheses," Working Papers 2021-11-06, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    10. Du, Zaichao, 2014. "Testing for serial independence of panel errors," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 248-261.
    11. Alejandra Cabaña & Enrique M. Cabaña & Marco Scavino, 2012. "Weak Convergence of Marked Empirical Processes for Focused Inference on AR(p) vs AR(p + 1) Stationary Time Series," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 793-810, September.
    12. Juan Carlos Escanciano & Chuan Goh, 2010. "Specification Analysis of Structural Quantile Regression Models," Working Papers tecipa-415, University of Toronto, Department of Economics.

    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. McPherson, Matthew Q. & Palardy, Joseph, 2007. "Are international stock returns predictable?: An examination of linear and non-linear predictability using generalized spectral tests," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 17(5), pages 452-464, December.
    2. Peter C. B. Phillips & Sainan Jin, 2014. "Testing the Martingale Hypothesis," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 537-554, October.
    3. Wang, Qiying & Wu, Dongsheng & Zhu, Ke, 2018. "Model checks for nonlinear cointegrating regression," Journal of Econometrics, Elsevier, vol. 207(2), pages 261-284.
    4. Zdeněk Hlávka & Marie Hušková & Claudia Kirch & Simos G. Meintanis, 2017. "Fourier--type tests involving martingale difference processes," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 468-492, April.
    5. Shao, Xiaofeng, 2011. "A bootstrap-assisted spectral test of white noise under unknown dependence," Journal of Econometrics, Elsevier, vol. 162(2), pages 213-224, June.
    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. George Kapetanios & Andrew P. Blake, 2007. "Testing the Martingale Difference Hypothesis Using Neural Network Approximations," Working Papers 601, Queen Mary University of London, School of Economics and Finance.
    8. Charles, Amélie & Darné, Olivier & Fouilloux, Jessica, 2011. "Testing the martingale difference hypothesis in CO2 emission allowances," Economic Modelling, Elsevier, vol. 28(1-2), pages 27-35, January.
    9. Gourieroux, Christian & Jasiak, Joann, 2019. "Robust analysis of the martingale hypothesis," Econometrics and Statistics, Elsevier, vol. 9(C), pages 17-41.
    10. Herman J. Bierens & Li Wang, 2017. "Weighted simulated integrated conditional moment tests for parametric conditional distributions of stationary time series processes," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 103-135, March.
    11. Escanciano, J. Carlos, 2006. "Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 531-541, June.
    12. Escanciano, Juan Carlos & Mayoral, Silvia, 2010. "Data-driven smooth tests for the martingale difference hypothesis," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1983-1998, August.
    13. Dilip Kumar & Srinivasan Maheswaran, 2014. "Are major global stock markets efficient? An application of the martingale difference hypothesis with wild bootstrap," American Journal of Finance and Accounting, Inderscience Enterprises Ltd, vol. 3(2/3/4), pages 217-233.
    14. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.
    15. Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
    16. Jinho Choi & Juan Carlos Escanciano & Junjie Guo, 2022. "Generalized band spectrum estimation with an application to the New Keynesian Phillips curve," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 1055-1078, August.
    17. Charles, Amélie & Darné, Olivier & Kim, Jae H., 2012. "Exchange-rate return predictability and the adaptive markets hypothesis: Evidence from major foreign exchange rates," Journal of International Money and Finance, Elsevier, vol. 31(6), pages 1607-1626.
    18. Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra.
    19. Hill, Jonathan B. & Motegi, Kaiji, 2019. "Testing the white noise hypothesis of stock returns," Economic Modelling, Elsevier, vol. 76(C), pages 231-242.
    20. Zhu, Ke & Li, Wai Keung, 2015. "A bootstrapped spectral test for adequacy in weak ARMA models," Journal of Econometrics, Elsevier, vol. 187(1), pages 113-130.

    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:98:y:2007:i:7:p:1321-1336. 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.