IDEAS home Printed from https://ideas.repec.org/a/wly/emjrnl/v19y2016i1p55-83.html
   My bibliography  Save this article

Nonparametric bootstrap tests for independence of generalized errors

Author

Listed:
  • Zaichao Du

Abstract

In this paper, we develop a general method of testing for independence when unobservable generalized errors are involved. Our method can be applied to testing for serial independence of generalized errors, and testing for independence between the generalized errors and observable covariates. The former can serve as a unified approach to testing the adequacy of time series models, as model adequacy often implies that the generalized errors obtained after a suitable transformation are independent and identically distributed. The latter is a key identification assumption in many nonlinear economic models. Our tests are based on a classical sample dependence measure, the Hoeffding–Blum–Kiefer–Rosenblatt‐type empirical process applied to generalized residuals. We establish a uniform expansion of the process, thereby deriving an explicit expression for the parameter estimation effect, which causes our tests not to be nuisance‐parameter‐free. To circumvent this problem, we propose a multiplier‐type bootstrap to approximate the limit distribution. Our bootstrap procedure is computationally very simple as it does not require a re‐estimation of the parameters in each bootstrap replication. Simulations and empirical applications to daily exchange rate data highlight the merits of our approach.

Suggested Citation

  • Zaichao Du, 2016. "Nonparametric bootstrap tests for independence of generalized errors," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 55-83, February.
  • Handle: RePEc:wly:emjrnl:v:19:y:2016:i:1:p:55-83
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/ectj.12059
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Donald J. Brown & Marten H. Wegkamp, 2002. "Weighted Minimum Mean-Square Distance from Independence Estimation," Econometrica, Econometric Society, vol. 70(5), pages 2035-2051, September.
    2. Corradi, Valentina & Swanson, Norman R., 2006. "Bootstrap conditional distribution tests in the presence of dynamic misspecification," Journal of Econometrics, Elsevier, vol. 133(2), pages 779-806, August.
    3. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
    4. Donald J. Brown & Rahul Deb & Marten H. Wegkamp, 2003. "Tests of Independence in Separable Econometric Models: Theory and Application," Cowles Foundation Discussion Papers 1395R2, Cowles Foundation for Research in Economics, Yale University, revised Dec 2007.
    5. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 130-168.
    6. Brown, Bryan W, 1983. "The Identification Problem in Systems Nonlinear in the Variables," Econometrica, Econometric Society, vol. 51(1), pages 175-196, January.
    7. Delgado, Miguel A. & Velasco, Carlos, 2007. "A new class of distribution-free tests for time series models specification," UC3M Working papers. Economics we078047, Universidad Carlos III de Madrid. Departamento de Economía.
    8. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    9. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    10. Yongmiao Hong, 2000. "Generalized spectral tests for serial dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 557-574.
    11. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
    12. 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.
    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. Zaichao Du & Juan Carlos Escanciano, 2017. "Backtesting Expected Shortfall: Accounting for Tail Risk," Management Science, INFORMS, vol. 63(4), pages 940-958, April.
    2. Nasri, Bouchra R., 2022. "Tests of serial dependence for multivariate time series with arbitrary distributions," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    3. Kilani Ghoudi & Bruno Rémillard, 2018. "Serial independence tests for innovations of conditional mean and variance models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 3-26, March.
    4. Nasri, Bouchra R. & Rémillard, Bruno N. & Bahraoui, Tarik, 2022. "Change-point problems for multivariate time series using pseudo-observations," Journal of Multivariate Analysis, Elsevier, vol. 187(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. González-Rivera, Gloria & Yoldas, Emre, 2012. "Autocontour-based evaluation of multivariate predictive densities," International Journal of Forecasting, Elsevier, vol. 28(2), pages 328-342.
    2. Chen, Bin & Hong, Yongmiao, 2014. "A unified approach to validating univariate and multivariate conditional distribution models in time series," Journal of Econometrics, Elsevier, vol. 178(P1), pages 22-44.
    3. Dovern, Jonas & Manner, Hans, 2016. "Robust Evaluation of Multivariate Density Forecasts," VfS Annual Conference 2016 (Augsburg): Demographic Change 145547, Verein für Socialpolitik / German Economic Association.
    4. Dovern, Jonas & Manner, Hans, 2016. "Order Invariant Evaluation of Multivariate Density Forecasts," Working Papers 0608, University of Heidelberg, Department of Economics.
    5. 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.
    6. Jonas Dovern & Hans Manner, 2020. "Order‐invariant tests for proper calibration of multivariate density forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 440-456, June.
    7. Du, Zaichao, 2014. "Testing for serial independence of panel errors," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 248-261.
    8. Zaichao Du & Juan Carlos Escanciano, 2017. "Backtesting Expected Shortfall: Accounting for Tail Risk," Management Science, INFORMS, vol. 63(4), pages 940-958, April.
    9. Zhiyuan Pan & Xianchao Sun, 2014. "Hedging Strategy Using Copula and Nonparametric Methods: Evidence from China Securities Index Futures," International Journal of Economics and Financial Issues, Econjournals, vol. 4(1), pages 107-121.
    10. Cees Diks & Valentyn Panchenko & Dick van Dijk, 2008. "Partial Likelihood-Based Scoring Rules for Evaluating Density Forecasts in Tails," Tinbergen Institute Discussion Papers 08-050/4, Tinbergen Institute.
    11. Bruno Feunou & Mohammad R. Jahan-Parvar & Roméo Tédongap, 2016. "Which parametric model for conditional skewness?," The European Journal of Finance, Taylor & Francis Journals, vol. 22(13), pages 1237-1271, October.
    12. Gordy, Michael B. & McNeil, Alexander J., 2020. "Spectral backtests of forecast distributions with application to risk management," Journal of Banking & Finance, Elsevier, vol. 116(C).
    13. Ryo Kinoshita, 2015. "Asset allocation under higher moments with the GARCH filter," Empirical Economics, Springer, vol. 49(1), pages 235-254, August.
    14. Rossi, Barbara & Sekhposyan, Tatevik, 2013. "Conditional predictive density evaluation in the presence of instabilities," Journal of Econometrics, Elsevier, vol. 177(2), pages 199-212.
    15. Yongmiao Hong & Xia Wang & Wenjie Zhang & Shouyang Wang, 2017. "An efficient integrated nonparametric entropy estimator of serial dependence," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 728-780, October.
    16. Bu, Ruijun & Hadri, Kaddour & Kristensen, Dennis, 2021. "Diffusion copulas: Identification and estimation," Journal of Econometrics, Elsevier, vol. 221(2), pages 616-643.
    17. Xiao-Ming Li & Qing Xu, 2007. "Evaluating density forecasts of the model with a conditional skewed-t distribution for China's stock markets," Applied Financial Economics, Taylor & Francis Journals, vol. 18(3), pages 213-227.
    18. Rossi, Barbara & Sekhposyan, Tatevik, 2019. "Alternative tests for correct specification of conditional predictive densities," Journal of Econometrics, Elsevier, vol. 208(2), pages 638-657.
    19. Shaw, Charles, 2018. "Conditional heteroskedasticity in crypto-asset returns," MPRA Paper 90437, University Library of Munich, Germany.
    20. Fantazzini , Dean, 2009. "Econometric Analysis of Financial Data in Risk Management," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 14(2), pages 100-127.

    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:wly:emjrnl:v:19:y:2016:i:1:p:55-83. 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: 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.