IDEAS home Printed from https://ideas.repec.org/p/ise/remwps/wp0592018.html
   My bibliography  Save this paper

Quasi-Maximum Likelihood and the Kernel Block Bootstrap for Nonlinear Dynamic Models

Author

Listed:
  • Paulo M.D.C. Parente
  • Richard J. Smith

Abstract

This paper applies a novel bootstrap method, the kernelblockbootstrap, to quasi-maximum likelihood estimation of dynamic models with stationary strong mixing data. The method rst kernel weights the components comprising the quasi-log likelihood function in an appropriate way and then samples the resultant transformed components using the standard "m out of n"bootstrap. We investigate the first order asymptotic properties of the KBB method for quasi-maximum likelihood demonstrating, in particular, its consistency and the rst-order asymptotic validity of the bootstrap approximation to the distribution of the quasi-maximum likelihood estimator. A set of simulation experiments for the mean regression model illustrates the efficacy of the kernel block bootstrap for quasi-maximum likelihood estimation.

Suggested Citation

  • Paulo M.D.C. Parente & Richard J. Smith, 2018. "Quasi-Maximum Likelihood and the Kernel Block Bootstrap for Nonlinear Dynamic Models," Working Papers REM 2018/59, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    • Handle: RePEc:ise:remwps:wp0592018
    as

    Download full text from publisher

    File URL: https://rem.rc.iseg.ulisboa.pt/wps/pdf/REM_WP_059_2018.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2014. "Bootstrapping Density-Weighted Average Derivatives," Econometric Theory, Cambridge University Press, vol. 30(6), pages 1135-1164, December.
    3. Smith, Richard J., 2005. "Automatic Positive Semidefinite Hac Covariance Matrix And Gmm Estimation," Econometric Theory, Cambridge University Press, vol. 21(1), pages 158-170, February.
    4. Smith, Richard J., 2011. "Gel Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1192-1235, December.
    5. Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," Journal of Econometrics, Elsevier, vol. 117(2), pages 369-399, December.
    6. Davidson, Russell & MacKinnon, James G, 1999. "Bootstrap Testing in Nonlinear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 487-508, May.
    7. Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," LSE Research Online Documents on Economics 6850, London School of Economics and Political Science, LSE Library.
    8. Inoue, Atsushi & Shintani, Mototsugu, 2006. "Bootstrapping GMM estimators for time series," Journal of Econometrics, Elsevier, vol. 133(2), pages 531-555, August.
    9. Camponovo, Lorenzo & Scaillet, Olivier & Trojani, Fabio, 2012. "Robust subsampling," Journal of Econometrics, Elsevier, vol. 167(1), pages 197-210.
    10. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
    11. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
    12. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, January.
    13. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-972, July.
    14. Shao, Xiaofeng, 2010. "The Dependent Wild Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 218-235.
    15. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-519, March.
    16. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    17. Javier Hidalgo, 2003. "An Alternative Bootstrap to Moving Blocks for Time Series Regression Models," STICERD - Econometrics Paper Series 452, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    18. Politis, D. N. & Romano, Joseph P. & Wolf, Michael, 1997. "Subsampling for heteroskedastic time series," Journal of Econometrics, Elsevier, vol. 81(2), pages 281-317, December.
    19. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    20. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    21. Lahiri, Soumendra Nath, 1996. "On Edgeworth Expansion and Moving Block Bootstrap for StudentizedM-Estimators in Multiple Linear Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 42-59, January.
    22. Gonçalves, Sílvia & White, Halbert, 2002. "The Bootstrap Of The Mean For Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1367-1384, December.
    23. Donald W. K. Andrews, 2002. "Higher-Order Improvements of a Computationally Attractive "k"-Step Bootstrap for Extremum Estimators," Econometrica, Econometric Society, vol. 70(1), pages 119-162, January.
    24. Paulo M.D.C. Parente & Richard J. Smith, 2018. "Generalised Empirical Likelihood Kernel Block Bootstrapping," Working Papers REM 2018/55, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    25. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    26. Hong, H. & Scaillet, O., 2006. "A fast subsampling method for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 133(2), pages 557-578, August.
    27. José A. F. Machado & Paulo Parente, 2005. "Bootstrap estimation of covariance matrices via the percentile method," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 70-78, March.
    28. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
    29. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    30. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    31. Donald W. K. Andrews, 2004. "the Block-Block Bootstrap: Improved Asymptotic Refinements," Econometrica, Econometric Society, vol. 72(3), pages 673-700, May.
    32. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    33. Timothy L. McMurry & Dimitris N. Politis, 2018. "Estimating MA Parameters through Factorization of the Autocovariance Matrix and an MA†Sieve Bootstrap," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(3), pages 433-446, May.
    34. Efstathios Paparoditis & Dimitris N. Politis, 2002. "The tapered block bootstrap for general statistics from stationary sequences," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 131-148, June.
    35. Paulo Parente & Richard J. Smith, 2018. "Kernel block bootstrap," CeMMAP working papers CWP48/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    36. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    37. Horowitz, J., 1996. "Bootstrap Critical Values For Tests Based On The Smoothed Maximum Score Estimator," SFB 373 Discussion Papers 1996,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    38. J.J. Heckman & E.E. Leamer (ed.), 2001. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 5, number 5.
    39. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    40. Joel L. Horowitz, 1996. "Bootstrap Critical Values for Tests Based on the Smoothed Maximum Score Estimator," Econometrics 9603003, University Library of Munich, Germany.
    41. Stanislav Anatolyev, 2005. "GMM, GEL, Serial Correlation, and Asymptotic Bias," Econometrica, Econometric Society, vol. 73(3), pages 983-1002, May.
    42. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
    43. Nze, Patrick Ango & Doukhan, Paul, 2004. "Weak Dependence: Models And Applications To Econometrics," Econometric Theory, Cambridge University Press, vol. 20(6), pages 995-1045, December.
    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. La Vecchia, Davide & Moor, Alban & Scaillet, Olivier, 2023. "A higher-order correct fast moving-average bootstrap for dependent data," Journal of Econometrics, Elsevier, vol. 235(1), pages 65-81.
    2. Paulo M.D.C. Parente & Richard J. Smith, 2018. "Generalised Empirical Likelihood Kernel Block Bootstrapping," Working Papers REM 2018/55, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

    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. La Vecchia, Davide & Moor, Alban & Scaillet, Olivier, 2023. "A higher-order correct fast moving-average bootstrap for dependent data," Journal of Econometrics, Elsevier, vol. 235(1), pages 65-81.
    2. Allen, Jason & Gregory, Allan W. & Shimotsu, Katsumi, 2011. "Empirical likelihood block bootstrapping," Journal of Econometrics, Elsevier, vol. 161(2), pages 110-121, April.
    3. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    4. Alain Guay & Jean-Francois Lamarche, 2005. "The Information Content of Implied Probabilities to Detect Structural Change," Working Papers 0804, Brock University, Department of Economics, revised Oct 2008.
    5. Paulo M.D.C. Parente & Richard J. Smith, 2018. "Generalised Empirical Likelihood Kernel Block Bootstrapping," Working Papers REM 2018/55, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    6. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
    7. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    8. Lee, Seojeong, 2016. "Asymptotic refinements of a misspecification-robust bootstrap for GEL estimators," Journal of Econometrics, Elsevier, vol. 192(1), pages 86-104.
    9. Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," CIRJE F-Series CIRJE-F-430, CIRJE, Faculty of Economics, University of Tokyo.
    10. Guggenberger, Patrik & Ramalho, Joaquim J.S. & Smith, Richard J., 2012. "GEL statistics under weak identification," Journal of Econometrics, Elsevier, vol. 170(2), pages 331-349.
    11. Lorenzo Camponovo & O. Scaillet & Fabio Trojani, 2013. "Predictability Hidden by Anomalous Observations," Swiss Finance Institute Research Paper Series 13-05, Swiss Finance Institute.
    12. repec:bla:ecorec:v:91:y:2015:i::p:1-24 is not listed on IDEAS
    13. Seojeong Lee, 2018. "Asymptotic Refinements of a Misspecification-Robust Bootstrap for Generalized Empirical Likelihood Estimators," Papers 1806.00953, arXiv.org, revised Jun 2018.
    14. Härdle, Wolfgang & Horowitz, Joel L. & Kreiss, Jens-Peter, 2001. "Bootstrap methods for time series," SFB 373 Discussion Papers 2001,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    15. Bravo, Francesco & Crudu, Federico, 2012. "Efficient bootstrap with weakly dependent processes," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3444-3458.
    16. Xuexin Wang, 2020. "A new class of tests for overidentifying restrictions in moment condition models," Econometric Reviews, Taylor & Francis Journals, vol. 39(5), pages 495-509, May.
    17. Lee, Seojeong, 2014. "Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 178(P3), pages 398-413.
    18. Politis, D N, 2009. "Higher-Order Accurate, Positive Semi-definite Estimation of Large-Sample Covariance and Spectral Density Matrices," University of California at San Diego, Economics Working Paper Series qt66w826hz, Department of Economics, UC San Diego.
    19. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    20. Alastair R. Hall, 2013. "Generalized Method of Moments," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 14, pages 313-333, Edward Elgar Publishing.
    21. Inoue, Atsushi & Shintani, Mototsugu, 2006. "Bootstrapping GMM estimators for time series," Journal of Econometrics, Elsevier, vol. 133(2), pages 531-555, August.

    More about this item

    Keywords

    Bootstrap; heteroskedastic and autocorrelation consistent inference; quasi-maximum likelihood estimation.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ise:remwps:wp0592018. 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: Sandra Araújo (email available below). General contact details of provider: https://rem.rc.iseg.ulisboa.pt/ .

    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.