IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v30y2021i2d10.1007_s11749-020-00719-x.html
   My bibliography  Save this article

Testing for the sandwich-form covariance matrix of the quasi-maximum likelihood estimator

Author

Listed:
  • Lijuan Huo

    (Beijing Institute of Technology)

  • Jin Seo Cho

    (Beijing Institute of Technology
    Yonsei University)

Abstract

This study tests for the sandwich-form asymptotic covariance matrices entailed by conditionally heteroskedastic and/or autocorrelated regression errors or conditionally uncorrelated homoskedastic errors. In doing so, we enable the empirical researcher to estimate the asymptotic covariance matrix of the quasi-maximum likelihood estimator by supposing a possibly misspecified model for error distribution. Accordingly, we provide test methodologies by extending the approaches in Cho and White (in: Chang Y, Fomby T, Park JY (eds) Advances in econometrics: essays in honor of Peter CB Phillips. Emerald Group Publishing Limited, West Yorkshire, 2014) and Cho and Phillips (J Econ 202:45–56, 2018a) to detect the influence of heteroskedastic and/or autocorrelated regression errors on the asymptotic covariance matrix. In particular, we establish a sequential testing procedure to achieve our goal. We affirm the theory on our test statistics through simulation and apply the test statistics to energy price growth rate data for illustrative purposes; here, we also apply our test methodology to test the fully correct model hypothesis.

Suggested Citation

  • Lijuan Huo & Jin Seo Cho, 2021. "Testing for the sandwich-form covariance matrix of the quasi-maximum likelihood estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 293-317, June.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:2:d:10.1007_s11749-020-00719-x
    DOI: 10.1007/s11749-020-00719-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-020-00719-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-020-00719-x?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
    ---><---

    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. Cho, Jin Seo & Kim, Tae-hwan & Shin, Yongcheol, 2015. "Quantile cointegration in the autoregressive distributed-lag modeling framework," Journal of Econometrics, Elsevier, vol. 188(1), pages 281-300.
    2. Jin Seo Cho & Halbert White, 2014. "Notations in "Testing the Equality of Two Positive-Definite Matrices with Application to Information Matrix Testing" by Cho and White (2014)," Working papers 2014rwp-67a, Yonsei University, Yonsei Economics Research Institute.
    3. Breusch, T S, 1978. "Testing for Autocorrelation in Dynamic Linear Models," Australian Economic Papers, Wiley Blackwell, vol. 17(31), pages 334-355, December.
    4. Serena Ng & Pierre Perron, 1996. "The Exact Error In Estimating The Spectral Density At The Origin," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(4), pages 379-408, July.
    5. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    6. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    7. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    8. Bai, Xiwen & Lam, Jasmine Siu Lee, 2019. "A copula-GARCH approach for analyzing dynamic conditional dependency structure between liquefied petroleum gas freight rate, product price arbitrage and crude oil price," Energy Economics, Elsevier, vol. 78(C), pages 412-427.
    9. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
    10. 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.
    11. Godfrey, Leslie G., 1978. "Testing for multiplicative heteroskedasticity," Journal of Econometrics, Elsevier, vol. 8(2), pages 227-236, October.
    12. Cho, Jin Seo & White, Halbert, 2011. "Generalized runs tests for the IID hypothesis," Journal of Econometrics, Elsevier, vol. 162(2), pages 326-344, June.
    13. Li, Yong & Yu, Jun & Zeng, Tao, 2018. "Specification tests based on MCMC output," Journal of Econometrics, Elsevier, vol. 207(1), pages 237-260.
    14. Jianqing Fan & Yuan Liao & Jiawei Yao, 2015. "Power Enhancement in High‐Dimensional Cross‐Sectional Tests," Econometrica, Econometric Society, vol. 83(4), pages 1497-1541, July.
    15. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    16. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    17. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    18. Xiaohong Chen & Norman R. Swanson (ed.), 2013. "Recent Advances and Future Directions in Causality, Prediction, and Specification Analysis," Springer Books, Springer, edition 127, number 978-1-4614-1653-1, June.
    19. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
    20. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2016. "Generalized Information Matrix Tests for Detecting Model Misspecification," Econometrics, MDPI, vol. 4(4), pages 1-24, November.
    21. P. M. Robinson, 1991. "Consistent Nonparametric Entropy-Based Testing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 437-453.
    22. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, May.
    23. Jin Seo Cho & Halbert White, 2014. "Testing the Equality of Two Positive-Definite Matrices with Application to Information Matrix Testing," Working papers 2014rwp-67, Yonsei University, Yonsei Economics Research Institute.
    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. Perera, Indeewara & Silvapulle, Mervyn J., 2023. "Bootstrap specification tests for dynamic conditional distribution models," Journal of Econometrics, Elsevier, vol. 235(2), pages 949-971.

    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. Lijuan Huo & Jin Seo Cho, 2019. "Testing for the Sandwich-Form Covariance Matrix Applied to Quasi-Maximum Likelihood Estimation Using Economic and Energy Price Growth Rates," Working papers 2019rwp-152, Yonsei University, Yonsei Economics Research Institute.
    2. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2019. "Consequences of Model Misspecification for Maximum Likelihood Estimation with Missing Data," Econometrics, MDPI, vol. 7(3), pages 1-27, September.
    3. Russell Davidson & Victoria Zinde‐Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(5), pages 1595-1631, December.
    4. Yongmiao Hong, 2013. "Serial Correlation and Serial Dependence," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    5. repec:wyi:journl:002087 is not listed on IDEAS
    6. Cho, Jin Seo & Phillips, Peter C.B., 2018. "Pythagorean generalization of testing the equality of two symmetric positive definite matrices," Journal of Econometrics, Elsevier, vol. 202(1), pages 45-56.
    7. José M. Belbute & Alfredo M. Pereira, 2021. "The Relationship between Consumption and CO 2 Emissions: Evidence for Portugal," Sustainability, MDPI, vol. 13(21), pages 1-16, November.
    8. Dragos Stefan Oprea & Elena Valentina Tilica, 2014. "Day-of-the-Week Effect in Post-Communist East European Stock Markets," International Journal of Academic Research in Accounting, Finance and Management Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Accounting, Finance and Management Sciences, vol. 4(3), pages 119-129, July.
    9. Adrian C. Darnell, 1994. "A Dictionary Of Econometrics," Books, Edward Elgar Publishing, number 118.
    10. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    11. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, January.
    12. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(1), pages 17-43, March.
    13. Aninday Banerjee & Markus Eberhardt & J James Reade, 2010. "Panel Estimation for Worriers," Discussion Papers 10-33, Department of Economics, University of Birmingham.
    14. James G. MacKinnon, 2012. "Thirty Years Of Heteroskedasticity-robust Inference," Working Paper 1268, Economics Department, Queen's University.
    15. Antonios ADAMOPOULOS, 2021. "Energy and economic growth. An empirical analysis," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(1(626), S), pages 151-166, Spring.
    16. Roberto Martínez-Espiñeira, 2007. "An Estimation of Residential Water Demand Using Co-Integration and Error Correction Techniques," Journal of Applied Economics, Taylor & Francis Journals, vol. 10(1), pages 161-184, May.
    17. Vadim Kufenko & Niels Geiger, 2017. "Stylized Facts of the Business Cycle: Universal Phenomenon, or Institutionally Determined?," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 13(2), pages 165-187, November.
    18. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January.
    19. Charles G. Renfro, 2009. "The Practice of Econometric Theory," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75571-5, July-Dece.
    20. Carla Norrlof & William C. Wohlforth, 2019. "Is US grand strategy self-defeating? Deep engagement, military spending and sovereign debt," Conflict Management and Peace Science, Peace Science Society (International), vol. 36(3), pages 227-247, May.
    21. Dragos Stefan Oprea, 2014. "The Halloween Effect Evidence from Romania," International Journal of Academic Research in Business and Social Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Business and Social Sciences, vol. 4(7), pages 463-471, July.

    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:spr:testjl:v:30:y:2021:i:2:d:10.1007_s11749-020-00719-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.