IDEAS home Printed from https://ideas.repec.org/a/bla/obuest/v70y2008is1p867-893.html
   My bibliography  Save this article

Model Selection for Nested and Overlapping Nonlinear, Dynamic and Possibly Mis‐specified Models

Author

Listed:
  • Massimiliano Marcellino
  • Barbara Rossi

Abstract

The literature on model comparison often requires the assumption that the true conditional distribution corresponds to that of one of the competing models. This strong assumption has been extended by the notion of encompassing and in likelihood based model comparisons. This paper takes the latter approach and develops tests for the comparison of competing nonlinear dynamic models, focusing on the nested and overlaping cases. The null hypothesis is that the models are equally close to the data generating process (DGP), according to a certain measure of closeness. The alternative is that one model is closer to the DGP. The models can be correctly specified or not. Their parameters can be estimated by a variety of methods, including (pseudo) maximum likelihood and ordinary least squares. The tests are symmetric and directional. Their asymptotic distribution under the null is either normal or a weighted sum of chi‐squared distributions, depending on the nesting characteristics of the competing models. The comparison of nested AR models, and of nested ARMA models with GARCH errors and exogenous forcing variables (ARMAX‐GARCH) are discussed as examples.

Suggested Citation

  • Massimiliano Marcellino & Barbara Rossi, 2008. "Model Selection for Nested and Overlapping Nonlinear, Dynamic and Possibly Mis‐specified Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 867-893, December.
    • Handle: RePEc:bla:obuest:v:70:y:2008:i:s1:p:867-893
    DOI: 10.1111/j.1468-0084.2008.00534.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1468-0084.2008.00534.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1468-0084.2008.00534.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
    ---><---

    References listed on IDEAS

    as
    1. Gouriéroux, Christian & Monfort, Alain, 1995. "Testing, Encompassing, and Simulating Dynamic Econometric Models," Econometric Theory, Cambridge University Press, vol. 11(2), pages 195-228, February.
    2. Hendry, David F. & Richard, Jean-Francois, 1982. "On the formulation of empirical models in dynamic econometrics," Journal of Econometrics, Elsevier, vol. 20(1), pages 3-33, October.
    3. Pesaran, M H & Deaton, Angus S, 1978. "Testing Non-Nested Nonlinear Regression Models," Econometrica, Econometric Society, vol. 46(3), pages 677-694, May.
    4. Gourieroux, C. & Monfort, A., 1989. "A General Framework for Testing a Null Hypothesis in a “Mixed” Form," Econometric Theory, Cambridge University Press, vol. 5(1), pages 63-82, April.
    5. 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.
    6. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    7. 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.
    8. Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
    9. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, January.
    10. Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-678, May.
    11. Sin, Chor-Yiu & White, Halbert, 1996. "Information criteria for selecting possibly misspecified parametric models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 207-225.
    12. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    13. Hidetoshi Shimodaira, 1998. "An Application of Multiple Comparison Techniques to Model Selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(1), pages 1-13, March.
    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. Gospodinov, Nikolay & Kan, Raymond & Robotti, Cesare, 2013. "Chi-squared tests for evaluation and comparison of asset pricing models," Journal of Econometrics, Elsevier, vol. 173(1), pages 108-125.
    2. Mayer, Walter J. & Liu, Feng & Dang, Xin, 2017. "Improving the power of the Diebold–Mariano–West test for least squares predictions," International Journal of Forecasting, Elsevier, vol. 33(3), pages 618-626.
    3. Christophe Bontemps & Grayham E. Mizon, 2008. "Encompassing: Concepts and Implementation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 721-750, December.
    4. Lavergne, Pascal & Bertail, Patrice, 2020. "Bootstrapping Quasi Likelihood Ratio Tests under Misspecification," TSE Working Papers 20-1102, Toulouse School of Economics (TSE).
    5. Bu Ruijun & Cheng Jie & Hadri Kaddour, 2017. "Specification analysis in regime-switching continuous-time diffusion models for market volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(1), pages 65-80, February.
    6. Francesco Battaglia & Mattheos Protopapas, 2012. "An analysis of global warming in the Alpine region based on nonlinear nonstationary time series models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 315-334, August.

    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. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
    2. Zhipeng Liao & Xiaoxia Shi, 2020. "A nondegenerate Vuong test and post selection confidence intervals for semi/nonparametric models," Quantitative Economics, Econometric Society, vol. 11(3), pages 983-1017, July.
    3. Susanne M. Schennach & Daniel Wilhelm, 2017. "A Simple Parametric Model Selection Test," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1663-1674, October.
    4. Gouriéroux, Christian, 1994. "Modèles économétriques : utilisation et interprétation (les)," CEPREMAP Working Papers (Couverture Orange) 9423, CEPREMAP.
    5. Chen, Yi-Ting & Kuan, Chung-Ming, 2002. "The pseudo-true score encompassing test for non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 106(2), pages 271-295, February.
    6. Arie Preminger & Shinichi Sakata, 2007. "A model selection method for S-estimation," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 294-319, July.
    7. Oh, Dong Hwan & Patton, Andrew J., 2016. "High-dimensional copula-based distributions with mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 349-366.
    8. PREMINGER, Arie & HAFNER, Christian, 2006. "Deciding between GARCH and stochastic volatility via strong decision rules," LIDAM Discussion Papers CORE 2006042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Jang, Tae-Seok, 2012. "Structural estimation of the New-Keynesian Model: a formal test of backward- and forward-looking expectations," MPRA Paper 40278, University Library of Munich, Germany.
    10. repec:bgu:wpaper:0603 is not listed on IDEAS
    11. Tae-Seok Jang, 2012. "Structural Estimation of the New-Keynesian Model: A Formal Test of Backward- and Forward-Looking Behavior," Advances in Econometrics, in: DSGE Models in Macroeconomics: Estimation, Evaluation, and New Developments, pages 421-467, Emerald Group Publishing Limited.
    12. Jang, Tae-Seok, 2012. "Structural estimation of the New-Keynesian Model: a formal test of backward- and forward-looking expectations," MPRA Paper 39669, University Library of Munich, Germany.
    13. Gourieroux, C. & Monfort, A., 2021. "Model risk management: Valuation and governance of pseudo-models," Econometrics and Statistics, Elsevier, vol. 17(C), pages 1-22.
    14. Coenen, Gunter & Wieland, Volker, 2005. "A small estimated euro area model with rational expectations and nominal rigidities," European Economic Review, Elsevier, vol. 49(5), pages 1081-1104, July.
    15. Timo Dimitriadis & iaochun Liu & Julie Schnaitmann, 2023. "Encompassing Tests for Value at Risk and Expected Shortfall Multistep Forecasts Based on Inference on the Boundary," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 412-444.
    16. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    17. Dimitriadis, Timo & Schnaitmann, Julie, 2021. "Forecast encompassing tests for the expected shortfall," International Journal of Forecasting, Elsevier, vol. 37(2), pages 604-621.
    18. Corradi, Valentina & Fosten, Jack & Gutknecht, Daniel, 2024. "Predictive ability tests with possibly overlapping models," Journal of Econometrics, Elsevier, vol. 241(1).
    19. Adrian C. Darnell, 1994. "A Dictionary Of Econometrics," Books, Edward Elgar Publishing, number 118.
    20. West, Kenneth D., 2001. "Encompassing tests when no model is encompassing," Journal of Econometrics, Elsevier, vol. 105(1), pages 287-308, November.
    21. Xiaoxia Shi, 2015. "A nondegenerate Vuong test," Quantitative Economics, Econometric Society, vol. 6(1), pages 85-121, March.

    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:obuest:v:70:y:2008:i:s1:p:867-893. 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/sfeixuk.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.