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

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  • 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
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    References listed on IDEAS

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    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.

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