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Unconditional pseudo-maximum likelihood and adaptive estimation in the presence of conditional heterogeneity of unknown form

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  • Douglas Hodgson

Abstract

We consider parametric non-linear regression models with additive innovations which are serially uncorrelated but not necessarily independent, and consider the consequences of maximum likelihood and related one-step iterative estimation when the innovations are treated as being iid from their unconditional density. We find that the estimators' asymptotic covariance matrices will generally differ from those that would obtain if the errors actually were iid, except for the special case of strictly exogenous regressors. One important application of these results is to analysis of the properties of adaptive estimators, which employ nonparametric kernel estimates of the unconditional density of the disturbances in the construction of one-step iterative estimators. In the presence of strictly exogenous regressors, adaptive estimators are found to be asymptotically equivalent to the one-step iterative estimators that use the correct unconditional density. We illustrate our results through a brief Monte Carlo study.

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  • Douglas Hodgson, 2000. "Unconditional pseudo-maximum likelihood and adaptive estimation in the presence of conditional heterogeneity of unknown form," Econometric Reviews, Taylor & Francis Journals, vol. 19(2), pages 175-206.
    • Handle: RePEc:taf:emetrv:v:19:y:2000:i:2:p:175-206
    DOI: 10.1080/07474930008800467
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    Cited by:

    1. Douglas J. Hodgson & Oliver Linton & Keith Vorkink, 2004. "Testing Forward Exchange Rate Unbiasedness Efficiently: A Semiparametric Approach," Journal of Applied Economics, Taylor & Francis Journals, vol. 7(1), pages 325-353, May.
    2. Fiorentini, Gabriele & Sentana, Enrique, 2021. "New testing approaches for mean–variance predictability," Journal of Econometrics, Elsevier, vol. 222(1), pages 516-538.
    3. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
    4. Douglas Hodgson, 2011. "Age–price profiles for Canadian painters at auction," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 35(4), pages 287-308, November.
    5. Keith Vorkink & Douglas J. Hodgson & Oliver Linton, 2002. "Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 617-639.
    6. Gabriele Fiorentini & Enrique Sentana, 2007. "On the Efficiency and Consistency of Likelihood Estimation in Multivariate Conditionally Heteroskedastic Dynamic Regression Models," Working Papers wp2007_0713, CEMFI.
    7. Douglas Hodgson, 2002. "Semiparametric Efficient Estimation of the Mean of a Time Series in the Presence of Conditional Heterogeneity of Unknown Form," Cahiers de recherche CREFE / CREFE Working Papers 146, CREFE, Université du Québec à Montréal.
    8. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 65-101, November.
    9. repec:rim:rimwps:38-07 is not listed on IDEAS

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