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Maximum Likelihood Estimation for Correctly Specified Generalized Autoregressive Score Models: Feedback Effects, Contraction Conditions and Asymptotic Properties

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  • Francisco Blasques

    (VU University Amsterdam)

  • Siem Jan Koopman

    (VU University Amsterdam, the Netherlands)

  • and André Lucas

    (VU University Amsterdam, the Netherlands, and Aarhus University, Denmark)

Abstract

The strong consistency and asymptotic normality of the maximum likelihood estimator in observation-driven models usually requires the study of the model both as a filter for the time-varying parameter and as a data generating process (DGP) for observed data. The probabilistic properties of the filter can be substantially different from those of the DGP. This difference is particularly relevant for recently developed time varying parameter models. We establish new conditions under which the dynamic properties of the true time varying parameter as well as of its filtered counterpart are both well-behaved and We only require the verification of one rather than two sets of conditions. In particular, we formulate conditions under which the (local) invertibility of the model follows directly from the stable behavior of the true time varying parameter. We use these results to prove the local strong consistency and asymptotic normality of the maximum likelihood estimator. To illustrate the results, we apply the theory to a number of empirically relevant models.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 14-074/III.

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Date of creation: 20 Jun 2014
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Handle: RePEc:dgr:uvatin:20140074

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Web page: http://www.tinbergen.nl

Related research

Keywords: Observation-driven models; stochastic recurrence equations; contraction conditions; invertibility; stationarity; ergodicity; generalized autoregressive score models;

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  1. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  2. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, Econometric Society, vol. 64(3), pages 575-96, May.
  3. Olivier Wintenberger, 2013. "Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 846-867, December.
  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  5. Konstantinos Fokianos & Anders Rahbek & Dag Tjøstheim, 2008. "Poisson Autoregression," Discussion Papers 08-35, University of Copenhagen. Department of Economics, revised Dec 2008.
  6. Drew Creal & Siem Jan Koopman & André Lucas, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 29(4), pages 552-563, October.
  7. Richard A. Davis, 2003. "Observation-driven models for Poisson counts," Biometrika, Biometrika Trust, Biometrika Trust, vol. 90(4), pages 777-790, December.
  8. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9781107630024.
  9. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, 08.
  10. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521574464.
  11. Wintenberger, Olivier, 2013. "Continuous invertibility and stable QML estimation of the EGARCH(1,1) model," MPRA Paper 46027, University Library of Munich, Germany.
  12. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, Econometric Society, vol. 66(5), pages 1127-1162, September.
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