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

Author

Listed:
  • Francisco Blasques

    (VU University Amsterdam, the Netherlands)

  • Siem Jan Koopman

    (VU University Amsterdam, the Netherlands)

  • André Lucas

    (VU University Amsterdam, the Netherlands, 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.

Suggested Citation

  • Francisco Blasques & Siem Jan Koopman & André Lucas, 2014. "Maximum Likelihood Estimation for correctly Specified Generalized Autoregressive Score Models: Feedback Effects, Contraction Conditions and Asymptotic Properties," Tinbergen Institute Discussion Papers 14-074/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20140074
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    References listed on IDEAS

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    6. Blasques, Francisco & van Brummelen, Janneke & Koopman, Siem Jan & Lucas, André, 2022. "Maximum likelihood estimation for score-driven models," Journal of Econometrics, Elsevier, vol. 227(2), pages 325-346.
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    8. André Lucas & Bernd Schwaab & Xin Zhang, 2014. "Conditional Euro Area Sovereign Default Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 271-284, April.
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    12. 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, August.
    13. 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.
    14. 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, vol. 40(4), pages 846-867, December.
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    16. Francisco Blasques & Siem Jan Koopman & Andre Lucas, 2012. "Stationarity and Ergodicity of Univariate Generalized Autoregressive Score Processes," Tinbergen Institute Discussion Papers 12-059/4, Tinbergen Institute.
    17. Andres, Philipp, 2014. "Maximum likelihood estimates for positive valued dynamic score models; The DySco package," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 34-42.
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    Citations

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    Cited by:

    1. Roman Frydman & Søren Johansen & Anders Rahbek & Morten Nyboe Tabor, 2017. "The Qualitative Expectations Hypothesis: Model Ambiguity, Consistent Representations of Market Forecasts, and Sentiment," CREATES Research Papers 2017-23, Department of Economics and Business Economics, Aarhus University.
    2. Mohamed Chikhi & Claude Diebolt & Tapas Mishra, 2019. "Measuring Success: Does Predictive Ability of an Asset Price Rest in 'Memory'? Insights from a New Approach," Working Papers 11-19, Association Française de Cliométrie (AFC).
    3. Mohamed CHIKHI & Claude DIEBOLT & Tapas MISHRA, 2019. "Memory that Drives! New Insights into Forecasting Performance of Stock Prices from SEMIFARMA-AEGAS Model," Working Papers 07-19, Association Française de Cliométrie (AFC).
    4. Hoeltgebaum, Henrique & Borenstein, Denis & Fernandes, Cristiano & Veiga, Álvaro, 2021. "A score-driven model of short-term demand forecasting for retail distribution centers," Journal of Retailing, Elsevier, vol. 97(4), pages 715-725.
    5. Olusanya E. Olubusoye & OlaOluwa S. Yaya, 2016. "Time series analysis of volatility in the petroleum pricing markets: the persistence, asymmetry and jumps in the returns series," OPEC Energy Review, Organization of the Petroleum Exporting Countries, vol. 40(3), pages 235-262, September.
    6. Francisco Blasques & Christian Francq & Sébastien Laurent, 2020. "A New Class of Robust Observation-Driven Models," Tinbergen Institute Discussion Papers 20-073/III, Tinbergen Institute.
    7. Mohamed CHIKHI & Claude DIEBOLT & Tapas MISHRA, 2019. "Does Predictive Ability of an Asset Price Rest in 'Memory'? Insights from a New Approach," Working Papers of BETA 2019-43, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    8. Roman Matkovskyy, 2019. "Extremal Economic (Inter)Dependence Studies: A Case of the Eastern European Countries," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(3), pages 667-698, September.

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    More about this item

    Keywords

    Observation-driven models; stochastic recurrence equations; contraction conditions; invertibility; stationarity; ergodicity; generalized autoregressive score models;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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