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Feasible Invertibility Conditions and Maximum Likelihood Estimation for Observation-Driven Models

Author

Listed:
  • Francisco Blasques

    (VU University Amsterdam, the Netherlands)

  • Paolo Gorgi

    (VU University Amsterdam, the Netherlands; University of Padua, Italy)

  • Siem Jan Koopman

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

  • Olivier Wintenberger

    (University of Copenhagen, Denmark; Sorbonne Universités, UPMC University Paris 06, France)

Abstract

Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used in practice to ensure the consistency of the maximum likelihood estimator for a wide class of observation-driven time series models. Our consistency results hold for both correctly specified and misspecified models. The practical relevance of the theory is highlighted in a set of empirical examples. We further obtain an asymptotic test and confidence bounds for the unfeasible “true” invertibility region of the parameter space.

Suggested Citation

  • Francisco Blasques & Paolo Gorgi & Siem Jan Koopman & Olivier Wintenberger, 2016. "Feasible Invertibility Conditions and Maximum Likelihood Estimation for Observation-Driven Models," Tinbergen Institute Discussion Papers 16-082/III, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20160082
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    References listed on IDEAS

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    1. Francisco Blasques & Paolo Gorgi & Siem Jan Koopman & Olivier Wintenberger, 2015. "A Note on “Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model”," Tinbergen Institute Discussion Papers 15-131/III, Tinbergen Institute.
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    8. Francisco Blasques & Siem Jan Koopman & Andre Lucas, 2014. "Maximum Likelihood Estimation for Score-Driven Models," Tinbergen Institute Discussion Papers 14-029/III, Tinbergen Institute, revised 23 Oct 2017.
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    12. 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.
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    Citations

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    Cited by:

    1. Harvey, A. & Palumbo, D., 2019. "Score-Driven Models for Realized Volatility," Cambridge Working Papers in Economics 1950, Faculty of Economics, University of Cambridge.
    2. Blazsek, Szabolcs & Escribano, Álvaro & Ayala, Astrid, 2019. "Score-driven time series models with dynamic shape : an application to the Standard & Poor's 500 index," UC3M Working papers. Economics 28133, Universidad Carlos III de Madrid. Departamento de Economía.
    3. Blazsek, Szabolcs & Escribano, Álvaro & Licht, Adrian, 2018. "Seasonal Quasi-Vector Autoregressive Models with an Application to Crude Oil Production and Economic Activity in the United States and Canada," UC3M Working papers. Economics 27484, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Luisa Bisaglia & Matteo Grigoletto, 2018. "A new time-varying model for forecasting long-memory series," Papers 1812.07295, arXiv.org.
    5. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    6. Blasques, F. & Gorgi, P. & Koopman, S.J., 2021. "Missing observations in observation-driven time series models," Journal of Econometrics, Elsevier, vol. 221(2), pages 542-568.
    7. Licht, Adrian & Escribano Saez, Alvaro & Blazsek, Szabolcs Istvan, 2020. "Prediction accuracy of bivariate score-driven risk premium and volatility filters: an illustration for the Dow Jones," UC3M Working papers. Economics 31339, Universidad Carlos III de Madrid. Departamento de Economía.
    8. Christian M. Hafner & Dimitra Kyriakopoulou, 2021. "Exponential-Type GARCH Models With Linear-in-Variance Risk Premium," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 589-603, March.
    9. Blazsek, Szabolcs & Licht, Adrian & Escribano, Álvaro, 2018. "Seasonality Detection in Small Samples using Score-Driven Nonlinear Multivariate Dynamic Location Models," UC3M Working papers. Economics 27483, Universidad Carlos III de Madrid. Departamento de Economía.
    10. Aknouche, Abdelhakim & Francq, Christian, 2019. "Two-stage weighted least squares estimator of the conditional mean of observation-driven time series models," MPRA Paper 97382, University Library of Munich, Germany.
    11. Babii, Andrii & Chen, Xi & Ghysels, Eric, 2019. "Commercial and Residential Mortgage Defaults: Spatial Dependence with Frailty," Journal of Econometrics, Elsevier, vol. 212(1), pages 47-77.
    12. Paolo Gorgi & Siem Jan Koopman, 2020. "Beta observation-driven models with exogenous regressors: a joint analysis of realized correlation and leverage effects," Tinbergen Institute Discussion Papers 20-004/III, Tinbergen Institute.
    13. Harvey, A. & Hurn, S. & Thiele, S., 2019. "Modeling directional (circular) time series," Cambridge Working Papers in Economics 1971, Faculty of Economics, University of Cambridge.
    14. Blazsek, Szabolcs & Escribano, Álvaro & Ayala, Astrid, 2019. "Maximum likelihood estimation of score-driven models with dynamic shape parameters : an application to Monte Carlo value-at-risk," UC3M Working papers. Economics 28638, Universidad Carlos III de Madrid. Departamento de Economía.

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    More about this item

    Keywords

    consistency; invertibility; maximum likelihood estimation; observation-driven models; stochastic recurrence equations;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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