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A General Framework for Observation Driven Time-Varying Parameter Models

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  • Drew Creal
  • Siem Jan Koopman
  • Andre Lucas

Abstract

We propose a new class of observation driven time series models that we refer to as Generalized Autoregressive Score (GAS) models. The driving mechanism of the GAS model is the scaled likelihood score. This provides a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, autoregressive conditional duration, autoregressive conditional intensity and single source of error models. In addition, the GAS specification gives rise to a wide range of new observation driven models. Examples include non-linear regression models with time-varying parameters, observation driven analogues of unobserved components time series models, multivariate point process models with time-varying parameters and pooling restrictions, new models for time-varying copula functions and models for time-varying higher order moments. We study the properties of GAS models and provide several non-trivial examples of their application.

Suggested Citation

  • Drew Creal & Siem Jan Koopman & Andre Lucas, 2009. "A General Framework for Observation Driven Time-Varying Parameter Models," Global COE Hi-Stat Discussion Paper Series gd08-038, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hst:ghsdps:gd08-038
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    Cited by:

    1. David E. Allen & Michael McAleer & Marcel Scharth, 2014. "Asymmetric Realized Volatility Risk," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 7(2), pages 1-30, June.
    2. Francisco Blasques & Siem Jan Koopman & André Lucas, 2014. "Information Theoretic Optimality of Observation Driven Time Series Models," Tinbergen Institute Discussion Papers 14-046/III, Tinbergen Institute.
    3. Francq, Christian & Zakoian, Jean-Michel, 2021. "Local asymptotic normality of general conditionally heteroskedastic and score-driven time-series models," MPRA Paper 106542, University Library of Munich, Germany.
    4. Hendrych, R. & Cipra, T., 2016. "On conditional covariance modelling: An approach using state space models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 304-317.
    5. Neil Shephard, 2013. "Martingale unobserved component models," Economics Series Working Papers 644, University of Oxford, Department of Economics.
    6. Delle Monache, Davide & Petrella, Ivan & Venditti, Fabrizio, 2019. "Price Dividend Ratio and Long-Run Stock Returns: a Score Driven State Space Model," CEPR Discussion Papers 14107, C.E.P.R. Discussion Papers.
    7. Hans Manner & Olga Reznikova, 2012. "A Survey on Time-Varying Copulas: Specification, Simulations, and Application," Econometric Reviews, Taylor & Francis Journals, vol. 31(6), pages 654-687, November.
    8. David E. Allen & Michael McAleer & Marcel Scharth, 2009. "Realized Volatility Risk," CARF F-Series CARF-F-197, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2010.
    9. Francisco Blasques & Vladim'ir Hol'y & Petra Tomanov'a, 2018. "Zero-Inflated Autoregressive Conditional Duration Model for Discrete Trade Durations with Excessive Zeros," Papers 1812.07318, arXiv.org, revised Apr 2020.
    10. Marco Bazzi & Francisco Blasques & Siem Jan Koopman & Andre Lucas, 2017. "Time-Varying Transition Probabilities for Markov Regime Switching Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(3), pages 458-478, May.
    11. Julia Kielmann & Hans Manner & Aleksey Min, 2021. "Stock Market Returns and Oil Price Shocks: A CoVaR Analysis based on Dynamic Vine Copula Models," Graz Economics Papers 2021-01, University of Graz, Department of Economics.
    12. Giuseppe Buccheri & Giacomo Bormetti & Fulvio Corsi & Fabrizio Lillo, 2018. "A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: an Application to High-Frequency Covariance Dynamics," Papers 1803.04894, arXiv.org, revised Mar 2019.
    13. Tsyplakov, Alexander, 2015. "Quasifiltering for time-series modeling," MPRA Paper 66453, University Library of Munich, Germany.
    14. Neves, César & Fernandes, Cristiano & Hoeltgebaum, Henrique, 2017. "Five different distributions for the Lee–Carter model of mortality forecasting: A comparison using GAS models," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 48-57.
    15. Andres, P. & Harvey, A., 2012. "The Dyanamic Location/Scale Model: with applications to intra-day financial data," Cambridge Working Papers in Economics 1240, Faculty of Economics, University of Cambridge.
    16. Zhang, Yi & Cheng, Chuntian & Cao, Rui & Li, Gang & Shen, Jianjian & Wu, Xinyu, 2021. "Multivariate probabilistic forecasting and its performance’s impacts on long-term dispatch of hydro-wind hybrid systems," Applied Energy, Elsevier, vol. 283(C).
    17. Xin Zhang & Drew Creal & Siem Jan Koopman & Andre Lucas, 2011. "Modeling Dynamic Volatilities and Correlations under Skewness and Fat Tails," Tinbergen Institute Discussion Papers 11-078/2/DSF22, Tinbergen Institute.
    18. Harvey, Andrew & Sucarrat, Genaro, 2014. "EGARCH models with fat tails, skewness and leverage," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 320-338.

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    More about this item

    Keywords

    dynamic models; time-varying parameters; non-linearity; exponential family; marked point processes; copulas;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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