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Quasi score-driven models

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  • Blasques, F.
  • Francq, Christian
  • Laurent, Sébastien

Abstract

This paper introduces the class of quasi score-driven (QSD) models. This new class inherits and extends the basic ideas behind the development of score-driven (SD) models and addresses a number of unsolved issues in the score literature. In particular, the new class of models (i) generalizes many existing models, including SD models, (ii) disconnects the updating equation from the log-likelihood implied by the conditional density of the observations, (iii) allows testing of the assumptions behind SD models that link the updating equation of the conditional moment to the conditional density, (iv) allows QML estimation of SD models, (v) and allows explanatory variables to enter the updating equation. We establish the asymptotic properties of the QLE, QMLE and MLE of the proposed QSD model as well as the likelihood ratio and Lagrange multiplier test statistics. The finite sample properties are studied by means of an extensive Monte Carlo study. Finally, we show the empirical relevance of QSD models to estimate the conditional variance of 400 US stocks.

Suggested Citation

  • Blasques, F. & Francq, Christian & Laurent, Sébastien, 2023. "Quasi score-driven models," Journal of Econometrics, Elsevier, vol. 234(1), pages 251-275.
    • Handle: RePEc:eee:econom:v:234:y:2023:i:1:p:251-275
    DOI: 10.1016/j.jeconom.2021.12.005
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    Cited by:

    1. Francq, Christian & Zakoian, Jean-Michel, 2024. "Finite moments testing in a general class of nonlinear time series models," MPRA Paper 121193, University Library of Munich, Germany.
    2. Eric A. Beutner & Yicong Lin & Andre Lucas, 2023. "Consistency, distributional convergence, and optimality of score-driven filters," Tinbergen Institute Discussion Papers 23-051/III, Tinbergen Institute.
    3. Blasques, F. & Francq, Christian & Laurent, Sébastien, 2024. "Autoregressive conditional betas," Journal of Econometrics, Elsevier, vol. 238(2).
    4. van Os, Bram & van Dijk, Dick, 2024. "Accelerating peak dating in a dynamic factor Markov-switching model," International Journal of Forecasting, Elsevier, vol. 40(1), pages 313-323.
    5. Ramon de Punder & Timo Dimitriadis & Rutger-Jan Lange, 2024. "Kullback-Leibler-based characterizations of score-driven updates," Papers 2408.02391, arXiv.org, revised Sep 2024.
    6. Yinhao Wu & Ping He, 2024. "The continuous-time limit of quasi score-driven volatility models," Papers 2409.14734, arXiv.org.
    7. Francisco Blasques & Noah Stegehuis, 2024. "A Score-Driven Filter for Causal Regression Models with Time- Varying Parameters and Endogenous Regressors," Tinbergen Institute Discussion Papers 24-016/III, Tinbergen Institute.

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    More about this item

    Keywords

    Score-driven models; GARCH; Fat-tails; Asymmetry; QLE; QMLE;
    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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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