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Quasi score-driven models

Author

Listed:
  • F. Blasques

    (VU University Medical Center [Amsterdam])

  • Christian Francq

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Sébastien Laurent

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

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

  • F. Blasques & Christian Francq & Sébastien Laurent, 2023. "Quasi score-driven models," Post-Print hal-04069143, HAL.
    • Handle: RePEc:hal:journl:hal-04069143
    DOI: 10.1016/j.jeconom.2021.12.005
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-04069143v1
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    Cited by:

    1. Blasques, F. & Francq, Christian & Laurent, Sébastien, 2024. "Autoregressive conditional betas," Journal of Econometrics, Elsevier, vol. 238(2).
    2. 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.
    3. Thomas Giroux & Julien Royer & Olivier David Zerbib, 2024. "Empirical Asset Pricing with Score-Driven Conditional Betas," Post-Print hal-05415058, HAL.
    4. Francisco Blasques & Janneke van Brummelen & Paolo Gorgi & Siem Jan Koopman, 2024. "Robust Multivariate Observation-Driven Filtering for a Common Stochastic Trend: Theory and Application," Tinbergen Institute Discussion Papers 24-062/III, Tinbergen Institute.
    5. 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.
    6. 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.
    7. Artemova, Mariia, 2025. "An order-invariant score-driven dynamic factor model," Journal of Econometrics, Elsevier, vol. 251(C).
    8. Yinhao Wu & Ping He, 2024. "The continuous-time limit of quasi score-driven volatility models," Papers 2409.14734, arXiv.org, revised Jun 2025.
    9. 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.
    10. Antonis Demos, 2025. "Statistical Properties of Two Asymmetric Stochastic Volatility in Power Mean Models," DEOS Working Papers 2546, Athens University of Economics and Business.
    11. Pierluigi Vallarino, 2024. "Dynamic kernel models," Tinbergen Institute Discussion Papers 24-082/III, Tinbergen Institute.
    12. 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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    Keywords

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    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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