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Functional GARCH models: The quasi-likelihood approach and its applications

Author

Listed:
  • Clément Cerovecki
  • 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, IP Paris - Institut Polytechnique de Paris)

  • Siegfried Hörmann
  • Jean-Michel Zakoïan

    (LFA - Laboratoire de Finance Assurance - Centre de Recherche en Économie et Statistique (CREST) - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique)

Abstract

The increasing availability of high frequency data has initiated many new research areas in statistics. Functional data analysis (FDA) is one such innovative approach towards modelling time series data. In FDA, densely observed data are transformed into curves and then each (random) curve is considered as one data object. A natural, but still relatively unexplored, context for FDA methods is related to financial data, where high-frequency trading currently takes a significant proportion of trading volumes. Recently, articles on functional versions of the famous ARCH and GARCH models have appeared. Due to their technical complexity, existing estimators of the underlying functional parameters are moment based—an approach which is known to be relatively inefficient in this context. In this paper, we promote an alternative quasi-likelihood approach, for which we derive consistency and asymptotic normality results. We support the relevance of our approach by simulations and illustrate its use by forecasting realised volatility of the S&P100 Index.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Clément Cerovecki & Christian Francq & Siegfried Hörmann & Jean-Michel Zakoïan, 2019. "Functional GARCH models: The quasi-likelihood approach and its applications," Post-Print hal-05417265, HAL.
    • Handle: RePEc:hal:journl:hal-05417265
    DOI: 10.1016/j.jeconom.2019.01.006
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    Cited by:

    1. Zouaoui Chikr-Elmezouar & Ali Laksaci & Ibrahim M. Almanjahie & Fatimah Alshahrani, 2025. "Nonparametric Estimation of Dynamic Value-at-Risk: Multifunctional GARCH Model Case," Mathematics, MDPI, vol. 13(12), pages 1-20, June.
    2. Lin, Boqiang & Wang, You, 2025. "Climate change and China's food security," Energy, Elsevier, vol. 318(C).
    3. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2020. "Forecasting value at risk with intra-day return curves," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1023-1038.
    4. Horváth, Lajos & Rice, Gregory & Zhao, Yuqian, 2022. "Change point analysis of covariance functions: A weighted cumulative sum approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. Yicong Lin & André Lucas, 2025. "Functional Location-Scale Models with Robust Observation-Driven Dynamics," Tinbergen Institute Discussion Papers 25-027/III, Tinbergen Institute.
    6. Baye Matar Kandji, 2023. "On the growth rate of superadditive processes and the stability of functional GARCH models," Working Papers 2023-07, Center for Research in Economics and Statistics.
    7. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2021. "Testing serial independence with functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 603-629, September.
    8. Gong, Xu & Wang, You & Lin, Boqiang, 2021. "Assessing dynamic China’s energy security: Based on functional data analysis," Energy, Elsevier, vol. 217(C).
    9. Chun, Dohyun & Cho, Hoon & Ryu, Doojin, 2023. "Discovering the drivers of stock market volatility in a data-rich world," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 82(C).
    10. Dohyun Chun & Donggyu Kim, 2022. "State Heterogeneity Analysis of Financial Volatility using high‐frequency Financial Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 105-124, January.
    11. Mihyun Kim & Piotr Kokoszka & Gregory Rice, 2024. "Projection-based white noise and goodness-of-fit tests for functional time series," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 693-724, October.
    12. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2023. "Exploring volatility of crude oil intraday return curves: A functional GARCH-X model," Journal of Commodity Markets, Elsevier, vol. 32(C).
    13. Alexander Aue & Sebastian Kuhnert & Gregory Rice & Jeremy VanderDoes, 2026. "An operator-level ARCH Model," Papers 2603.10272, arXiv.org, revised Mar 2026.
    14. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2021. "Exploring volatility of crude oil intra-day return curves: a functional GARCH-X Model," MPRA Paper 109231, University Library of Munich, Germany.

    More about this item

    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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