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

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  • Cerovecki, Clément
  • Francq, Christian
  • Hormann, Siegfried
  • Zakoian, Jean-Michel

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.

Suggested Citation

  • Cerovecki, Clément & Francq, Christian & Hormann, Siegfried & Zakoian, Jean-Michel, 2018. "Functional GARCH models: the quasi-likelihood approach and its applications," MPRA Paper 83990, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:83990
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    Cited by:

    1. 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.
    2. 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).
    3. 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.
    4. 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.
    5. Gong, Xu & Wang, You & Lin, Boqiang, 2021. "Assessing dynamic China’s energy security: Based on functional data analysis," Energy, Elsevier, vol. 217(C).
    6. 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).
    7. Dohyun Chun & Donggyu Kim, 2021. "State Heterogeneity Analysis of Financial Volatility Using High-Frequency Financial Data," Papers 2102.13404, arXiv.org.
    8. 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).
    9. 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.
    10. 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.

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    More about this item

    Keywords

    Functional time series; High-frequency volatility models; Intraday returns; Functional QMLE; Stationarity of functional GARCH;
    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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