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

Clément Cerovecki, Christian Francq, Siegfried Hörmann, Jean Michel Zakoïan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)353-375
Number of pages23
JournalJournal of Econometrics
Issue number2
Publication statusPublished - 1 Apr 2019


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

ASJC Scopus subject areas

  • Economics and Econometrics


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