Varying coefficient GARCH models

P. Cizek, V. Spokoiny

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review


This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. We consider varying–coefficient parametric models, such as ARCH and GARCH, whose coefficients may arbitrarily vary with time. This includes global parametric, smooth transition, and change–point models as special cases. The method is based on an adaptive pointwise selection of the largest interval of homogeneity with a given right–end point, which is obtained by a local change–point analysis.We construct locally adaptive volatility estimates that can perform this task and investigate them both from the theoretical point of view and by Monte Carlo simulations. Additionally, the proposed method is applied to stock–index series and shown to outperform the standard parametric GARCH model.
Original languageEnglish
Title of host publicationHandbook of Financial Time Series
EditorsT.G. Andersen, R.A. Davis, J.P. Kreis, T. Mikosch
Place of PublicationBerlin
PublisherSpringer Verlag
Publication statusPublished - 2009


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