Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models

P. Cizek, W. Haerdle, V. Spokoiny

Research output: Contribution to journalArticleScientificpeer-review

Abstract

This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. Our general, local parametric approach particularly applies to general varying-coefficient parametric models, such as GARCH, whose coefficients may arbitrarily vary with time. Global parametric, smooth transition and change-point models are special cases. The method is based on an adaptive pointwise selection of the largest interval of homogeneity with a given right-end point by a local change-point analysis. We construct locally adaptive estimates that can perform this task and investigate them both from the theoretical point of view and by Monte Carlo simulations. In the particular case of GARCH estimation, the proposed method is applied to stock-index series and is shown to outperform the standard parametric GARCH model.
Original languageEnglish
Pages (from-to)248-271
JournalThe Econometrics Journal
Volume12
Issue number2
Publication statusPublished - 2009

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Adaptive estimation
Conditional heteroscedasticity
Coefficients
Change point
Generalized autoregressive conditional heteroscedasticity
Parametric model
Homogeneity
Smooth transition
Monte Carlo simulation
Stationarity
GARCH model
Financial time series
Stock index

Cite this

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title = "Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models",
abstract = "This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. Our general, local parametric approach particularly applies to general varying-coefficient parametric models, such as GARCH, whose coefficients may arbitrarily vary with time. Global parametric, smooth transition and change-point models are special cases. The method is based on an adaptive pointwise selection of the largest interval of homogeneity with a given right-end point by a local change-point analysis. We construct locally adaptive estimates that can perform this task and investigate them both from the theoretical point of view and by Monte Carlo simulations. In the particular case of GARCH estimation, the proposed method is applied to stock-index series and is shown to outperform the standard parametric GARCH model.",
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Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models. / Cizek, P.; Haerdle, W.; Spokoiny, V.

In: The Econometrics Journal, Vol. 12, No. 2, 2009, p. 248-271.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models

AU - Cizek, P.

AU - Haerdle, W.

AU - Spokoiny, V.

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PY - 2009

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AB - This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. Our general, local parametric approach particularly applies to general varying-coefficient parametric models, such as GARCH, whose coefficients may arbitrarily vary with time. Global parametric, smooth transition and change-point models are special cases. The method is based on an adaptive pointwise selection of the largest interval of homogeneity with a given right-end point by a local change-point analysis. We construct locally adaptive estimates that can perform this task and investigate them both from the theoretical point of view and by Monte Carlo simulations. In the particular case of GARCH estimation, the proposed method is applied to stock-index series and is shown to outperform the standard parametric GARCH model.

M3 - Article

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SP - 248

EP - 271

JO - The Econometrics Journal

JF - The Econometrics Journal

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