Adaptive Pointwise Estimation in Time-Inhomogeneous Time-Series Models

CentER Discussion Paper Series No. 2007-35

46 Pages Posted: 18 Jun 2007

See all articles by Pavel Cizek

Pavel Cizek

Tilburg University - Department of Econometrics & Operations Research

Wolfgang Karl Härdle

Blockchain Research Center Humboldt-Universität zu Berlin; Charles University; National Yang Ming Chiao Tung University; Asian Competitiveness Institute

V. Spokoiny

Weierstras Institute for Applied Analysis and Stochastics (WIAS)

Date Written: May 2007

Abstract

This paper offers a new method for estimation and forecasting of the linear and nonlinear time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient parametric models, such as AR or GARCH, whose coefficients may arbitrarily vary with time. Global parametric, smooth transition, and changepoint 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.

Keywords: adaptive pointwise estimation, autoregressive models, conditional heteroscedasticity models, local time-homogeneity

JEL Classification: C13, C14, C22

Suggested Citation

Cizek, Pavel and Härdle, Wolfgang Karl and Spokoiny, Vladimir, Adaptive Pointwise Estimation in Time-Inhomogeneous Time-Series Models (May 2007). CentER Discussion Paper Series No. 2007-35, Available at SSRN: https://ssrn.com/abstract=993368 or http://dx.doi.org/10.2139/ssrn.993368

Pavel Cizek (Contact Author)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Wolfgang Karl Härdle

Blockchain Research Center Humboldt-Universität zu Berlin ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

National Yang Ming Chiao Tung University ( email )

No. 1001, Daxue Rd. East Dist.
Hsinchu City 300093
Taiwan

Asian Competitiveness Institute ( email )

Singapore

Vladimir Spokoiny

Weierstras Institute for Applied Analysis and Stochastics (WIAS) ( email )

Mohrenstr. 39
Berlin, 10117
Germany

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