Adaptive Pointwise Estimation in Time-Inhomogeneous Time-Series Models

P. Cizek, W. Haerdle, V. Spokoiny

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages46
Volume2007-35
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper
Volume2007-35

Keywords

  • adaptive pointwise estimation
  • autoregressive models
  • conditional heteroscedasticity models
  • local time-homogeneity

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  • Cite this

    Cizek, P., Haerdle, W., & Spokoiny, V. (2007). Adaptive Pointwise Estimation in Time-Inhomogeneous Time-Series Models. (CentER Discussion Paper; Vol. 2007-35). Econometrics.