Bootstrapping nonparametric estimators of the volatility function

We prove that the bootstrap works in a quite general sense for nonparametric estimators of the trend and volatility functions in nonlinear AR-ARCH-models. We illustrate the implications of this result by constructing uniform confidence bands for those functions based on localized nonparametric funct...

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Bibliographic Details
Published in:Journal of econometrics 2004, Vol.118 (1), p.189-218
Main Authors: Franke, Jürgen, Neumann, Michael H., Stockis, Jean-Pierre
Format: Article
Language:English
Subjects:
ARCH process
Bootstrap
Confidence band
Econometric models
Econometrics
Economic methodology
Economic models
Economic theory
Estimation
Mathematical economics
Nonparametric estimates
Rates of return
Studies
Time series
Volatility
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Summary:We prove that the bootstrap works in a quite general sense for nonparametric estimators of the trend and volatility functions in nonlinear AR-ARCH-models. We illustrate the implications of this result by constructing uniform confidence bands for those functions based on localized nonparametric function estimates. As an application, we study the trend and volatility of a time series of high frequency foreign exchange rate returns.
ISSN:0304-4076
1872-6895
DOI:10.1016/S0304-4076(03)00140-4