Confidence bands in nonparametric time series regression
The Annals of Statistics · 2008 · Volume 36 · Issue 4
Abstract
We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct. The imposed dependence structure allows applications in many linear and nonlinear auto-regressive processes. The results are applied to the S&P 500 Index data.
Keywords
62G08, 62G15, long-range dependence, model validation, Moderate deviation, nonlinear time series, Nonparametric regression, short-range dependence
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