Simultaneous nonparametric inference of time series

Details Simultaneous nonparametric inference of time series Simultaneous nonparametric inference of time series

2010-10-20

arxiv.org/abs/1010.4182v1

Annals of Statistics 2010, Vol. 38, No. 4, 2388-2421

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS789 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS789

We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and regression estimates are asymptotically Gumbel. Our results substantially generalize earlier ones which were obtained under independence or beta mixing assumptions. The asymptotic results can be applied to assess patterns of marginal densities or regression functions via the construction of simultaneous confidence bands for which one can perform goodness-of-fit tests. As an application, we construct simultaneous confidence bands for drift and volatility functions in a dynamic short-term rate model for the U.S. Treasury yield curve rates data.

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