  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.
