  In a wide range of applications, the stochastic properties of the observed
time series change over time. The changes often occur gradually rather than
abruptly: the prop- erties are (approximately) constant for some time and then
slowly start to change. In such situations, it is frequently of interest to
locate the time point where the properties start to vary. In contrast to the
analysis of abrupt changes, methods for detecting smooth or gradual change
points are less developed and often require strong paramet- ric assumptions. In
this paper, we develop a fully nonparametric method to estimate a smooth change
point in a locally stationary framework. We set up a general procedure which
allows to deal with a wide variety of stochastic properties including the mean,
(auto)covariances and higher-order moments. The theoretical part of the paper
estab- lishes the convergence rate of the new estimator. In addition, we
examine its finite sample performance by means of a simulation study and
illustrate the methodology by applications to temperature and financial return
data.
