  Motivated by global warming issues, we consider a time se- ries that consists
of a nondecreasing trend observed with station- ary fluctuations, nonparametric
estimation of the trend under monotonicity assumption is considered. The
rescaled isotonic es- timators at an interior point are shown to converge to
Chernoff's distribution under minimal conditions on the stationary errors.
Since the isotonic estimators suffer from the spiking problem at the end point,
two modifications are proposed. The estima- tion errors for both estimators of
the boundary point are shown to have interesting limiting distributions.
Approximation accu- racies are assessed through simulations. One highlight of
our treatment is the proof of the weak convergence results which involve
several recent techniques developed in the study of con- ditional central limit
questions. These weak convergences can be shown to hold conditionally given the
starting values.
