Abstract: The estimation of a monotone trend that has been obscured by stationary fluctuations is considered and illustrated by global temperature anomalies. At an interior point, the rescaled isotonic estimators are shown to converge in distribution to Chernoff's distribution under minimal conditions on the stationary errors; and two modifications for estimating the value at an end point are compared. The asymptotic results are shown to hold conditionally given the starting values and, so, allow some relaxation of the stationarity assumption. The quality of the implicit approximations is assessed by simulation and found to be quite good for several models.
Key words and phrases: Asymptotic distribution, Brownian motion, cumulative sum diagram, greatest convex minorant, least squares, maximal inequality, spiking problem, stationary processes.