On periodically isotonic climate change

In a view of the past two millennia, is the recent 160-year global warmth an anomaly or a continuation of past climate pattern? In this work, we present two non-parametric χ2 tests based on the U-test for the isotonic change-point problem proposed in an unpublished work by G. Shen and H. Xu (henceforth abbreviated as SX (unpublished)) and apply them to the global warming data. Our tests do not require any structure assumption on the underlying the deterministic mean process {μt} under the periodically isotonic alternative, but accommodate a large class of the models for the random error process. Being more attractive, the two tests obviate estimation of {μt} and possess explicit asymptotic distributions for short-range dependence data, and have asymptotic power 1 even under the local alternative.