Trends? Complicated answers to a simple question

Abstract

ABSTRACT Trend significance of time series that are serially correlated is once more addressed. Most conventional techniques to “pre-whiten” the series prior to calculating trends rely on the assumption of autoregressive residual noise, AR(1). Monthly recordings of 40 water level stations in Germany are investigated, revealing strong memory up to lag 2. A new scheme (PW(p) ) is introduced that extends pre-whitening to AR(p) with p > 1. It performs well on surrogate series with prescribed trend and memory. For seven series the estimated trends are unrealistically off, raising doubts about the validity of the basic assumptions of short-memory noise. The series are characterized by a hockey stick pattern from which any pre-whitening produces trends that are all but plausible. The pattern also reveals that pre-whitening is not invariant under time reversal. Regardless of the validity of the noise model, these special cases serve as a warning for using pre-whitening in general.