HAC robust trend comparisons among climate series with possible level shifts

Abstract

Comparisons of trends across climatic data sets are complicated by the presence of serial correlation and possible step-changes in the mean. We build on heteroskedasticity and autocorrelation robust methods, specifically the Vogelsang-Franses (VF) nonparametric testing approach, to allow for a step-change in the mean (level shift) at a known or unknown date. The VF method provides a powerful multivariate trend estimator robust to unknown serial correlation up to but not including unit roots. We show that the critical values change when the level shift occurs at a known or unknown date. We derive an asymptotic approximation that can be used to simulate critical values, and we outline a simple bootstrap procedure that generates valid critical values and p-values. Our application builds on the literature comparing simulated and observed trends in the tropical lower troposphere and mid-troposphere since 1958. The method identifies a shift in observations around 1977, coinciding with the Pacific Climate Shift. Allowing for a level shift causes apparently significant observed trends to become statistically insignificant. Model overestimation of warming is significant whether or not we account for a level shift, although null rejections are much stronger when the level shift is included.