HAC robust trend comparisons among climate series with possible level shifts
Ross R. McKitrick, and Timothy J. Vogelsang
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.
For visiting ABC reporters there is a good summary of the paper by McKitrick at Steve McIntyre's Climate Audit.
Over the 55-years from 1958 to 2012, climate models not only significantly over-predict observed warming in the tropical troposphere, but they represent it in a fundamentally different way than is observed. Models represent the interval as a smooth upward trend with no step-change. The observations, however, assign all the warming to a single step-change in the late 1970s coinciding with a known event (the Pacific Climate Shift), and identify no significant trend before or after. In my opinion the simplest and most likely interpretation of these results is that climate models, on average, fail to replicate whatever process yielded the step-change in the late 1970s and they significantly overstate the overall atmospheric response to rising CO2 levels.