Premium
HAC robust trend comparisons among climate series with possible level shifts
Author(s) -
McKitrick Ross R.,
Vogelsang Timothy J.
Publication year - 2014
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.2294
Subject(s) - autocorrelation , heteroscedasticity , estimator , econometrics , climate change , statistics , series (stratigraphy) , nonparametric statistics , multivariate statistics , troposphere , mathematics , climatology , environmental science , geology , paleontology , oceanography
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. © 2014 The Authors. Environmetrics published by John Wiley & Sons, Ltd.