Robust testing for stationarity of global surface temperature

Abstract

Surface temperature is a major indicator of climate change. To test for the presence of an upward trend in surface-temperature (global warming), sophisticated statistical methods are typically used which depend on implausible and/or unverifiable assumptions, in particular on the availability of a very large number of measurements. In this paper, the validity of these methods is challenged. It is argued that the available series are simply not long enough to justify the use of methods which are based on asymptotic arguments, because only a small fraction of the information contained in the data is utilizable to distinguish between a trend and natural variability. Thus, a simple frequency-domain test is proposed for the case when all but a very small number of frequencies may be corrupted by transitory fluctuations. Simulations confirm its robustness against short-term autocorrelation. When applied to a global surface-temperature series, significance can be achieved with far fewer frequencies than required by conventional tests.

Keywords:

• global warming
• linear trend
• fractionally integrated process
• frequency-domain test
• stationarity test

2010 Mathematics Subject Classifications :

• 62G10
• 62M10
• 62M15
• 62P12

Acknowledgements

I very much appreciate the referees’ comments, which substantially improved this manuscript.