Penalized Maximal t Test for Detecting Undocumented Mean Change in Climate Data Series

Abstract

In this paper, a penalized maximal t test (PMT) is proposed for detecting undocumented mean shifts in climate data series. PMT takes the relative position of each candidate changepoint into account, to diminish the effect of unequal sample sizes on the power of detection. Monte Carlo simulation studies are conducted to evaluate the performance of PMT, in comparison with the most popularly used method, the standard normal homogeneity test (SNHT). An application of the two methods to atmospheric pressure series recorded at a Canadian site is also presented. It is shown that the false-alarm rate of PMT is very close to the specified level of significance and is evenly distributed across all candidate changepoints, whereas that of SNHT can be up to 10 times the specified level for points near the ends of series and much lower for the middle points. In comparison with SNHT, therefore, PMT has higher power for detecting all changepoints that are not too close to the ends of series and lower power for detecting changepoints that are near the ends of series. On average, however, PMT has significantly higher power of detection. The smaller the shift magnitude ? is relative to the noise standard deviation σ, the greater is the improvement of PMT over SNHT. The improvement in hit rate can be as much as 14%?25% for detecting small shifts (? < σ) regardless of time series length and up to 5% for detecting medium shifts (? = σ?1.5σ) in time series of length N < 100. For all detectable shift sizes, the largest improvement is always obtained when N < 100, which is of great practical importance, because most annual climate data series are of length N < 100.