The tenth IMSC, Beijing, China, 2007 - International Meetings on ...

Penalized maximal t-test for detecting undocumented mean change
Speaker: Xiaolan L. Wang
Xiaolan L. Wang
Climate Research Division, ASTD, STB, Environment Canada
Xiaolan.Wang@ec.gc.ca
Qiuzi H. Wen and Yuehua Wu
Department of Mathematics and Statistics, York University, Canada
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 basically evenly distributed across all candidate changepoints, while that of
SNHT can be up to 10 times higher than the specified level for points near the ends of series
and much lower for the middle points. In comparison with SNHT, consequently, 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. <strong>The</strong> smaller the shift magnitude Δ relative to
the noise standard deviation σ , the greater the improvement of PMT over SNHT. <strong>The</strong>
improvement in hit rate can be as much as 14-25% for detecting small shifts (Δ < σ) regardless
of time series length, and up to 5% for detecting medium shifts (Δ = 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 is of
length N < 100.
Penalized maximal F-test for detecting undocumented mean-shift
Speaker: Xiaolan L. Wang
Xiaolan L. Wang
Climate Research Division, ASTD, STB, Environment Canada
Xiaolan.Wang@ec.gc.ca
In this study, a penalized maximal F-test (PMFT) is proposed for detecting undocumented
mean-shifts that are not accompanied by any sudden change in the linear trend of time series.
PMFT aims to even out the uneven distribution of false alarm rate and detection power of the
corresponding unpenalized maximal F-test that is based on a common trend two-phase
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