Hypothesis testing for autocorrelated short climate time series
Guemas, Virginie ; Auger, Ludovic ; Doblas-Reyes, Francisco J.
Commonly used statistical tests of hypothesis, also termed inferential tests, which are available to meteorologists and climatologists all require independent data in the time series to which they are applied. Unfortunately, most of the time series, which are usually handled, are actually serially dependent. A common approach to deal with such a serial dependence is to replace in those statistical tests the actual number of data by an estimated effective number of independent data which is computed from a classical and widely used formula relying on the autocorrelation function. In spite of being perfectly demonstrable under some hypotheses, this formula provides unreliable results on practical cases, for two different reasons. First, the formula has to be applied using the estimated autocorrelation function which bears a large uncertainty due to the usual shortness of the available time series. After illustrating the impact of this uncertainty, we make some recommendations of preliminary treatment of the time series prior to any application of this formula. Second, the derivation of this formula is done under the hypothesis of identically distributed data which is often not valid in real climate or meteorological problems. We show how this issue is due to real physical processes that induce temporal coherence and we warn about how not respecting the hypotheses impacts the results provided by the formula.
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