Hypothesis Testing for Autocorrelated Short Climate Time Series

Commonly used statistical tests of hypothesis, also termed inferential tests, that are available to meteorologists and climatologists all require independent data in the time series to which they are applied. However, most of the time series that are usually handled are actually serially dependent. A common approach to handle such a serial dependence is to replace in those statistical tests the actual number of data by an estimated effective number of independent data that is computed from a classical and widely used formula that relies on the autocorrelation function. Despite 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 because of the usual shortness of the available time series. After the impact of this uncertainty is illustrated, some recommendations of preliminary treatment of the time series prior to any application of this formula are made. 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. It is shown how this issue is due to real physical processes that induce temporal coherence, and an illustration is given of how not respecting the hypotheses affects the results provided by the formula.