Technical note: On extracting independent peak values from correlated time series for assessing extremes

The methods of extracting independent peaks from ergodic, but correlated, time series are usually called “declustering”, and the principal method is to select the largest peak value between successive up- and down-crossings of the mean. It is shown that the independent peak values will follow the Poisson point process model if the declustering process uses an optimal low-pass filter to detect the crossings of the mean. When the correlated time series is a mixture of two, or more, processes a second, higher threshold may be applied that passes only those peaks from the dominant process, otherwise the resulting process will remain “mixed” and must be analysed accordingly.