TimeSeries / FFTAutocorrelation / 0.1.0

Takes a time series and returns the autocorrelation plot of that time series as an array. The size of the entry at i of the autocorrelation plot is a measure of how similar the signal is to a lagged version of itself. Note that the 0th entry of the output is the correlation of the signal with itself (no lag) and is always the largest value. Nonzero values at lat 1 are indicative of a linear trend. Beyond 1, positive values index i indicate a periodic signal with period i. Thus, the most interested entry is that with the second largest value - specifically, the index of this entry is the period of the strongest seasonal trend in the signal. It is recommended that the signal have linear trends removed (as by application of the /TimeSeries/LinearDetrend algorithm) before applying this algorithm, as linear trends make the results of autocorrelation more difficult to interpret. See http://en.wikipedia.org/wiki/Autocorrelation for more information.

This is based on an implementation of the Fast Fourier Transform (in this the real Fourier Transform in the JTranforms library - https://sites.google.com/site/piotrwendykier/software/jtransforms) Note that there are many different conventions used in signal processing, so be careful as the ones chosen here may not be the ones you need.