document: Fast window correlations over uncooperative time series Data arriving in time order ( a data stream ) arises in fields including physics , finance , medicine , and music , to name a few . Often the data comes from sensors ( in physics and medicine for example ) whose data rates continue to improve dramatically as sensor technology improves . Further , the number of sensors is increasing , so correlating data between sensors becomes ever more critical in order to distill knowlege from the data . In many applications such as finance , recent correlations are of far more interest than long-term correlation , so correlation over sliding windows ( windowed correlation ) is the desired operation . Fast response is desirable in many applications ( e.g. , to aim a telescope at an activity of interest or to perform a stock trade ) . These three factors -- data size , windowed correlation , and fast response -- motivate this work . Previous work ( 10 , 14 ) showed how to compute Pearson correlation using Fast Fourier Transforms and Wavelet transforms , but such techniques do n't work for time series in which the energy is spread over many frequency components , thus resembling white noise . For such `` uncooperative '' time series , this paper shows how to combine several simple techniques -- sketches ( random projections ) , convolution , structured random vectors , grid structures , and combinatorial design -- to achieve high performance windowed Pearson correlation over a variety of data sets .
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