Identification of Time Lags

As can be seen, there is a peak at = 4, meaning that there is an estimated time lag between process input and process output of 4 sampling intervals. The process output should then be shifted four sampling intervis backward in time to make a static principal component analysis meaningful. 

As mentioned, the cross correlation function is used to determine the correlation between two series of data. The most common use is to determine the correlation between the input and output of a process. It indicates how a measurement of the process output is related to the process input (also likely to be measurements), several sampling periods ago. It can also be used to determine the maximnm number of neurons in the input layer of a neural network used for the historical input data (neural network with delayed inputs). 

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