Does it make sense to take the autocorrelation of a nonstationary signal or sequence? Or does it not matter in which case the interpretation will be affected (if at all)? Do we need to do some pre-processing before taking the autocorrelation of such a signal, or are the results as such valid?
i think you have mixed many things, autocorrelation is not a method which we can apply on a data, but it is actually data type. a particular variable may be autocorrelated or not. e.g. your current weight depend on the weight you had one month ago. actually when you take some measurements over a time of a particular variable (weight, height, income, any chemical process,or activity , speed of a vehical ) and it seems that current measurement have some relation with prevous one then measurement recorded are said to be autocorrelated. and if you feel successive measurement are independent, and donot follow any pattern, then there is no autocorrelation. Now non stationarity is related to time, measurements taken our time (whether autocorrelated or not ) have same distribution (paramters ,mean variance , covariance remain same ) over time then the variable is called stationary and opposite to it is non stationary. (stationarity has types but i tried to tell you simply just to understand). Now depending upon your variable you have to decide the autocorrelation, which is usually narrated in the literature that which variable is autocorrealated. and thn testing for stationarity and then go for further analysis. hope this will help
When your data is nonstationary (inhomogeneous), autocorrelation can still be defined and computed, but will now depend on the pivot (=reference) point as well, nut just the distance (=delay, lag) between points. As a result, the autocorrelation becomes a functional, no longer a function. In the discretized (sampled) case, this functional becomes a matrix. For one example of what the autocorrelation matrix can look like, see e.g. Fig. 2 in my paper 'Optimizing Low-Frequency Mode Stirring Performance Using Principal Component Analysis'.
Dear Laya Das,
In some applications computing autocorrelation of a nonstationary signal iteratively(autocorrelation of the autocorrelation and so on) turns out to be more meaningful. This is called Recursive Autocorrelation. Check out this link: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20130009152.pdf
It might look irrelevant but it is worth considering since the idea is so attractive.
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