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I have a set of data I'm trying to analyse. It's a time series of number of objects, and it follows the general trend of increasing with time. Although I've not observed a reduction at any time step this is still possible by the definition of the system (objects are added and taken away, just the addition is significantly more likely and typically an order of magnitude greater than a subtraction). I've looked into time series analysis and Wikipedia says they can either be analysed in the frequency domain or the time domain, the the frequency domain page lists:

Fourier transform – nonrepetitive signals, transients

Which sounds like my sort of data. Now what I'm interested in is why sort of result might I get from applying an FFT to a time series like I've described above? I don't understand what the frequencies would actually mean. So I understand that if I was analysing speech then it would show me the specific frequencies of sound, but what are the frequencies of discrete counts like this?

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Usually frequency domain analysis is done with the autocovariance function of time series. Autocovariance function is an time domain tool for analyzing structure of your time series.

Frequency domain analysis transforms this autocovariance function.

Here is discussion:

http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/csa/node58.html

In frequency domain, spectra tells you something about the concentration of components of series variation. It might be that long run trend dominates variation of series but in other series cyclical factors might rule. For example ice cream factory might produce most output just before summer and during summer.

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