The motivation for this question is from Finance. I have some market data (daily time series) for the price of some securities and I would like to generate synthetic versions of these which are statistically "similar" (in some sense) for testing trading strategies. Is there literature on this subject?
I was hoping there would be a way of manipulating the market data that I have in a deterministic way (such as, say, taking the first difference between consecutive values and swapping these around) rather than extracting statistical information about the time series e.g. autocorrelation and then generating new random variables etc. to get a new time series.
I am being deliberately vague about what I mean by "similar" as I don't know how realistic my question is and don't want to constrain it further.
There is are several papers under the label of "surrogate data" in the nonlinear data-analysis literature which deals with the question of how to generate data that have "similar" properties to some reference data. This data is then used to run tests to see whether there is additional (nonlinear/chaotic) structure in the data that is not covered by the surrogate-creation technique.
There are many different papers on this issue. Theiler and colleagues worked on it:
and they do use spectral methods with Fourier and Wavelet-transforms…