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I'm looking for an algorithm to generate discrete-time pseudorandom sequences based on other sequences I already have that would be used to train the algorithm.

More specifically, I have some time-based discrete-time measurements of some real-live event (for example: sunspot number, stock market, sea height at a beach...). I have long sequences of those measurements and I would like to generate other sequences having the same long-term and short-term properties that the sequences I already have.

For example, in the case of the sunspot number, it shows some random short-term noise and a clear long-term periodicity. I would like to produce more like those sequences.

I have been looking at Markov chains, but they would be valid just for the short-term, and just for a discrete set of values.

It doesn't look like a new problem so I suppose it has been solved elsewhere and has a name :) but I can't find it.

siritinga
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    What you are looking for is called a generative model. This question is also incredibly broad, as there is a very wide range of models to choose from, and an introductory textbook like Elements of Statistical Learning would be a good place to start. Since there is no computational science issue here, it might be better to ask this on http://stats.stackexchange.com/, but providing much more detail about your problem. – Kirill May 28 '15 at 06:53

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You can model your time series with Gaussian processes. Once you have decided on the correct covaraince functions and estimated their hyperparameters you can draw new series from this process. But I agree with Kirill, this is only one of many possible ways to do this.

Bort
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