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.