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I am curious how one can generate simulated time series data. I found a list of simulated series here and a similar tool for stock market. What is the best way to generate domain specific time series data with some desired patterns? How should one approach this problem? I know this question is not very complete yet so please feel free to suggest modifications.

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  • $\begingroup$ Could you explain what you mean by "domain specific" and "desired patterns"? Is it about numerical solutions (aka simulations) of stochastic ordinary differential equations? If so, have a look at the books by Peter Kloeden and Eckhard Platen. Are you looking for numerical algorithms or (non exclusive or) for software? $\endgroup$ Oct 6, 2010 at 15:57
  • $\begingroup$ Hidden Markov models are used for many such models where the hidden state, that which isn't observed, is discrete. When the hidden state is continuous, one could use Linear Dynamical Systems. However, I agree with Tim, the question needs to be "fleshed out" before a good answer can be given. $\endgroup$ Aug 30, 2013 at 14:25

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An example: Simulate an AR1 process in MATLAB by

alpha = 0.8; % smaller than 1 for stationarity`
sigma = 1.3;

M = 1e3; X = zeros(M, 1); X(1) = randn; % Initialize

for k = 2:M
    X(k) = alpha*X(k-1) + randn*sigma;
end

This generates M points in time of the model:

$$X_k = \alpha X_{k-1} + \sigma u_k,$$

where $u_k$ is a standard normal variable. A simple model and a good starting point in simulating time series.

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