I want to generate series of 0s and 1s that exhibit some clustering. By this I mean that 1s and 0s should occur together. So I envisage series of 0s and 1s that will exhibit similar clustering of these elements, and not just random series of 0s and 1s.
In essence, for a single time series, I would go about that by thresholding a Markov chain with a 2x2 transition matrix, with some stochastic added on to it. Now, I'm not too certain on how to do this, but since I would like to produce several of these series, I was wondering whether there's something straightforward that I have missed.
I plan to use these series to simulate data availability (0 or 1) in a data acquisition system and to do some Monte Carlo simulations of how this affects what we can do with the data.
In order for the above simulations to be realistic, I would like to fit real observations to this model, so that the simulated time series share temporal correlation with the data. I would initially do this by calculating lag autocorrelations of both series and tweaking model parameters until I get something that resembles my observations, but unsure whether this is the best way.