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Just want to make a little survey,

What are, according to you, the best approach to model categorical time series?

I'm building a model able to generate time series reproduicing the characteristics of a set of data. The available data is a discrete time, discrete-valued time serie. I have generated synthetic time serie using Markov chain, semi-markov chain and moving block bootstrap, I would like to know if you think of better way to do that job.

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  • $\begingroup$ Are the discrete values ordinal or just categorical with no ordering? And what is the purpose of your modeling? To predict the next value, to cluster or categorize time series into classes, or predict something else as a function of the time series? $\endgroup$
    – highBandWidth
    Commented Aug 11, 2011 at 16:30
  • $\begingroup$ I would say the discrete values are nominal. The data come from a process which can enter only in three different states. In each state it can access the 2 other. To make it simple, imagine a car, the first state is when the car is moving, the second its when the engine is turned but the car is not moving, the last state it's when the the is not moving and the engine is stopped. The purpose of my modeling is to generate synthetic time series to use them as input for another model. $\endgroup$
    – Mickaël S
    Commented Aug 11, 2011 at 17:11
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    $\begingroup$ In that case I think a Markov model or a hidden Markov model would be my first choice. $\endgroup$
    – highBandWidth
    Commented Aug 11, 2011 at 17:25
  • $\begingroup$ what is your opinion on resampling approach (like bootstrap) to do that kind of work? $\endgroup$
    – Mickaël S
    Commented Aug 11, 2011 at 17:46

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