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Time series with Gauss-Markov processes

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Alex on 29 Jun 2012
I'm trying to do an stochastic model for a time series in Matlab code. I suppose that the time series that I have is a sum of different first-order Gauss-Markov processes such as:
xk1 = exp(0.1/Tc1)*xk1_1 + std1*w % discrete time gauss-markov 1
xk2 = exp(0.1/Tc2)*xk2_1 + std2*w % discrete time gauss-markov 2
X = xk1 + xk2; % stochastic model
where w is a white noise, xk is a variable with previous value xk_1.
I'm wondering if there is a function in Matlab that can help me to obtain the parameters Tc1, Tc2, std1 and std2 of these Gauss-Markov processes in order to create the stochastic model of the time series.
BTW, the original time series has a lenght of 2500000 samples.
I'd appreciate any guidance.
Alex on 2 Jul 2012
Thanks Sargondjani for your answer. So you mean that I can obtain these parameters Tc1, Tc2,..,std2 using HMM? even if I have more than two gauss-markov processes?

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