Time series with Gauss-Markov processes

Hello!

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.

Thanks!

[Sargondjani]

im not familiar with this type of model, but have a look at the function "HMM". it might be what you are looking for

[Alex]

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?