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I would like to estimate this system with state space modeling in order to perform some initial tests as an empirical analysis.

$ \begin{cases} x_t = \mu_t + \beta_1x_t + \varepsilon \\ \mu_t = c_{t-1} + \gamma \mu_{t-1} + \epsilon_{1,t}\\ c_{t} = \rho c_{t-1} + \epsilon_{2,t} \end{cases} $

Do you know if there is a standard toolbox (R or Matlab) that allows me to express the two states equation with the autoregressive component? I've already checked some toolboxes but I wasn't able to express the states equation in this way.

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  • $\begingroup$ There are important details missing. What variables are observed and which are not? Are you interested in estimating the parameters or the latent states (i.e. are the parameters known)? Are the error terms correlated? $\endgroup$ – hejseb May 26 '16 at 20:43
  • $\begingroup$ Hi Hejseb, I'm sorry you are right. There is also a typo on the dependent (it's obviously y and not x). The observed are y and x, the other are latent while the error terms are supposed to be uncorrelated. $\endgroup$ – Marco May 27 '16 at 5:55
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Have you considered Matlab's Systems identification toolbox? If the standard state space modeling functions don't cut it, perhaps the grey box modeling functions will.

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