I'm struggling with Reinsel's book "Elements of Multivariate Time Series Analysis," because I thought that it would be a good idea to switch from Vector ARMA to state-space representations; particularly after reading What are disadvantages of state-space models and Kalman Filter for time-series modelling?, and after struggling with parameter estimation of VARMA processes.

The problem is that I can't see how correlation between two time series can be modeled in state-space representations. Is it that the correlation appears in the error covariance matrices? It sounds weird to me, particularly coming from VARMA. (Switching to state-space models is being harder than I thought!)


Correlation can be introduced via the covariance matrices, but also through non zero off-diagonal terms in the transition or observation matrix.

  • $\begingroup$ About your kind answer: (1) if I introduce the correlation in the transition matrix (off-diagonal elements), isn't it that I'm forcing a deterministic correlation? I mean that it seems that I'm forcing say x1 and x2 to be always varying by the same amount. (If the off-diagonal matrix entry is 2, I am saying that x2 will "always" be double the value of x1.) (2) Do you know of any good resource where i can find how to estimate the state-space of two cross-correlated time series? $\endgroup$ – Sonntag Apr 16 '14 at 8:54
  • $\begingroup$ (1) no, because the total correlation will include the error covariance. (2) see my answer here $\endgroup$ – Aksakal Apr 16 '14 at 13:35
  • $\begingroup$ @Sonntag, as pointed in the previous comment, if in one of your state equations you have x1(t+1) = ax1(t) + bx2(t) + eps(t), the connection between x1(t) and x2(t) is not deterministic, for it is affected by the state equation noise eps(t). $\endgroup$ – F. Tusell Apr 16 '14 at 13:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.