I am studying time-series econometrics and in particular Dynamic Linear Models for multivariate time-series.
Someone can help me in understanding which is the difference between SUTSE (Seemingly Unrelated Time Series Equations) and SUR (Seemingly Unrelated Regression) Dynamic Linear Models?
How can I specify a SUTSE and a SUR model on r? I think dlmModPoly may be of help but I am a bit stuck
This answer might not be complete enough for your taste, but here goes: The SUTSE model comes from the "structural time series" literature, that is using a state-space formulation. My understanding is that basically you take a univariate formulation, for example the observation equation could be $y_t = m_t + e_t$, and then you suddenly turn the scalar variables into k-dim vectors.
Since the k-th components of $m_t$ and $e_t$ only enter the k-th component of $y_t$ these equations of the multivariate system are "unrelated". But they are only "seemingly" unrelated because the covariance matrix of $e_t$ can be non-diagonal, connecting the equations at least a little bit. And similarly for the state equation.
On how to do this in R I would refer you to: Giovanni Petris and Sonia Petrone (2011), "State Space Models in R", Journal of Statistical Software May 2011, Volume 41, Issue 4. (https://www.jstatsoft.org/article/view/v041i04/v41i04.pdf) Especially section 3.3, where they say "Multivariate state space models can be analyzed in R using package dlm and package KFAS."
In contrast, SUR is not really a model, it's an estimator, namely an incarnation of generalized least squares (GLS). What it does is take a system of (linear) equations that could be estimated by classical OLS, but then it also allows the (contemporaneous) cross-equation covariance matrix to be non-diagonal and takes this covariance structure into account to estimate the system more efficiently than with OLS.
This system of equations to be estimated with SUR can, but doesn't have to, be a dynamic system with lagged terms. The R package "systemfit" and its documentation should be helpful (but to be honest, I haven't used it myself, I'm not doing these things with R).
One thing that SUTSE and SUR seem to have in common is that they work with systems where each "dependent" or "endogenous" variable can only appear in one equation, hence the "seemingly unrelated" label.
