I am using a Kalman Filter to estimate the return dynamics of a forwards curve on a particular commodity. My state space is the initial forwards values, and an initial guess of the drift functions for each forward (initially just the first observed price change). These are for OTC products, my estimates for uncertainty are based on market consensus standard deviations. My Estimate of the Q matrix (process covariance noise) is based on the average variance, and my estimate for the R matrix (covariance observation noise) is based on each days market consensus standard deviation.
From the resulting Posteriori Covariance matrix, I estimate the correlation matrix. The result is constant correlation. Basically the off diagonal is roughly 72% almost everywhere. I am not sure why this should be the linearly optimal result, or perhaps there is a flaw in my understanding of the Kalman filter?
I can not provide the data I used for this experiment, but I am more than happy to answer clarifying questions if it would help the community to better answer my question: Particularly, what could be the cause of observational constant correlation?