This question follows the one asked there.
I am trying to filter an equity index (Stoxx 600) time series using kalman filter. I'm using the R package dlm and my code is inspired from the dlm vignette with the Nile data filtering.
I was first trying to understand why my filtered data was similar to my observations and it turns out (as it has been said in the question mentioned above) that when estimating my model parameters, the variance of my measurement equation is extremely small (around 10e-5) compared to the one of the state equation (above 300). I am actually quite surprised by those results as I get similar ones for other financial time series (including macroeconomic ones) and those kind of time series are well known to be noisy.
Could you please explain to me if it is the model that I'm not specifying well or if it is the MLE fitting process that is not working correctly?
As in the Nile example of the dlm vignette, I'm using a random walk plus noise, with unknown system and observation variances.
Here's the code I'm using. The a variable is a vector with monthly historical data for the Stoxx 600 since 1999 :