Hi,
I am trying to do maximum likelihood estimation on a univariate structural
model with diffuse components in dlm.
The package already has an MLE function, but I would like to implement two
enhancements, both of which are discussed in Harvey's Forecasting structural
time series models and the Kalman Filter, section 3.4:
1. drop the d first components for diffusive terms to construct a proper prior
2. swap in the concentrated univariate likelihood for the standard multivariate
(concentrated variance being the prediction error variance).
The first item is easy, so my question surrounds item (2). My hope is to re-use
the MLE calculation apparatus in dlm, but swap out either one line in dlmLL
that augments the likelihood.
The concentrated likelihood requires two ingredients that come from the filter:
the one step ahead prediction error and its variance. I believe that the
prediction errors are easy to find. There are functions that produce it outside
dlmLL and also it is pretty easy to find in dlmLL itself. I am less clear how
to obtain the variance, which is the univariate Var(y(t)|y(t-1)) and is denoted
f_t in Harvey's book. Here y is the observation. My confidence is low because
the function is written for a multivariate filter with SVD expression and my R
skills are beginning-intermediate. At best I think f is here in SVD form and
I'm concerned I might have to cast it or something if I want to work with it as
a scalar.
Can anyone help me with an example of how to obtain f_t? Either within dlmLL or
without? I appreciate any hints I can get.
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