# [R] "dlm" Package: Calculating State Confidence Intervals

Mon Mar 26 08:51:36 CEST 2018

```To Whom It May Concern,

I estimated a model with 6 states (3 time-varying Regression parameters and 3 quarterly seasonality trends).  The model is saved in the object titled "mod."

Following the example in the documentation and using the commands below, I am attempting to use the function "dlmSvd2var" to implement SVD and calculate the 90% confidence errors for each time-varying state.

outF <- dlmFilter(y,mod)
v <- unlist(dlmSvd2var(outF\$U.C, outF\$D.C))
pl <- dropFirst(outF\$m) + qnorm(0.05, sd=sqrt(v[-1]))
pu <- dropFirst(outF\$m) + qnorm(0.95, sd=sqrt(v[-1]))

Since the dataset has 100 observations, I end up with a vector v that comprises 3636 atomic components: (1 + 100) x (6 x 6).  If I discard the 1st 36 of them, then v comprises 3600 atomic components.  The question is how to extract the variance of each state (6 states) in the 36 atomic components representing each time (1:100).

Said differently, how do I extract the variance of each state (6 states) in the 6 x 6 matrix generated by the "dlmDvd2var" function in time t?  Is this information provided in the diagonal elements, element (1,1) for state 1, element (2,2) for state 2, and so on?