We show that when a model has more shocks than observed variables the estimated filtered and smoothed shocks will be correlated. This is despite no correlation being present in the data generating process. Additionally the estimated shock innovations may be autocorrelated. These correlations...

In a number of time times models there are I(1) variables that appear in data sets in differenced from. This note shows that an emerging practice of assuming that observed data relates to model variables through the use of "measurement error shocks" when estimating these models can imply that...