Problem with historical and smoothed variables


How are they different? Just a shift in mean? Or different dynamics? The smoothed variables are typically saved as deviations from the mean. If the data mean is not 0, there will appear a shift.


That looks weird. Please provide the codes to replicate the issue.


There must be something in the model that tightly links these. But I still wonder what happens that there are differences in observed and smoothed series, because this requires measurement error.