I’m trying to understand the best way to perform a smoothing exercise with a calibrated model with a single shock, matching only the last six observations of a longer time series. The logic of the exercise is that a single shock captures well what happened in those six dates, but before that additional shocks should be added to reasonably match the data.
If running the smoother only on those six observations, the contribution of initial values is obviously large.
Is there a conceptual problem with running the smoother on the full time series, to make sure that the contribution of initial values is negligible, and then plotting only the last six dates?
In other words, what is the conceptual difference between including initial values on the six dates (oo_.SmoothedVariables) vs running the smoother on a longer sample and plotting only the shock decomposition (oo_.shock_decomposition( ‘var’, 1, end-6:end) , which is equal to oo_.shock_decomposition( ‘var’, 3, end-6:end) as initial values are zero)?
I am not entirely sure I get the point. If I understand you correctly, you would like to run the smoother first on the initial sample without the last couple of observations with all shocks and then use the smoothed states in the last period as initial values in the Kalman filter in a smoother run with only one shock. That would allow you to more precisely estimate the initial condition compared to when running the smoother only on 6 observations.
Thanks for the reply!
Almost correct. In the model, I only have one shock. But, economically, having this one shock makes sense only for the last part of the sample. I would like to run the smoother first on the full sample, and then discard the period before convergence to zero of the initial values.
In a sense, this should be similar to use the smoothed states as initial values in the Kalman filter (as you are saying), but additionally also setting the initial variance to zero, as if we knew the initial condition with certainty.
I don’t understand how that is feasible. The initial condition reflects the cumulated shocks that happened before the sample starts. If you are saying that there were other shocks that happened earlier, they will be contained in the initial condition. Assuming them away should not be correct.