UCM Local Level Model Component

[Jerry]

Hello -

Another question here: I examined the level component of the output and found the 'filtered' and 'smoothed' versions are very close, where the "smoothed" version does not seem to be smooth. How do we explain and is there anyway to obtain a smoothed level component? Thank you!

Jerry

[Chad Fulton]

Hi Jerry,

In the context of state space models, "smoothed" refers to an estimate of a value for the time period `t` constructed using the entire sample (including data prior to time `t` and also after time `t`), while "filtered" refers to an estimate that only uses data through period `t` (but not after).

So there's nothing that really guarantees that the results will be particularly smooth.  You can sometimes achieve a smoother estimate of the "level" of the series by trying a different model (for example, the "smooth trend" model is often smoother than e.g. "local level"; alternatively, it can sometimes help to include an autoregressive component).

Best,

Chad

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[sweep2009]

Very helpful information. Thank you, Chad!

Jerry

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