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Re: st: RE: filters in stata


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: filters in stata
Date   Tue, 4 Dec 2007 12:16:03 -0500

Juliusz Jabłecki <juliusz.jablecki@student.uw.edu.pl>:

I disagree that replacing missings by zeros in an infinite sum should
be fine.  I think the programming is fairly easy, but given that the
task seems like a bad idea, not worth the time.  Consider what such a
method would do to a time series of 10 obs with b=0.5, picking some
arbitrary nonzero X_t values for t in [1,10].  The obs near t=1 and
t=10 will be smoothed toward zero, for no good reason.

You could get very close to what you claim to want by running -lpoly-
(possibly within panel using -statsby- perhaps) to do local mean
smoothing using a Gaussian kernel and an appropriately chosen
bandwidth, I think.  But again, it's not clear to me that this is a
good idea.

On 12/4/07, Juliusz Jabłecki <juliusz.jablecki@student.uw.edu.pl> wrote:
> > The difficulty here is the infinite window width. In practice you
> > cannot set up an infinitely long dataset in Stata, so you
> > must compromise somewhere. Is there any scope for doing this
> > in the frequency domain? I never got as far as doing Fourier
> > transforms in my head.
>
> Sorry for not making that clear from the outset. Lucas's idea was to replace
> the missing observations by zeros, and that should be fine, except I don't
> have a clue as to how to actually program such a filter. Again, I'm trying
> to smooth a series X_t with the following filter (dependent on b):
>
> X_t(b)=[1-b/1+b]*[\sum(k=-inf/inf)b^|k|*X_(t+k)], 0<b<1
>
> and we replace the infinitely many missing observations by zeros.
> Any ideas?
> Juliusz

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