Re: [Gretl-users] exponential moving average
On Fri, 25 Sep 2015, Sven Schreiber wrote:
Am 25.09.2015 um 11:05 schrieb Raul Gimeno:
> I want to choose the optimal parameter a that minimizes the SSE.
> Would it be possible to include these feature within the menu
> without having to run a script?
I am not convinced that minimizing the SSE is the universally appropriate
goal here. The trivial solution to obtaining a perfect fit is not to smooth
in the first place, so somehow this problem strikes me as ill-defined.
I am open for discussion, but as of now I would be opposed to this
"feature".
I share Sven's skepticism on this point. And as I've mentioned, it's
easy to do this using the "nls" command if you really want to.
IMO, calculating the min-SSE parameter makes sense only if one uses
the Hunter version of the EMA, s(t) = a*y(t-1) + (1-a)*s(t-1), in
which case you can't get a trivial perfect fit. But I notice that in
this case there's no guarantee that the "optimal" a satisfies 0 < a <
1.
Interestingly enough, the example given on the NIST website
http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc431.htm has a
local SSE minimum at about a = -0.12 and a global minimum at about
1.68, with nothing resembling a minimum in the "legitimate" range.
(Although they talk about applying the Marquardt procedure they don't
mention the result!)
Allin