Re: [Gretl-users] exponential moving average
On Thu, 24 Sep 2015, Raul Gimeno wrote:
Dear Allin
Thank you for your answer.
Could you please remove the restriction for the exponential moving
average filter to allow up to T/2 observations for the mean
calculation?
As Jack said, that's now done in CVS. It will be in the snapshots
shortly.
It would be helpful if all the fillters you find under
"variable"
like the exponential moving average have their own short explanation
in the Gretl's guide.
The more elaborate filters (e.g. Butterworth, Polynomial trend) have a
Help button in the set-up dialog box which gives some details. I think
the best thing here might be to add some help text for the EMA also.
I am using the Roberts formula but I get a different result from
Gretl
with alpha = 0.1
Value one-step forecast
Y(T) Y^ (T-1)
T = 0 351.2917
T = 1 362 352.363 = 0.1(362) + 0.9(351.2917) --> Gretl:
354.2625
T = 2 381
There seems to be a difference over dating assumptions here. What
gretl does is to put the initializer for the EMA into the first
observation of the output series (which gretl calls t = 1, there's no
t = 0). Then the first actual computed value is EMA(2) = a*Y(2) +
(1-a)*EMA(1). It seems you are placing the EMA initializer before the
data start, and then doing the first EMA calculation using Y(1).
So far as I can tell, the procedure gretl uses is that given by NIST
(http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc324.htm ) but
I'm not sure if there's a truly canonical approach here. (It's the
sort of thing that won't make any difference asymptotically.)
Would it be possible to include a solver function like in Excel in
order to do minimizing calculations to find the optimal alpha?
The BFGSmax function can do this sort of thing. See the chapter on
Numerical methods in the User's Guide.
Allin Cottrell