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[amibroker] Re: re:Ehlers Modified Optimal Elliptal filter



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--- In amibroker@xxxxxxxxxxxxxxx, "Corey Saxe" <res1wgwl@xxxx> wrote:
> From Stocks & Commodities V. 18:7 (July 2000) (pp. 20-29): Optimal 
Detrending by John F. Ehlers
> 
> modified optimum elliptic filter in TradeStation EasyLanguage:
> 
> Smooth = 0.13785*(2*Price - Price[1]) + 0.0007*(2*Price[1] -
> 
> Price[2]) + 0.13785*(2*Price[2] -Price[3]) + 1.2103*Smooth[1] -
> 
> 0.4867*Smooth[2]
> 
> Or, algebraically:
> 
> Smooth = 0.13785 (2 x Price - Price[t-1]) + 0.0007 (2 x Price[t-1] -
> 
> Price[t-2]) + 0.13785 (2 x Price[t-2] - Price[t-3]) + 1.2103
> 
> (Smooth[t-1] - 0.4867 x Smooth[t-2])
> 
> where Price=(High+Low)/2
> 
> 
> 
> -CS
> 
> ----- Original Message ----- 
> 
>   From: raven4ns 
>   To: amibroker@xxxxxxxxxxxxxxx 
>   Sent: Saturday, October 23, 2004 7:58 AM
>   Subject: [amibroker] re:Ehlers Modified Optimal Elliptal filter
> 
> 
> 
>   Hello,
>   Does anyone know where I might find this filter? I was looking at 
>   the new Jurik MA and this certainly looked like a reasonable 
>   substitute. Thank you.
> 
>   Tim

I'm not convinced this filter is all that "optimal".  According to 
Ehlers:

"... I have been curious about how to design an optimum smoothing 
filter.  I set one criterion to be that the smoother could have no 
more than a one bar lag.  An elliptic filter provides the maximum 
amount of smoothing under the constraint of a given lag.  So, using 
MATLAB, I designed an elliptic filter ..."

The problem here is that sometimes you *want* significant lag.  Here's 
the sitch: most filters affect both signal and noise. Filtering noise 
is good: that's what you want to get rid of. But filtering signal is 
bad: that's where lag and attenuation comes from.  So in areas of low 
signal-to-noise ratio, you want a lot of filtering, and in areas of 
high SNR, you want little or no filtering. The only way to accomplish 
this for non-stationary, non-linear time series like financial data is 
with an adaptive moving average. Most AMAs are basically variable 
EMAs, but Jurik denies this is what his AMA is. Maybe so. For the rest 
of us "home-brewers", the key is to find the best data-adaptive 
smoothing factor possible.

Good trading,
kut2k2






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