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At 06:45 PM 1/13/2007, Adrian Pitt wrote:
>Would it be possible for Alex or Bob to publish a before and after scenario.
>They don't have to reveal the system, but simply show, using the exact same
>rules, what effect switching from say regular Bollinger Bands to JMA/T3
>based bands can do to various profitability numbers. Would this be
>possible?
I could do that but it would take a lot of time and really prove
nothing. Instead, I will offer the following example that I posted to
another list long ago.
This relates to the undesirable "artifacts" that show up when you use
a simple moving average. There are many:
> Value dropping out of the back end of the average creates noise
Why should the value "Length" bars ago have the same impact as
the new bar?
> It rejects cycles with period = Length (See below)
> All values in the average have equal weight
Shouldn't more recent values have higher weight?
> Has a poor response to fast changes
> Offers very little smoothing (filtering of noise).
The attached picture shows a periodic test signal at the top made to
simulate a cycle in the price of a security. It has a period of 22
bars and repeats exactly every 22 bars.
The lower part of the chart shows the Bollinger Band bandwidth for
Lengths of 19, 20, 21, 22, 23, 24 bars. You can see that when the
length of the indicator equals the length of the cycle in the price
(22), the resulting signal completely disappears - becomes a constant.
This is true of any technical indicator that uses a simple moving
average where all values inside the averaging window have the same
weighting. This is because the value dropping out the back-end of the
window is exactly equal to the value being added at the front of the
window. In engineering terms, the indicator has a null in it's
frequency response for signals with a period equal to the Length (and
Length/2, and Length/3, etc.).
This is true of Bollinger Bands, standard deviation, the simple moving
average (SMA), some implementations of Stochastic, and any indicator
that uses the SMA internally. It is also true of any indicator that
uses the linear regression line such as common measurements of Alpha and Beta.
If we are using an indicator with a fixed-length of 20 and the cycle
in the signal we are analyzing varies from 18 to 22, we can see that
we can get all kinds of strange effects.
Most of our technical indicators were designed way back before we
understood these things. Signal processing engineers today would never
use a simple moving average for such things. Neither do I.
Bob Fulks
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Markets.201.png
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