Hull Moving average

["ChasW" <cwwaring@xxxxxxxxxxxxxx>]

December 2005 Trading Tips Newsletter
----- Original Message ----- 
From: Ensign Software
To: Ensign User
Sent: Friday, December 30, 2005 11:33 AM
Subject: Trading Tips Newsletter - December 2005 issue




Hull Moving Average
by Alan Hull
www.alanhull.com
The Hull Moving Average solves the age old dilemma of making a moving
average more responsive to current price activity whilst maintaining curve
smoothness.  In fact the HMA almost eliminates lag altogether and manages to
improve smoothing at the same time.  To understand how it achieves both of
these opposing outcomes simultaneously we need to start with an easily
understood frame of reference.  The following chart contains a 16 week
simple moving average which constantly lags the price activity and has poor
smoothness.

Firstly, solving the problem of curve smoothing can be done by taking an
average of the average, i.e.. 16 period SMA(16 period SMA(Price)). The bad
news is that it causes a huge increase in lag as seen below.

Solving the problem of lag is a bit more involved and requires an
explanation with numbers rather than charts.  Consider a series of 10
numbers from '0' to '9' inclusive and imagine that they are successive price
points on a chart with 9 being the most recent price point at the right hand
leading edge.  If we take the 10 period simple average of these numbers
then, not surprisingly, we will determine the midpoint of 4.5 which
significantly lags behind the most recent price point of 9.  Here's the
clever bit…first let's halve the period of the average to 5 and apply it to
the most recent numbers of 5,6,7,8, and 9, the result being the midpoint of
7.

Finally, to remove the lag we take the midpoint of 7 and add the difference
between the two averages which equals 2.5 (7 - 4.5). This gives a final
answer of 9.5 (7 + 2.5) which is a slight overcompensation.  But this
overcompensation is very handy because it offsets the lagging effect of the
nested averaging.  Hence the result of combining these 2 techniques is a
near perfect balance between lag reduction and curve smoothing.

The HMA manages to keep up with rapid changes in price activity whilst
having superior smoothing over an SMA of the same period.  The HMA employs
weighted moving averages and dampens the smoothing effect (and resulting
lag) by using the square root of the period instead of the actual period
itself…as seen below.

WMA (2 x  WMA(Price,Integer(Period/2)) -
WMA(Price,Period),Integer(SquareRoot(Period)))



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