Ultimate Algorithmic Trading System

28
STOCHASTICS AND AVERAGES AND RSI! OH, MY!
The ADX index incorporates moving averages of true range and both +DM
and −DM. Data averaging is also the same as data smoothing. A moving average
function cuts down the impact of abnormal data points and creates a more robust
model of the data. Wilder created his indicators without the use of a computer
and created a shortcut to average his data points. This Wilder’s smoothing is more
like an exponential calculation. Different trading/testing/charting platforms use
different smoothing functions for Wilder’s indicators, so be sure to check your
user’s manual and see which form is being utilized by your particular software.
Assuming a 14-day ADX length, Wilder would sum up the first 14-day values and
then divide by 14. Once these initial averages were calculated the subsequent bar
values were calculated by first dividing the previous sum by 14 and subtracting it
from the previous sum and then adding today’s values:
previous plusDM14
plusDM14 = previous plusDM14 − + plusDM today
14
This form of smoothing eliminates keeping track of the prior 14 bar values and
accomplishes the desired effect (reducing the impact of outlying data points) on
plus DM, minus DM, and true range. Remember, Wilder probably had the use of
just a calculator, and instead of inputting 42 numbers (summing three sets of 14
numbers), he simply used the above formula and whipped out the values in a minute
or less. Most of today’s charting software utilizes an exponential moving average to
smooth the ADX. This smoothing method creates results that can be quite different
than Wilder’s original method.
Wilders:
Exponential:
ADX =((priorADX ∗ 13)+DX)∕14
ADX = priorADX + 2∕15 ∗ (DX − priorADX)
The smoothing factor (2/(N+1)) or in this case (2/15) can be changed to (1/N)
to arrive at Wilder’s calculation. This becomes more like a 27 period exponential
moving average than a 14. However, this exponential method is considered accurate,
but, in some cases, different charting software will offer both versions: ADX and
Wilder ADX.
Calculation for a 14-day ADX:
1. Calculate the true range (TR), plus directional movement (+DM), and minus
directional movement (−DM) for each bar.
2. True range (TR ) = max(C[1],H) − min(C[1],L). In other words: Take the
higher of yesterday’s close and today’s high and subtract the lower of yesterday’s
close and today’s low. Basically, you are expanding today’s range to incorporate
the prior day’s close if it is outside of today’s range.
3. Smooth these periodic values using a 14-day moving average. You will either
have to wait until 14 days have transpired or you can simply look at 14 days of
prior history before commencing the ADX calculation.
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