In Wilder's words "Directional Movement is the most fascinating concept I have studied. Defining it is a little like chasing the end of the rainbow... you can see it, you know it's there, but the closer you get to it the more elusive it becomes. I have probably spent more time studying directional movement than any other concept. Certainly one of my most satisfying achievements was the day I was actually able to reduce this concept to an absolute mathematical equation. 1"
Today's ADX = Previous ADX times n-1 plus today's DX
where n = smoothing (default 11)
DX = ABS( (+DI) - (-DI) ) ] / ( (+DI) + (-DI)
The formula is rather complex as there are 11 separate calculations needed to compute the directional movement index (DX), one more to compute the average directional movement index (ADX) and one more to compute average directional movement index rating (ADXR). Forturnately we have computers to do the work for us. Wilder measures directional movement (DM) based on the true range (TR) of today's prices compared to yesterday's prices, which are then accumulated to produce movement over some period of time (i.e., smoothing). He then compares the up days (+DI) with the down days (-DI) which produces DX. "The more directional the movement of a commodity or stock, the greater will be the difference between +DI and -DI." Like many technical indicators, raw data moves up and down too rapidly to be useful. Wilder eliminates the noise through the use of moving averages. ADX is the exponential moving average of DX and ADXR is the exponential moving average of ADX.
Conceptually, Wilder, through the ADX is quantifying the extent to which a market is trending. ADX measures the strength of the trend regardless of direction. Two additional components of the system (+DI and -DI) allow you to determine whether that trend is up or down. The trend is up when +DI crosses above -DI and down when -DI crosses above +DI.
The display of DMI may have up to 4 components... +DI, -DI, ADX and ADXR. All of Trendsetter's products allow you to view any combination of the components. Here, for example, is ADX by itself followed by the more standard display of ADX with +DI and -DI...
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1 J. Welles Wilder. New Concepts in Technical Trading Systems (p. 35) 1978