Name, Sometimes Called:
Directional Movement Index
Sometimes abbreviated to DX (preferred by the original author –
see History below), or more recently, DMI.
See Directional Movement (DM) and the Directional Movement Index
(DX) under History below.
Brief Description:
The Directional Movement Index (DMI), one of a set
of technical analysis indicators developed by Welles Wilder, indicates
the direction of a trend, but not its strength. It is used here
with the Average Directional Movement Index (ADX), another Wilder-developed
TAI, which indicates the strength of a trend, but not its direction.
DX is derived from two other Wilder-developed indicators called
the Positive Directional Indicator, sometimes written +DI, (here
we write that as DI(plus) or PDI) and the Negative Directional Indicator
or –DI (here, DI(minus) or MDI).
Definitions, Formulas:
DMI is a complex indicator that indicates the direction
of the current trend.
DMI is derived from two other indicators that Wilder developed,
called the Positive Directional Indicator and the Negative Directional
Indicator:
DI(plus) = HTODAY
- HYESTERDAY
DI(minus) = LYESTERDAY - LTODAY
where
HTODAY = today’s high
price
HYESTERDAY = yesterday’s
high price
LYESTERDAY = yesterday’s
low price
LTODAY = today’s low price
We then make these adjustments:
If DI(plus) is less than DI(minus), then DI(plus) = 0
If DI(minus) is less than DI(plus), then DI(minus) = 0
If DI(plus) is negative, then DI(plus) = 0
If DI(minus) is negative, then DI(minus) = 0
It is possible that both DI(plus) and DI(minus) may be set to zero.
Next, smooth DI(plus) and DI(minus) using a 27-day exponential
moving average:
smoothed DI(plus) = EMA(27)(DI(plus))
smoothed DI(minus) = EMA(27)(DI(minus))
The Average Directional Movement Index
(ADX) is used in tandem with the DMI indicator.
Positive Development Calculation:
The DMI TAI is used in tandem with the ADX TAI. A new
positive development (NPD)
occurs when:
DI(plus) x+ DI(minus)
AND either:
ADX rises while DI(plus)
and ADX are above DI(minus)
or
ADX turns up from below
DI(plus) and DI(minus)
This TAI is no longer positive when
DI(plus) crosses under DI(minus).
That is, when DI(plus)
x- DI(minus).
If this TAI is still positive tomorrow, it will no longer be new,
but will be a cumulative positive development (CPD).
If this TAI was a new positive development (NPD)
yesterday, and is still positive today, then it becomes a cumulative
positive development (CPD).
History:
J. Welles Wilder, Jr., in his book New Concepts
in Technical Trading Systems (Trend Research, PO Box 128, McLeansville,
NC 27301, 1978), asserts that markets exhibit strong trends only
about 30 percent of the time. To determine when such strong trends
occur, Wilder created a set of indicators, among them DX. Since
DX indicates a trend‘s direction but not its strength, it
can be used with ADX (as here), which indicates a trend’s
strength but not its direction.
Directional Movement (DM) and the Directional
Movement Index (DX)
DM is a family of indicators that Wilder created to help
determine if a security is trending. The DM family of indicators
has also been called the Directional Movement Index (DMI). This
confuses the family of indicators with the single indicator called
the Directional Movement Indicator (but abbreviated DX).
The indicators and their abbreviations are:
- Plus Directional Indicator
or Positive Directional
Indicator (+DI or DI(plus) or PDI)
- Minus Directional Indicator
or Negative Directional
Indicator (-DI or DI(minus) or MDI)
- Directional Movement Indicator (DX)
- Average Directional Movement Indicator (ADX)
- Average Directional Movement Index Rating (ADXR)
This chart shows the DMI indicators for the last quarter of 2005
for Panera Bread (PNRA). The vertical green and red histogram shows
the difference between PDI (Plus Directional Indicator) and MDI
(Minus Directional Indicator) making it easier to see not only the
crossover points, but the relative strengths of PDI over MDI or
vice versa. The thicker, black line is the ADX.
Purple line A shows the initial event, when PDI crosses over the
MDI. At that point ADX is below 20 and MDI is about 22. Because
the cross over was between days the positive development is the
next day.
Purple line B shows the new positive development when ADX is rising
and, at 17, ADX is higher than PDI at 16. So what is purple line
C? An investor might have been concerned that ADX was at a non-trending
level and wanting to wait. At purple line C ADX tested a low of
about 14 and was on the way back up. Purple line D is an even more
cautious investor who wanted to wait for ADX to be solidly in the
trending range. At that point ADX had reached 23 and fallen, but
not below 20. Purple line D is when ADX turned back up.
Late December 2005 PDI x- MDI and this was no longer a positive
development. Notice that from about 12/14/2005 the relative strength
of PDI over MDI was weakening. This might be an early exit signal
or a caution.
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