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### 10.12 Directional Movement Index

The directional movement index by J. Welles Wilder expresses so-called directional movement, from high to high, or low to low, as a percentage of true range (see True Range).

When today’s high is above yesterday’s high, the increase is upwards directional movement, written DM+. If today’s high is not above yesterday’s then DM+ is zero. Conversely when today’s low is less than yesterday’s low the decrease is downward directional movement, written DM-. Again if today’s low is not below yesterday’s then DM- is zero. Both DM+ and DM- are positive numbers, the “+” and “-” signs just refer to the direction of the movement.

On an “inside day” where today’s trading range is entirely within yesterday’s both DM+ and DM- are zero. On an “outside day” where today’s trading goes both above and below yesterday’s range, only the larger of DM+ and DM- is used and the other is set to zero.

The two DM+ and DM- series are each smoothed with an N-day exponential moving average (see Exponential Moving Average) and expressed as a percentage of average true range (see Average True Range). The ATR uses the same N-day EMA smoothing. Two lines are formed, the upwards directional index DI+ and downwards directional index DI-.

```            EMA[N] of DM+                 EMA[N] of DM+
DI+ = 100 * -------------     DI+ = 100 * -------------
ATR[N]                        ATR[N]
```

In Chart, DI+ is drawn in green (for upwards) and DI- is drawn in red (for downwards).

The smoothing N is by Wilder’s reckoning of EMA smoothing period (as discussed in Exponential Moving Average), the default is the 14 he recommended.

An extreme of 100 is approached on DI+ when each day trades entirely above yesterday’s range (eg. runaway gaps), and then closes at the high of the day. This is rather rare, usually there’s some pullbacks. Essentially DM+ counts just the advance, the true range in the denominator counts the backtracking too. For DI-, an extreme of 100 is approached similarly when each day trades entirely lower the previous, and closes at its low.

#### 10.12.1 Average Directional Index

The average directional index (ADX) combines DI+ and DI-, expressing their difference (ignoring the sign) as a percentage of the total, forming a single line ranging 0 to 100,

```            abs(DI+ - DI-)