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# Average Directional Index

The Directional Movement Index is an oscillator that indicates whether or not a market is trending. The indicator consists of two lines: the Plus Directional indicator line (+DI) and the Minus Directional Indicator (-DI). They are usually plotted on the same chart as their associated moving average, the Average Directional Index (ADX).

The indicators range in value between 0 and 100. A low value indicates the trend is weak, a high value that the trend is strong.

The +DI measures how strongly the price is moving upwards. The -DI shows how strongly price is moving in a downward direction. +DI generally moves with price; if price increases +DI increases; as price decreases +DI decreases. –DI on the other hand, generally moves opposite to price, rising as price falls and falling as price rises.

If the +DI is above the –DI and rising, then the dominant trend is upwards. If the –DI is above the +DI and rising, then the dominant trend is downwards.

The +DI and -DI are shown in combination with the ADX indicator, which shows the strength of a current trend.

As with the DI, the ADX indicator fluctuates between 0 and 100. Unlike the +DI and –DI, the direction in which the ADX moves does not indicate if the trend if up or down, rather it shows if the trend is strong or weak. Values below 20 indicate a week non-trending market whilst values above 40 indicate a strong trend. The indicator is useful in providing a warning that the market is changing direction from trading sideways to trending (and vice-versa).

As a trend starts to emerge, the ADX will strengthen moving from below 20 to above 20. Further increases between 20 and 40 provide confirmation of an emerging trend; a value of 40 or above indicates that there is a very strong trend; then as the ADX again turns lower, this indicates the market is reversing the current trend.

The default period used to calculate the +DI and –DI is 14. This can be adjusted to suit your trading strategy and style.

Trading strategies that can be applied to the +DI, -DI and ADX indicator:

• Bullish signal: +DI crosses above -DI
• Bearish signal: -DI crosses above +DI
• ADX rising above 20 implies trend beginning to emerge
• ADX rising above 40 implies strong trend
• ADX falling implies change of trend

## Average Directional Index Formula

The calculation of the ADX requires multiple steps. Firstly calculate the True Range by getting the maximum of the difference between the High, Low and previous Past Close price:

$\displaystyle \text{True Range} = \displaystyle MAX \left ( (\text{HIGH } - \text{ LOW), (HIGH } - \text{ PAST CLOSE), (PAST CLOSE } - \text{LOW}) \right )$

Now calculate the positive Directional Movement, which is the High minus the Past High, if the High minus the Past High is greater than the Past Low minus the Low, and the High is greater than the Past High:

$\displaystyle \text{+DM} = \displaystyle \quad IF \qquad (\text{HIGH } - \text{ PAST HIGH }) > (\text{ PAST LOW } - \text{ LOW}) \qquad AND \qquad (\text{HIGH } > \text{ PAST HIGH}) \quad THEN \qquad (\text{HIGH } - \text{ PAST HIGH}) \quad ELSE \qquad 0$

The negative Directional Movement is calculated using the same principals with the following formula:

$\displaystyle \text{-DM} = \displaystyle \quad IF \qquad (\text{PAST LOW } - \text{ LOW }) > (\text{HIGH } - \text{ PAST HIGH }) \qquad AND \qquad (\text{LOW } < \text{ PAST LOW}) \quad THEN \qquad (\text{PAST LOW } - \text{ LOW }) \quad ELSE \qquad 0$

The sum of the True Range and Directional Movement values on each interval is calculated over $\displaystyle n$ periods, where the default is 14 periods:

$\displaystyle \text{TRn} = \displaystyle \displaystyle \sum_{1}^n (\text{True Range})$

$\displaystyle \text{+DMn} = \displaystyle \displaystyle \sum_{1}^n (\text{+DM})$

$\displaystyle \text{-DMn} = \displaystyle \displaystyle \sum_{1}^n (\text{-DM})$

On each incremental interval after the summation of the True Range and Directional Movement values over $\displaystyle n$ periods, the summation values are adjusted by adding the True Range for the current interval and adjust the summation value using the following formula:

$\displaystyle \text{TRn} = \displaystyle \text{TRn } - (\text{TRn } / n) + \text{True Range}$

$\displaystyle \text{+DMn} = \displaystyle \text{+DMn } - (\text{+DMn } / n) + \text{+DM}$

$\displaystyle \text{-DMn} = \displaystyle \text{-DMn } - (\text{-DMn } / n) + \text{-DM}$

where the default $\displaystyle n$ is typically 14.

Now calculate the positive and negative Directional Index, which is the summation of the Directional Movement divided by the summation of the True Range:

$\displaystyle \text{+DI} = \displaystyle (\text{+DMn }/ \text{ TRn} ) * 100$

$\displaystyle \text{-DI} = \displaystyle (\text{-DMn }/ \text{ TRn} ) * 100$

To calculate the ADX, the Directional Index difference has to be calculated:

$\displaystyle \text{DI Difference} = \displaystyle \text{Absolute Value of }(\text{+DI } - \text{ -DI})$

Then calculate the sum of the Directional Index values:

$\displaystyle \text{DI Summation} = \displaystyle \text{+DI } + \text{ -DI}$

Lastly to calculate the ADX value, divide the DI Difference by the DI Summation

$\displaystyle \text{ADX} = \displaystyle \text{DI Difference } / \text{ DI Summation}$

## Average Directional Index Indicator

The Average Directional Index indicator can be displayed on the TimeToTrade charts. To add the Average Directional Index indicator to the TimeToTrade charts, go to the chart settings and click on the 'Add Indicator' button. Click on the search box and type the name of the indicator that you are looking for, or for example type Average Directional Index and scroll through the results:

After adding the Average Directional Index indicator, within the chart settings, click on it to set the parameters and change colours.

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