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# Average Directional Movement Index (ADX)

**The Average Directional Index**, or **ADX**, was developed by J. Welles Wilder to determine trend forces, whether the trend will grow on or will gradually lose its positions. This indicator lets analyze the market tendencies and make trading decisions in the Forex market.

In fact, **ADX** relates to the class of oscillators, which changes positions in a range from 0 up to 100. Though the indicator's fluctuations are in a range from 0 and up to 100, it seldom goes over a point of 60. If the value is lower than 20 demonstrates a weak trend, if the value is over 40 shows a strong trend. Position above 40 indicates both strong descending, and a strong ascending trend.

**1 variant - calculation**:

Calculation of positive and negative directed movement (Directional Movement or DM) - **+DM _{j}** and

**-DM**

_{j}If High

_{j}(a maximum of a current bar)> High

_{j}-1 (a maximum of the previous bar),

That +DM

_{j}= High

_{j}- High

_{j-1}, differently +DM

_{j}= 0

If Low

_{j}(a minimum of a current bar) < Low

_{j-1}(a minimum of the previous bar),

That -DM

_{j}= Low

_{j-1}- Low

_{j}, differently -DM

_{j}= 0

If +DM

_{j}> -DM

_{j},

That -DM

_{j}= 0

If -DM

_{j}> +DM

_{j},

That +DM

_{j}=0

If +DM

_{j}= -DM

_{j},

That +DM

_{j}=0, -DM

_{j}=0

Determination of the true range - TR_{j}

TR = maximal module of three values

|High - Low |, |High - Close_{j-1} |, |Low - Close_{j-1} |.

Close_{j-1} - the close price of the previous period.

Note: In most cases module |High - Low| will be maximal on forex in absence of price breaks.

The determination of the indicator of a positive direction and the indicator of a negative direction - **+DI _{j}** and

**-DI**(Directional Index). +DI

_{j}_{j}= Exponential Moving Averagej (+SDI, N) -DI

_{j}= Exponential Moving Averagej (-SDI, N) Where, if TR

_{j}not =0, That +SDI

_{j}= +DM

_{j}/ TR

_{j}; -SDI

_{j}=-DM

_{j}/ TR

_{j}If TR

_{j}= 0, That +SDI

_{j}= 0, -SDI

_{j}= 0,

Determination of the average directional index- ADX_{j}

ADX_{j} = Exponential Moving Average_{j} (DX, N)
Where DXj it is calculated under the formula

**ADX** looks as follows.

Sometimes ADX helps to determine potential market changes. Once the indicator grows over 20 points from below upwards, maybe, it is a sign of the trend's change and its further development. When the indicator shows value less than 40, falling from higher level, it means that the trend has lost its positions. ADX descends from two other indicators, which were also developed by Wilder. The first one is called Positive Directional Indicator, or just "+DI," the second one is -Negative Directional Indicator, or "-DI". On the chosen time interval +DI - shows force of upwards movements, and -DI on the contrary shows force of downwards movements for the certain period. ADX indicates the trend's force and coalesces +DI and -DI smoothing data with changing average.

### The use

Usually buy and sell signals act on crossings +DI/-DI as following: a sale signal occurs, when -DI crosses +DI from the top; the buy signal occurs, when +DI crosses -DI from below.

It is crucial for the trader it to notice a trend at an early stage of development to gain maximum benefit from his deals. ADX helps him in that. For that purpose, it is quite important to watch currency pairs where ADX crosses 20 from below upwards. Correspondingly decreasing ADX less than 40 points indicates that the ongoing trend is weakened and the trading range starts. Now, ADX demonstrates a presence or absence of a trend, and for determining a direction of an input and input points you should better use other kinds of indicators.

### The weaknesses

The input signal submitted by crossing of +DI and -DI in many cases occurs false if the currency pair remains in a trading range. Here is an example of ADX calculation:

ADX is a DX, smoothed by the exponential moving average for "the n periods": ADX = MA (DX, n, E)

DX is a distinction between +DI and -DI; it is also calculated according to this fact. It provides the value with truly directed movement. The sum of -DI and +DI gives the value of total amount of directed movement during this period. Here's an example of calculating DX for "n periods":

Here's an example of calculating DX for "n periods":

DX (n) = 100% * (PDI (n) - MDI (n)) / (PDI(n) + MDI(n)).

The previously mentioned index determines, in percents, a part of the directed movement for "n the periods" in all fluctuations for these "n the periods". It lets define the trend's force of on a scale from 0 up to 100, independently from the fact if the trend downwards or upwards is directed. The size of the value depends on the strength of the trend.

Here's an example of calculating MDI and PDI:

PDI = MA (PDM, n) / MA (TR, n);

MDI = MA (MDM, n) / MA (TR, n).

TR = max (abs (High - Low), abs(High - Closei-1), abs(Low - Closei-1)).

TR - True Range, positive number.

**2 variant - calculation:**

Other variant of calculation of ADX:

ADX - is a DX, smoothed by the exponential moving average for the n periods:

ADX = MA(DX, n, E)

DX is calculated as a difference between +DI and -DI and it gives the value of truly directed movement. The sum of +DI and-DI gives the value of total amount of directed movement within period. DX for n periods is calculated by the following formula:

DX(n) = 100% * (PDI(n) - MDI(n)) / (PDI(n) + MDI(n)).

The given index defines in percentage a part of the directed movement for n periods in all movement for these n periods. It allows expressing force of a trend on a scale numbered from 0 up to 100, without dependence from those, the trend downwards or upwards is directed. The value is as big as the trend is strong.

Where PDI and MDI are calculated by the following formulas:

PDI = MA(PDM,n) / MA(TR,n),

MDI = MA(MDM,n) / MA(TR,n).

TR = max(abs(High - Low), abs(High - Closei-1), abs(Low - Closei-1)).

TR – True Range, positive number.

In the falling market, -DI grows, and +DI goes down, and the market moving upwards +DI rises, and-DI goes down. If the trend is strong and quick, the corresponding movement DI will be as strong and quick. If +DI and-DI are set against each other, in the market there was a balance and there is a movement sideways. The market tendency changes at crossing of DI lines; if +DI has fallen below -DI, it means sellers became more active and the market starts moving downwards, if +DI crosses -DI upwards, in the market there is a bull situation with the majority of buyers. So crossing of lines DI is a sign to sell or buy.