ADX / DMI - Indicator Formula

J. Welles Wilder Jr.has developed a quantitative heuristic system derived from the idea that the predominance of demand over supply (or vice versa) is identifiable through the observation of increases between maximum values and decreases between minimum values, period after period.

If we proceed in this way, we can say that, in a given period of time, the prevalence of increases among the maximums over decreases among the minimums is an indication of the existence of an upward trend in the market.

The result is a series of interlinked algorithms that can be used to define the nature of the current market phase and to manage market positions.

In order to develop the algorithms it is necessary to introduce the necessary quantities, described as follows: Maximum, minimum and closing values of each period t.

The basic quantities of the system are:

1) ES significant range.

It is a measure of the magnitude of the maximum movement occurring between two time intervals or of the volatility of a price defined as the greater quantity of the two:

the distance between the maximum and the minimum of the session (price range);

the difference between the maximum of the session in question and the closing price of the previous one;

the difference between the closing of the previous session and the minimum of the one under examination.

ES( t ) = the maximum between

( t ) - L( t )

ABS( C( t - 1 ) - H( t ) )

ABS( C( t - 1 ) - L( t ) )

where:

ES( t ) = Significant deviation of the current day

H( t ) = Maximum of the current day

L( t ) = Minimum of the current day

C( t - 1 ) = Share closing of the previous day

ABS( ) = function that returns the absolute value

2) Positive directional movement PDM.

It occurs when H( t ) > H( t - 1 ) and L( t ) >= L( t - 1 ).

In this case:

PDM( t ) = H( t ) - H( t - 1 )

NDM( t ) = 0

3) Negative directional movement NDM.

It occurs when L( t ) < L( t - 1 ) and H( t ) <= H( t - 1 ).

In this case:

PDM( t ) = 0

NDM( t ) = ABS( L( t ) - L( t - 1 ) )

4) Neutral directional movement.

It occurs when L( t ) = L( t - 1 ) and H( t ) = H( t - 1 ).

In this case:

PDM( t ) = 0

NDM( t ) = 0

5) Dual directional movement.

It occurs when L( t ) < L( t - 1 ) and H( t ) > H( t - 1 ).

This situation has two subcases:

a) if ( H( t ) - H( t - 1 ) ) > ABS( L( t ) - L( t - 1 ) ) then:

PDM( t ) = H( t ) - H( t - 1 )

NDM( t ) = 0

b) if ( H( t ) - H( t - 1 ) ) < ABS( L( t ) - L( t - 1 ) ) then:

PDM( t ) = 0

NDM( t ) = L( t ) - L( t - 1 )

At this point, the three defined quantities( PDM( ), NDM( ), SES( ) ) are toned down by an exponential moving average equalisation process (Smoothing):

SES( ) = Exponential Smoothing of ES( )

SPDM( ) = Exponential Smoothing of PDM( ) to NP

SNDM( ) = Exponential Smoothing of NDM( ) to NP

where:

ES( ) = Significant deviation

SES( ) = Significant deviation toned down by the Exponential Smoothing

PDM( ) = Positive directional movement

NDM( ) = Negative directional movement

SPDM( ) = Positive directional movement toned down by the Exponential Smoothing

SNDM( ) = Negative directional movement toned down by the Exponential Smoothing

NP = Number of calculation periods of the indicator

the Directional Movement +DI ( PDI ) and Directional Movement -DI ( NDI ) are calculated:

PDI( t ) = ( SPDM( t ) / SES( t ) ) * 100

NDI( t ) = ( SNDM( t ) / SES( t ) ) * 100

where:

PDI( t ) = Current directional Movement +DI

NDI( t ) = Current directional Movement -DI

SPDM( t ) = Current positive directional movement toned down by the E. Smoothing

SNDM( t ) = Present negative directional movement toned down by the E. Smoothing

SES( t ) = Current significant deviation toned down by E. Smoothing

The Directional Movement Index (DMI) and the Average Directional Index (ADX) are calculated:

DMI( t ) = 100 * ( ABS( PDI( t ) - NDI( t ) ) / ( PDI( t ) + NDI( t ) ) )

ADX( ) = Exponential Smoothing of the DMI( ) to NP

where:

NP = Number of calculation periods of the indicator

A +DI line above the -DI line and the -DI line is falling means there is more upward pressure on prices than downward pressure.

A -DI line above the +DI line and the -DI is falling means there is more downward pressure on prices than upward pressure.

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