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# How is the Average Directional Index (ADX) calculated and what is the formula?

The average directional index, or ADX, is the primary technical indicator among the five indicators that make up a technical trading system developed by J. Welles Wilder, Jr. and is calculated using the other indicators that make up the trading system. The ADX is primarily used as an indicator of momentum, or trend strength, but the total ADX system is also used as a directional indicator.

To calculate the ADX, first determine the + and - directional movement, or DM. The +DM and -DM are found by calculating the "up-move," or current high minus the previous high, and "down-move," or current low minus the previous low. If the up-move is greater than the down-move and greater than zero, the +DM equals the up-move; otherwise, it equals zero. If the down-move is greater than the up-move and greater than zero, the -DM equals the down-move; otherwise, it equals zero.

The positive directional indicator, or +DI, equals 100 times the exponential moving average (EMA) of +DM divided by the average true range over a given number of time periods. Welles usually used 14 periods. The negative directional indicator, or -DI, equals 100 times the exponential moving average of -DM divided by the average true range (ATR). The ADX indicator itself equals 100 times the exponential moving average of the absolute value of (+DI minus -DI) divided by (+DI plus -DI).

The ADX is used to indicate market direction, the existence or nonexistence of a trend and market momentum. Market direction is determined by the levels of the +DI and -DI. If +DI is the higher number, market direction is up; if -DI is the greater number, market direction is down. The ADX indicator, which varies in value from zero to 100, is the primary momentum indicator. A value over 20 indicates the existence of a trend; a value over 40 indicates a strong trend.

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