Charting and Studies User Guide - CQG.com

Adaptive Moving Average (AMA)
Page 213
The Adaptive Moving Average (AMA) study is similar to the exponential moving average (EMA),
except the AMA uses a scalable constant instead of a fixed constant for smoothing the data.
The formula for the exponential moving average is:
EMA(today) = C*(price(today) – EMA(yesterday)) + EMA(yesterday)
C is a smoothing constant where C = 2(N+1), and N is a number used to approximate a simple
moving average. C ranges between 0 and 1. For example, to use an EMA with similar
characteristics to a 10-bar simple moving average, use N= 10. Therefore, C = 2/(10+1) = 2/11
= 0.1818.
The formula for the AMA is:
AMA(today) = SC*(price(today) – AMA(yesterday)) + AMA(yesterday)
Where SC = Scalable Constant
The AMA uses two constants based on a fast EMA (short look back period) and a slow EMA
(long look back period). The scalable constant, which has a range between 0 and 1, weights the
AMA calculation between the two exponential moving averages by adjusting the constant. This
weighting is based on the degree of market direction relative to market volatility. The higher
the degree of trending by the market, the more the weighting shifts to the fast exponential
moving average constant. If the market is moving in congestion, then the weighting shifts to
the slow exponential moving average constant.
The scalable constant uses a market Efficiency Ratio to determine the degree of trend by the
market. The ratio is direction relative to volatility.
Direction is the difference between the current bar’s close and the close N bars back.
Volatility is the difference between each close over N bars back. The absolute value of each
difference is summed:
ER =Abs(Direction/Volatility) where,
Direction = Price(today) – Price(N bars back)
and
Here, the volatility measurement is the sum of the absolute value of the one bar difference in
closes over the look back period N. The default for N is 10 bars.
If the direction and the volatility readings are similar (i.e., the market is trending), the ratio
approaches 1. If the direction and the volatility readings are not similar (i.e., the market is in
congestion), the ratio approaches 0.
The Efficiency Ratio is used to scale between the two constants from the two exponential
moving averages (fast and slow). The default values are 2-bar and 30-bar EMAs. Therefore, the
default constants are as follows:
Fast = 2/(2+1) and Slow = 2/(30+1)
Fast = 0.6667 and Slow = 0.0645
The formula for weighting or scaling the constant is as follows:
Charting and Studies User Guide