Powered Kaufman Adaptive Moving Average

Introduction

The ability the Kaufman adaptive moving average (KAMA) has to be flat during ranging markets and close to the price during trending markets is what make this moving average one of the most useful in technical analysis. KAMA is calculated by using exponential averaging using the efficiency ratio (ER) as smoothing variable where 1 > ER > 0. An increasing efficiency ratio indicate a trending market. Based on one of my latest indicator (see Kaufman Adaptive Bands) i propose this modified KAMA that allow to emphasis the abilities of KAMA by powering the efficiency ratio. I also added a new option that allow for even more adaptivity.

The Indicator

The indicator is a simple KAMA of period length that use a powered ER with exponent factor.



When factor = 1 the indicator is a simple KAMA, however when factor > 1 there can be more emphasis on the flattening effect of KAMA.



You can also restrain this effect by using 1 > factor > 0



Note that when the exponent is lower than 1 and greater than 0 you are basically applying a nth square root to the value, for example pow(2,0.5) = sqrt(2) because 1/0.5 = 2, in our case :

pow(ER,factor > 1) < ER and pow(ER,1 > factor > 0) > ER

Self Powered P-KAMA

When the self powered option is checked you are basically powering ER with the reciprocal of ER as exponent, however factor does no longer change anything. This can give interesting results since the exponent depend on the market trend strength.



In orange the self powered KAMA of period length = 50 and in blue a basic powered KAMA with a factor of 3 and a period of length = 50.

Conclusion

Applying basic math to indicators is always fun and easy to do, if you have adaptive moving averages using exponential averaging try powering your smoothing variable in order to see interesting results. I hope you like this indicator. Thanks for reading !