The Next Level in TRADING ALGORITHMS : FRAMA

FRAMA = Fractal Adaptive Moving Average

by John Ehlers, MESA

Basis of Theory:
Insight of Signal Sampling & Signal Processing
(approximating price patterns to cyclic, repeatable 1D or 2D non-linear functions / signals)

FRAMA theory :
The "weight or exponent" of a MA,  DYNAMICALLY ADAPTS  EVERY DAY,  by a FACTOR "D" (Fractal Dimension),

D =  Defines the "most possible" DIMENSION of the FRACTAL (1d or 2D, or in between! ) that the current trend is developing  into ....

Basic Maths of EMA :
EMA = EMA(1) + α * (Close – EMA(1))

But Alpha in an EMA is α = 2 / (N + 1) so it remains constant


FRAMA
For the FRAMA α = EXP(W*(D – 1)) making it adapt as the Fractal Dimension changes.


http://etfhq.com/blog/2010/09/30/fractal-adaptive-moving-average-frama/

http://www.mesasoftware.com/aboutjohnehlers.htm - John Ehlers

FRAMA TEST RESULTS (vis a vi EMA / SMA) :

The FRAMA is astoundingly effective as both a fast and a slow moving average and will outperform any SMA or EMA.

We selected a modified FRAMA with a “FC” of 4, a “SC” of 300 and a “FRAMA” period of 126 as being the most effective fast FRAMA although the settings for a standard FRAMA will also produce excellent results.

For a slower or longer term average the best results are likely to come from a “FC” of 40, a “SC” of 250 and a “FRAMA” period of 252.

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The Mathematically  / Programming,  inclined are urged to explore ANN (Neural Networks)  to MAs . FRAMA & Neural Networks have the same Logical basis ...
SIGNALS REPEAT OVER TIME & CAN A COMPUTER CAN BE TRAINED TO IDENTIFY THEM !

MASTER THE MATHS & EXPERIENCE THE POWER OF ALGORITHMIC TRADING :-)
cheers
SMO