FrAMA: Fractal Adaptive Moving Average

ایده به زبان ساده

A trending market draws a fairly straight path; a choppy one draws a jagged, space-filling path. FrAMA measures this roughness (its "fractal dimension") and follows the price quickly when the path is straight and slowly when it is jagged.

روش محاسبه

It compares the price range of the first half of the window, the second half and the whole window. If the whole range is about the sum of the halves, the path is straight (trend); if it is much smaller, the path doubled back (noise). That sets the speed of an exponential average.

N1 = range of first half ÷ half length,  N2 = range of second half ÷ half length
N3 = range of whole window ÷ window length
D = (log(N1 + N2) − log(N3)) ÷ log(2)
speed a = exp(−4.6 × (D − 1)), kept between 0.01 and 1
FrAMA today = a × price + (1 − a) × FrAMA yesterday

نحوه استفاده

• Use it as a trend line that stays put in sideways markets and moves fast in trends.
• Price crossing a flat FrAMA is less meaningful than crossing a sloping one.

نتیجه‌گیری

• A sudden tilt in a previously flat FrAMA often marks a breakout.

مراقب این‌ها باشید

• It can jump when the volatility pattern changes abruptly.

کمی تاریخچه

John Ehlers described FrAMA in Technical Analysis of Stocks & Commodities in 2005, applying fractal geometry ideas made popular by Benoit Mandelbrot.