FRAMA (Fractal Adaptive Moving Average) in Python

Introduction

The aim of this repository is to provide functions of FRAMA written in python for both educational and industrial purposes. FRAMA is a state of the art Moving Average estimator(or was by the time u read this...). It is used in economics for stock prices and Wall Street stuff, but it can also be used from anyone as a better moving average algorithm. It works better on time series which present the same shape despite the length of the data timestamps type (sec, minutes, hours, days,...).

Libraries & Dependencies

• Numpy

• Works both in Python 2.7.6 and Python 3+

More Details

To present more details we will use a top-down approach. The algorithm uses an adaptive low-pass filter with one term alpha. So it should look something like this:

    for i in range(1,N):
        Filt[i+1] = alpha * InputPrice[i] + (1 - alpha) * Filt[i]

Now the problem is how do we calculate alpha at each step?

alpha is changed according to something called the fractal dimension.

So alpha is calculated as

The fractal dimension id D needs to be computed at every iteration step. The fractal dimension is defined by this relation:

where N1 and N2 are defined as:

    N1 = (max(v1) - min(v1)) / batch
    N2 = (max(v2) - min(v2)) / batch    

where v1 is a batch of the input and v2 is exactly the next batch of the input. batch is the number of data points per batch.

Now N3 is defined as

    N3 = (max([v1,v2]) - min([v1,v2])) / (2*batch)

and is the maximum over both batches and devided by the number of data points inside them.

Now, if you go from down up it will result in the code inside frama_numpy.py.

If still not satisfied from the explanation check the code and the References.

Results Galery

Feel free to send me your own examples! Thanks!

References

1. Ehlers, John. "FRAMA–Fractal Adaptive Moving Average." Technical Analysis of Stocks & Commodities (2005).