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,...).
-
Numpy
-
Compiled with
Python 2.7.6
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.
Feel free to send me your own examples! Thanks!
- Ehlers, John. "FRAMA–Fractal Adaptive Moving Average." Technical Analysis of Stocks & Commodities (2005).