fractalmarkets

Motivation

We are hard pressed to find a concrete implementation of both Benoit Mandelbrot's "A Multifractal Model of Asset Returns" and Edgar E. Peters' "Fractal Market Analysis" so, with apologies to the Authors, we attempt to fill this vacancy.

Installation

pip install fractalmarkets

Features

This package offers time series simulation processes as well as rescaled range analysis.

The time series simulations are implemented as per Benoit Mandelbrot's description in "A Multifractal Model of Asset Returns", and further elaborated on within "Scaling in financial prices: III. Cartoon Brownian motions in multifractal time".

The rescaled range analysis is implemented as per Edgar E. Peters "Fractal Market Analysis".

Simulation Processes

• fractalmarkets
  • mmar
    • BrownianMotion
    • BrownianMotionMultifractalTime
  • rs
    • RS

Usage

To simulate timeseries with fractalmarkets, instantiate the simulation process that you want with the required parameters and run simulate.

Brownian Motion in Multifractal Time

from fractalmarkets.mmar.brownian_motion_multifractal_time import BrownianMotionMultifractalTime
import matplotlib
import matplotlib.pyplot as plt; plt.style.use('ggplot')
from scipy import interpolate
import numpy as np

bmmt = BrownianMotionMultifractalTime(9, x=0.457, y=0.603, randomize_segments=True, randomize_time=True, M=[0.6, 0.4])
data = bmmt.simulate() # [ [x, y], ..., [x_n, y_n]]

f = interpolate.interp1d(data[:,0], data[:,1])

y = f(np.arange(0, 1, .001))
x = np.linspace(0, 1, len(y), endpoint=True)

y_diff = [b - a for a, b in zip(y[:-1], y[1:])]

fig, axs = plt.subplots(2)
fig.suptitle('Brownian Motion in Multifractal Time')

axs[0].plot(x, y, 'b-')
axs[1].bar(x[:-1],y_diff,align='edge',width=0.001,alpha=0.5)
bar_list=filter(lambda x: isinstance(x,matplotlib.patches.Rectangle),axs[1].get_children())
for bar,ret in zip(bar_list,y_diff):
    if ret >= 0:
        bar.set_facecolor('green')
    else:
        bar.set_facecolor('red')

z1 = np.array(y)
z2 = np.array([0] * len(y))

axs[0].fill_between(x, y, 0,
                where=(z1 >= z2),
                alpha=0.30, color='green', interpolate=True)

axs[0].fill_between(x, y, 0,
                where=(z1 < z2),
                alpha=0.30, color='red', interpolate=True)

plt.show()

Brownian Motion

from fractalmarkets.mmar.brownian_motion import BrownianMotion
import matplotlib
import matplotlib.pyplot as plt; plt.style.use('ggplot')
from scipy import interpolate
import numpy as np

bm =  BrownianMotion(9, .457, .603, randomize_segments=True)
data = bm.simulate() # [ [x, y], ..., [x_n, y_n]]

f = interpolate.interp1d(data[:,0], data[:,1])

y = f(np.arange(0, 1, .001))
x = np.linspace(0, 1, len(y), endpoint=True)

y_diff = [b - a for a, b in zip(y[:-1], y[1:])]

fig, axs = plt.subplots(2)
fig.suptitle('Brownian Motion')

axs[0].plot(x, y, 'b-')
axs[1].bar(x[:-1],y_diff,align='edge',width=0.001,alpha=0.5)
bar_list=filter(lambda x: isinstance(x,matplotlib.patches.Rectangle),axs[1].get_children())
for bar,ret in zip(bar_list,y_diff):
    if ret >= 0:
        bar.set_facecolor('green')
    else:
        bar.set_facecolor('red')

z1 = np.array(y)
z2 = np.array([0] * len(y))

axs[0].fill_between(x, y, 0,
                where=(z1 >= z2),
                alpha=0.30, color='green', interpolate=True)

axs[0].fill_between(x, y, 0,
                where=(z1 < z2),
                alpha=0.30, color='red', interpolate=True)

plt.show()

RS Analysis

from fractalmarkets.rs.rs import RS
from fractalmarkets.mmar.brownian_motion_multifractal_time import BrownianMotionMultifractalTime

bmmt = BrownianMotionMultifractalTime(9, x=4/9, y=0.603, randomize_segments=False, randomize_time=False, M=[0.6, 0.4])
data = bmmt.simulate()

rs = RS(data[1:,1]) # timeseries starts at zero which must be omitted to avoid division error
(H, c) = rs.get_Hc()
print("Estimated H from RS Analysis: {}".format(H))

rs.plot_vstat() # plot vstat and RS

>> Estimated H from RS Analysis: 0.6237751068336207

Developer Guide

Install virtualenv

pip install virtualenv

Create a virtual environment

// from fractal_market_analysis directory
python -m virtualenv venv
// sometimes that does not work so try below
// virtualenv venv

Start the virtual environment

// from fractal_market_analysis directory
source venv/Scripts/activate
// it is possible that your venv has a bin directory rather than a Scripts directory. If so run the following
// source venv/bin/activate

Install proper packages

// from fractal_market_analysis directory
pip install -r requirements.txt

Install our application and watch for edits

// from fractal_market_analysis directory. This will allow us to use fma imports in our modules.
pip install -e .

Bonus for the anaconda users...

// from fractal_market_analysis directory
conda env create -f environment.yml
conda activate fractalmarkets

Run an example

// from fractal_market_analysis directory
python examples/rs_analysis.py // or any other file

Run the Tests

// from fractal_market_analysis directory
pytest