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.
pip install fractalmarkets
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".
- fractalmarkets
- mmar
- BrownianMotion
- BrownianMotionMultifractalTime
- rs
- RS
- mmar
To simulate timeseries with fractalmarkets, instantiate the simulation process that you want with the required parameters and run simulate.
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()
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()
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
pip install virtualenv// from fractal_market_analysis directory
python -m virtualenv venv
// sometimes that does not work so try below
// virtualenv venv// 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// from fractal_market_analysis directory
pip install -r requirements.txt// from fractal_market_analysis directory. This will allow us to use fma imports in our modules.
pip install -e .// from fractal_market_analysis directory
conda env create -f environment.yml
conda activate fractalmarkets// from fractal_market_analysis directory
python examples/rs_analysis.py // or any other file// from fractal_market_analysis directory
pytest