lppls 0.1.12

A Python module for fitting the LPPLS model to data.

Log Periodic Power Law Singularity (LPPLS) Model

lppls is a Python module for fitting the LPPLS model to data.

Overview

The LPPLS model provides a flexible framework to detect bubbles and predict regime changes of a financial asset. A bubble is defined as a faster-than-exponential increase in asset price, that reflects positive feedback loop of higher return anticipations competing with negative feedback spirals of crash expectations. It models a bubble price as a power law with a finite-time singularity decorated by oscillations with a frequency increasing with time.

Here is the model:

where:

• expected log price at the date of the termination of the bubble
• critical time (date of termination of the bubble and transition in a new regime)
• expected log price at the peak when the end of the bubble is reached at
• amplitude of the power law acceleration
• amplitude of the log-periodic oscillations
• degree of the super exponential growth
• scaling ratio of the temporal hierarchy of oscillations
• time scale of the oscillations

The model has three components representing a bubble. The first, , handles the hyperbolic power law. For when the price growth becomes unsustainable, and at the growth rate becomes infinite. The second term, , controls the amplitude of the oscillations. It drops to zero at the critical time . The third term, , models the frequency of the osciallations. They become infinite at .

Important links

• Official source code repo: https://github.com/Boulder-Investment-Technologies/lppls
• Download releases: https://pypi.org/project/lppls/
• Issue tracker: https://github.com/Boulder-Investment-Technologies/lppls/issues

Installation

Dependencies

lppls requires:

• Pandas (>= 0.25.0)
• Python (>= 3.6)
• NumPy (>= 1.17.0)
• SciPy (>= 1.3.0)
• Matplotlib (>= 3.1.1)

User installation If you already have a working installation of numpy and scipy, the easiest way to install scikit-learn is using pip

pip install -U lppls

Example Use

from datetime import datetime
from lppls import lppls
import numpy as np
import pandas as pd
%matplotlib inline
SECONDS_IN_A_MONTH = 2.628e+6

data = pd.read_csv('data/sp500.csv', index_col='Date', parse_dates=True)
timestamp = [datetime.timestamp(dt) for dt in data.index]
price = [np.log(p) for p in data['Adj Close']]
first_ts = timestamp[0]
last_ts = timestamp[-1]
x_seconds = (last_ts - first_ts) * 0.2
observations = np.array([timestamp, price])
# set limits for non-linear params
search_bounds = [
    (last_ts - x_seconds, last_ts + x_seconds), # Critical Time 
    (0.1, 0.9),                                 # m : 0.1 ≤ m ≤ 0.9
    (6, 13),                                    # ω : 6 ≤ ω ≤ 13
]
MAX_SEARCHES = 25
lppls_model = lppls.LPPLS(use_ln=True, observations=observations)
tc, m, w, a, b, c = lppls_model.fit(observations, MAX_SEARCHES, search_bounds, minimizer='Nelder-Mead')
lppls_model.plot_fit(tc, m, w, observations)
# should give a plot like the following...

References

• Filimonov, V. and Sornette, D. A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model. Physica A: Statistical Mechanics and its Applications. 2013
• Sornette, D. Why Stock Markets Crash: Critical Events in Complex Financial Systems. Princeton University Press. 2002.