lppls 0.1.6

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 LPPL 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 osciallations
• 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 lppls import lppls
import pandas as pd
import tqdm
import time 

if __name__ == '__main__':
    start = time.time()
    data = pd.read_csv('<location>.csv', index_col='<index_col>', parse_dates=True)
    signals_list = []
    asset_list = data.columns.tolist()
    window = 126
    for seq in tqdm(range(data.shape[0] - window)):
        window_data = data.iloc[seq:seq + window].copy()
        lppl_model = lppls.LPPLS(window_data, asset_list)
        signals_list.append(lppl_model.fetch_indicators(126, 5, 21, 5))
    end = time.time()
    duration = end - start
    print(duration)

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.