From 2c48a268617b4c52e96fb8fe7c6194355d559813 Mon Sep 17 00:00:00 2001 From: Joshua Nielsen Date: Tue, 30 Jan 2024 21:11:26 -0700 Subject: [PATCH] Quantile Regression (#101) * add subclass for quantile regression. * add usage quantile regression example notebook. * update readme. * bump version --- README.md | 5 ++ lppls/lppls_q.py | 35 ++++++++ notebooks/quantile_regression.ipynb | 123 ++++++++++++++++++++++++++++ setup.py | 2 +- 4 files changed, 164 insertions(+), 1 deletion(-) create mode 100644 lppls/lppls_q.py create mode 100644 notebooks/quantile_regression.ipynb diff --git a/README.md b/README.md index 9289748..93451f0 100644 --- a/README.md +++ b/README.md @@ -120,6 +120,10 @@ If you wish to store `res` as a pd.DataFrame, use `compute_indicators`. +## Quantile Regression +Based on the work in Zhang, Zhang & Sornette 2016, quantile regression for LPPLS uses the L1 norm (sum of absolute differences) instead of the L2 norm +and applies the q-dependent loss function during calibration. Please refer to the example usage [here](https://github.com/Boulder-Investment-Technologies/lppls/blob/master/notebooks/quantile_regression.ipynb). + ## Other Search Algorithms Shu and Zhu (2019) proposed [CMA-ES](https://en.wikipedia.org/wiki/CMA-ES) for identifying the best estimation of the three non-linear parameters ($t_c$, $m$, $\omega$). > The CMA-ES rates among the most successful evolutionary @@ -141,3 +145,4 @@ Performance Note: this works well for single fits but can take a long time for c - Shu, M. and Zhu, W. Real-time Prediction of Bitcoin Bubble Crashes. 2019. - Sornette, D. Why Stock Markets Crash: Critical Events in Complex Financial Systems. Princeton University Press. 2002. - Sornette, D. and Demos, G. and Zhang, Q. and Cauwels, P. and Filimonov, V. and Zhang, Q., Real-Time Prediction and Post-Mortem Analysis of the Shanghai 2015 Stock Market Bubble and Crash (August 6, 2015). Swiss Finance Institute Research Paper No. 15-31. + - Zhang, Q., Zhang, Q., and Sornette, D. Early Warning Signals of Financial Crises with Multi-Scale Quantile Regressions of Log-Periodic Power Law Singularities. PLOS ONE. 2016. DOI:10.1371/journal.pone.0165819 \ No newline at end of file diff --git a/lppls/lppls_q.py b/lppls/lppls_q.py new file mode 100644 index 0000000..af09012 --- /dev/null +++ b/lppls/lppls_q.py @@ -0,0 +1,35 @@ +from lppls.lppls import LPPLS +import numpy as np + + +class QLPPLS(LPPLS): + def __init__(self, observations, q=0.5): + super().__init__(observations) + self.q = q + + def func_restricted(self, x, *args): + """ + Finds the least absolute differences adjusted for the q-dependent loss function. + Args: + x(np.ndarray): 1-D array with shape (n,). + args: Tuple of the fixed parameters needed to completely specify the function. + Returns: + (float) + """ + + tc = x[0] + m = x[1] + w = x[2] + observations = args[0] + + rM = self.matrix_equation(observations, tc, m, w) + a, b, c1, c2 = rM[:, 0].tolist() + + delta = [self.lppls(t, tc, m, w, a, b, c1, c2) for t in observations[0, :]] + delta = np.subtract(delta, observations[1, :]) + + # Use the L1 norm (sum of absolute differences) instead of the L2 norm + # Apply the q-dependent loss function using the given quantile + loss = np.sum([-(1 - self.q) * e if e < 0 else self.q * e for e in np.abs(delta)]) + + return loss \ No newline at end of file diff --git a/notebooks/quantile_regression.ipynb b/notebooks/quantile_regression.ipynb new file mode 100644 index 0000000..1fc4949 --- /dev/null +++ b/notebooks/quantile_regression.ipynb @@ -0,0 +1,123 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 7, + "id": "49096439-bd36-4537-9ea8-12a4437d03fe", + "metadata": {}, + "outputs": [], + "source": [ + "import sys\n", + "sys.path.append('../') # Go up one level from 'notebooks' to 'lppls'" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "375d6a50-7c83-4dff-a4e2-3d091142aacf", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from lppls import lppls, lppls_q\n", + "import numpy as np\n", + "import pandas as pd\n", + "import yfinance as yf\n", + "from datetime import datetime as dt\n", + "from matplotlib import pyplot as plt\n", + "import os\n", + "\n", + "FILE_NAME = 'sp500.csv'\n", + "\n", + "# fetch data if we haven't already\n", + "if not os.path.exists(FILE_NAME):\n", + " ticker_symbol = \"^GSPC\" # S&P 500\n", + " start_date = \"1984-07-30\" # start date from the paper\n", + " end_date = \"1987-06-12\" # end date from the paper\n", + "\n", + " data = yf.download(ticker_symbol, start=start_date, end=end_date)\n", + " data.to_csv(FILE_NAME, index=False)\n", + "else:\n", + " data = pd.read_csv(FILE_NAME)\n", + "\n", + "\n", + "time = data.index\n", + "time = (time - time.min()) / (time.max() - time.min()) # scale to [0, 1]\n", + "\n", + "price = np.log(data['Adj Close'].values)\n", + "price = (price - price.min()) / (price.max() - price.min()) # scale to [0, 1]\n", + "\n", + "observations = np.array([time, price])\n", + "\n", + "quantiles = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]\n", + "\n", + "plt.figure(figsize=(12, 8))\n", + "plt.plot(time, price, label='S&P 500', color='black', linewidth=1)\n", + "\n", + "# plot the quantile fits\n", + "for i, q in enumerate(quantiles):\n", + "\n", + " # instantiate a new QLPPLS model with the specified quantile\n", + " qlppls_model = lppls_q.QLPPLS(observations=observations, q=q)\n", + "\n", + " # fit the model to the data and get back the params\n", + " tc, m, w, a, b, c, c1, c2, O, D = qlppls_model.fit(25)\n", + "\n", + " # generate predictions up to t2\n", + " predictions = [qlppls_model.lppls(t, tc, m, w, a, b, c1, c2) for t in time]\n", + "\n", + " # color from green to red\n", + " color = (i / len(quantiles), 1 - i / len(quantiles), 0)\n", + "\n", + " # plot the fit\n", + " plt.plot(time, predictions, label=f'q={q}', color=color, alpha=0.5)\n", + "\n", + "# plot standard fit\n", + "lppls_model = lppls.LPPLS(observations=observations)\n", + "tc, m, w, a, b, c, c1, c2, O, D = lppls_model.fit(25) \n", + "predictions = [lppls_model.lppls(t, tc, m, w, a, b, c1, c2) for t in time]\n", + "plt.plot(time, predictions, label=f'Standard LPPLS fit', color='blue', alpha=0.5)\n", + "\n", + "# show plot\n", + "plt.title('Quantile Regression LPPLS Fit to the S&P 500 Dataset')\n", + "plt.xlabel('Time')\n", + "plt.ylabel('Scaled Log Price')\n", + "plt.legend()\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/setup.py b/setup.py index 4a0ecdf..039e4fd 100644 --- a/setup.py +++ b/setup.py @@ -4,7 +4,7 @@ long_description = fh.read() setuptools.setup(name='lppls', - version='0.6.11', + version='0.6.12', description='A Python module for fitting the LPPLS model to data.', packages=['lppls'], author='Josh Nielsen',