Quantile Regression (#101)

* add subclass for quantile regression.

* add usage quantile regression example notebook.

* update readme.

* bump version

README.md

@@ -120,6 +120,10 @@ If you wish to store `res` as a pd.DataFrame, use `compute_indicators`.
 
 </details>
 
+## 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

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

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',