#!/usr/bin/python
# -*- coding: utf8 -*-
import numpy as np
import pandas as pd
from statsmodels.regression.quantile_regression import QuantReg
from statsmodels.tsa.tsatools import lagmat
from pyFTS.common import SortedCollection, fts
from pyFTS.probabilistic import ProbabilityDistribution
[docs]class QuantileRegression(fts.FTS):
"""Façade for statsmodels.regression.quantile_regression"""
def __init__(self, **kwargs):
super(QuantileRegression, self).__init__(**kwargs)
self.name = "QAR"
self.detail = "Quantile Regression"
self.is_high_order = True
self.has_point_forecasting = True
self.has_interval_forecasting = True
self.has_probability_forecasting = True
self.uod_clip = False
self.benchmark_only = True
self.min_order = 1
self.alpha = kwargs.get("alpha", 0.05)
self.dist = kwargs.get("dist", False)
self.upper_qt = None
self.mean_qt = None
self.lower_qt = None
self.dist_qt = None
[docs] def train(self, data, **kwargs):
if self.indexer is not None and isinstance(data, pd.DataFrame):
data = self.indexer.get_data(data)
lagdata, ndata = lagmat(data, maxlag=self.order, trim="both", original='sep')
mqt = QuantReg(ndata, lagdata).fit(0.5)
if self.alpha is not None:
uqt = QuantReg(ndata, lagdata).fit(1 - self.alpha)
lqt = QuantReg(ndata, lagdata).fit(self.alpha)
self.mean_qt = [k for k in mqt.params]
if self.alpha is not None:
self.upper_qt = [k for k in uqt.params]
self.lower_qt = [k for k in lqt.params]
if self.dist:
self.dist_qt = []
for alpha in np.arange(0.05,0.5,0.05):
lqt = QuantReg(ndata, lagdata).fit(alpha)
uqt = QuantReg(ndata, lagdata).fit(1 - alpha)
lo_qt = [k for k in lqt.params]
up_qt = [k for k in uqt.params]
self.dist_qt.append([lo_qt, up_qt])
self.shortname = "QAR({})-{}".format(self.order,self.alpha)
[docs] def linearmodel(self,data,params):
#return params[0] + sum([ data[k] * params[k+1] for k in np.arange(0, self.order) ])
return sum([data[k] * params[k] for k in np.arange(0, self.order)])
[docs] def point_to_interval(self, data, lo_params, up_params):
lo = self.linearmodel(data, lo_params)
up = self.linearmodel(data, up_params)
return [lo, up]
[docs] def interval_to_interval(self, data, lo_params, up_params):
lo = self.linearmodel([k[0] for k in data], lo_params)
up = self.linearmodel([k[1] for k in data], up_params)
return [lo, up]
[docs] def forecast(self, ndata, **kwargs):
l = len(ndata)
ret = []
for k in np.arange(self.order, l+1): #+1 to forecast one step ahead given all available lags
sample = ndata[k - self.order : k]
ret.append(self.linearmodel(sample, self.mean_qt))
return ret
[docs] def forecast_interval(self, ndata, **kwargs):
l = len(ndata)
ret = []
for k in np.arange(self.order , l):
sample = ndata[k - self.order: k]
ret.append(self.point_to_interval(sample, self.lower_qt, self.upper_qt))
return ret
[docs] def forecast_ahead_interval(self, ndata, steps, **kwargs):
smoothing = kwargs.get("smoothing", 0.01)
l = len(ndata)
ret = []
nmeans = self.forecast_ahead(ndata, steps, **kwargs)
for k in np.arange(0, self.order):
nmeans.insert(k,ndata[k])
for k in np.arange(self.order, steps+self.order):
intl = self.point_to_interval(nmeans[k - self.order: k], self.lower_qt, self.upper_qt)
tmpk = k-self.order
ret.append([intl[0]*(1 - (tmpk*smoothing)), intl[1]*(1 + (tmpk*smoothing))])
return ret[-steps:]
[docs] def forecast_distribution(self, ndata, **kwargs):
ret = []
l = len(ndata)
for k in np.arange(self.order, l + 1):
dist = ProbabilityDistribution.ProbabilityDistribution(type="histogram",
uod=[self.original_min, self.original_max])
intervals = []
for qt in self.dist_qt:
sample = ndata[k - self.order: k]
intl = self.point_to_interval(sample, qt[0], qt[1])
intervals.append(intl)
dist.append_interval(intervals)
ret.append(dist)
return ret
[docs] def forecast_ahead_distribution(self, ndata, steps, **kwargs):
smoothing = kwargs.get("smoothing", 0.01)
l = len(ndata)
ret = []
nmeans = self.forecast_ahead(ndata, steps, **kwargs)
for k in np.arange(0, self.order):
nmeans.insert(k, ndata[k])
for k in np.arange(self.order, steps + self.order):
dist = ProbabilityDistribution.ProbabilityDistribution(type="histogram",
uod=[self.original_min, self.original_max])
intervals = [[nmeans[self.order], nmeans[self.order]]]
for qt in self.dist_qt:
intl1 = self.point_to_interval(nmeans[k - self.order: k], qt[0], qt[1])
tmpk = k - self.order
intl2 = [intl1[0] * (1 - (tmpk * smoothing)), intl1[1] * (1 + (tmpk * smoothing))]
intervals.append(intl2)
dist.append_interval(intervals)
ret.append(dist)
return ret