"""
EnsembleFTS wraps several FTS methods to ensemble their forecasts, providing point,
interval and probabilistic forecasting.
Silva, P. C. L et al. Probabilistic Forecasting with Seasonal Ensemble Fuzzy Time-Series
XIII Brazilian Congress on Computational Intelligence, 2017. Rio de Janeiro, Brazil.
"""
import numpy as np
import pandas as pd
from pyFTS.common import SortedCollection, fts, tree
from pyFTS.models import chen, cheng, hofts, hwang, ismailefendi, sadaei, song, yu
from pyFTS.probabilistic import ProbabilityDistribution
import scipy.stats as st
[docs]def sampler(data, quantiles):
ret = []
for qt in quantiles:
ret.append(np.nanpercentile(data, q=qt * 100))
return ret
[docs]class EnsembleFTS(fts.FTS):
"""
Ensemble FTS
"""
def __init__(self, **kwargs):
super(EnsembleFTS, self).__init__(**kwargs)
self.shortname = "EnsembleFTS"
self.name = "Ensemble FTS"
self.flrgs = {}
self.is_wrapper = True
self.has_point_forecasting = True
self.has_interval_forecasting = True
self.has_probability_forecasting = True
self.is_high_order = True
self.models = []
"""A list of FTS models, the ensemble components"""
self.parameters = []
"""A list with the parameters for each component model"""
self.alpha = kwargs.get("alpha", 0.05)
"""The quantiles """
self.point_method = kwargs.get('point_method', 'mean')
"""The method used to mix the several model's forecasts into a unique point forecast. Options: mean, median, quantile, exponential"""
self.interval_method = kwargs.get('interval_method', 'quantile')
"""The method used to mix the several model's forecasts into a interval forecast. Options: quantile, extremum, normal"""
[docs] def append_model(self, model):
"""
Append a new trained model to the ensemble
:param model: FTS model
"""
self.models.append(model)
if model.order > self.order:
self.order = model.order
if model.is_multivariate:
self.is_multivariate = True
if model.has_seasonality:
self.has_seasonality = True
if model.original_min < self.original_min:
self.original_min = model.original_min
elif model.original_max > self.original_max:
self.original_max = model.original_max
[docs] def train(self, data, **kwargs):
pass
[docs] def get_models_forecasts(self,data):
tmp = []
for model in self.models:
if model.is_multivariate or model.has_seasonality:
forecast = model.forecast(data)
else:
if isinstance(data, pd.DataFrame) and self.indexer is not None:
data = self.indexer.get_data(data)
sample = data[-model.order:]
forecast = model.predict(sample)
if isinstance(forecast, (list,np.ndarray)) and len(forecast) > 0:
forecast = forecast[-1]
elif isinstance(forecast, (list,np.ndarray)) and len(forecast) == 0:
forecast = np.nan
if isinstance(forecast, list):
tmp.extend(forecast)
else:
tmp.append(forecast)
return tmp
[docs] def get_point(self,forecasts, **kwargs):
if self.point_method == 'mean':
ret = np.nanmean(forecasts)
elif self.point_method == 'median':
ret = np.nanpercentile(forecasts, 50)
elif self.point_method == 'quantile':
alpha = kwargs.get("alpha",0.05)
ret = np.percentile(forecasts, alpha*100)
elif self.point_method == 'exponential':
l = len(self.models)
if l == 1:
return forecasts[0]
w = np.array([np.exp(-(l - k)) for k in range(l)])
w = w / np.nansum(w)
ret = np.nansum([w[k] * forecasts[k] for k in range(l)])
return ret
[docs] def get_interval(self, forecasts):
ret = []
if self.interval_method == 'extremum':
ret.append([min(forecasts), max(forecasts)])
elif self.interval_method == 'quantile':
qt_lo = np.nanpercentile(forecasts, q=self.alpha * 100)
qt_up = np.nanpercentile(forecasts, q=(1-self.alpha) * 100)
ret.append([qt_lo, qt_up])
elif self.interval_method == 'normal':
mu = np.nanmean(forecasts)
sigma = np.sqrt(np.nanvar(forecasts))
ret.append(mu + st.norm.ppf(self.alpha) * sigma)
ret.append(mu + st.norm.ppf(1 - self.alpha) * sigma)
return ret
[docs] def get_distribution_interquantile(self,forecasts, alpha):
size = len(forecasts)
qt_lower = int(np.ceil(size * alpha)) - 1
qt_upper = int(np.ceil(size * (1- alpha))) - 1
ret = sorted(forecasts)[qt_lower : qt_upper]
return ret
[docs] def forecast(self, data, **kwargs):
if "method" in kwargs:
self.point_method = kwargs.get('method','mean')
l = len(data)
ret = []
for k in np.arange(self.order, l+1):
sample = data[k - self.max_lag : k]
tmp = self.get_models_forecasts(sample)
point = self.get_point(tmp)
ret.append(point)
return ret
[docs] def forecast_interval(self, data, **kwargs):
if "method" in kwargs:
self.interval_method = kwargs.get('method','quantile')
if 'alpha' in kwargs:
self.alpha = kwargs.get('alpha',0.05)
l = len(data)
ret = []
for k in np.arange(self.order, l+1):
sample = data[k - self.order : k]
tmp = self.get_models_forecasts(sample)
interval = self.get_interval(tmp)
if len(interval) == 1:
interval = interval[-1]
ret.append(interval)
return ret
[docs] def forecast_ahead_interval(self, data, steps, **kwargs):
if 'method' in kwargs:
self.interval_method = kwargs.get('method','quantile')
if 'alpha' in kwargs:
self.alpha = kwargs.get('alpha', self.alpha)
ret = []
samples = [[k] for k in data[-self.order:]]
for k in np.arange(self.order, steps + self.order):
forecasts = []
lags = {}
for i in np.arange(0, self.order): lags[i] = samples[k - self.order + i]
# Build the tree with all possible paths
root = tree.FLRGTreeNode(None)
tree.build_tree_without_order(root, lags, 0)
for p in root.paths():
path = list(reversed(list(filter(None.__ne__, p))))
forecasts.extend(self.get_models_forecasts(path))
samples.append(sampler(forecasts, np.arange(0.1, 1, 0.2)))
interval = self.get_interval(forecasts)
if len(interval) == 1:
interval = interval[0]
ret.append(interval)
return ret
[docs] def forecast_distribution(self, data, **kwargs):
ret = []
smooth = kwargs.get("smooth", "KDE")
alpha = kwargs.get("alpha", None)
uod = self.get_UoD()
for k in np.arange(self.order, len(data)):
sample = data[k-self.order : k]
forecasts = self.get_models_forecasts(sample)
if alpha is None:
forecasts = np.ravel(forecasts).tolist()
else:
forecasts = self.get_distribution_interquantile(np.ravel(forecasts).tolist(), alpha)
dist = ProbabilityDistribution.ProbabilityDistribution(smooth, uod=uod, data=forecasts,
name="", **kwargs)
ret.append(dist)
return ret
[docs] def forecast_ahead_distribution(self, data, steps, **kwargs):
if 'method' in kwargs:
self.point_method = kwargs.get('method','mean')
smooth = kwargs.get("smooth", "KDE")
alpha = kwargs.get("alpha", None)
ret = []
start = kwargs.get('start', self.order)
uod = self.get_UoD()
sample = data[start - self.order: start]
for k in np.arange(self.order, steps+self.order):
forecasts = []
lags = {}
for i in np.arange(0, self.order): lags[i] = sample[k-self.order]
# Build the tree with all possible paths
root = tree.FLRGTreeNode(None)
tree.build_tree_without_order(root, lags, 0)
for p in root.paths():
path = list(reversed(list(filter(None.__ne__, p))))
forecasts.extend(self.get_models_forecasts(path))
sample.append(sampler(forecasts, np.arange(0.1, 1, 0.1)))
if alpha is None:
forecasts = np.ravel(forecasts).tolist()
else:
forecasts = self.get_distribution_interquantile(np.ravel(forecasts).tolist(), alpha)
dist = ProbabilityDistribution.ProbabilityDistribution(smooth, uod=uod, data=forecasts,
name="", **kwargs)
ret.append(dist)
return ret
[docs]class AllMethodEnsembleFTS(EnsembleFTS):
"""
Creates an EnsembleFTS with all point forecast methods, sharing the same partitioner
"""
def __init__(self, **kwargs):
super(AllMethodEnsembleFTS, self).__init__(**kwargs)
self.min_order = 3
self.shortname ="Ensemble FTS"
[docs] def train(self, data, **kwargs):
fo_methods = [song.ConventionalFTS, chen.ConventionalFTS, yu.WeightedFTS, cheng.TrendWeightedFTS,
sadaei.ExponentialyWeightedFTS, ismailefendi.ImprovedWeightedFTS]
ho_methods = [hofts.HighOrderFTS, hwang.HighOrderFTS]
for method in fo_methods:
model = method(partitioner=self.partitioner)
self.set_transformations(model)
model.fit(data, **kwargs)
self.append_model(model)
for method in ho_methods:
for o in np.arange(1, self.order+1):
model = method(partitioner=self.partitioner)
if model.min_order >= o:
model.order = o
self.set_transformations(model)
model.fit(data, **kwargs)
self.append_model(model)
