# Copyright 2019 The TensorTrade Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License
#
# Reference Source: Marcos Lopez De Prado - Advances in Financial Machine Learning
# Chapter 5 (Pg. 82) - Fractionally Differentiated Features
import pandas as pd
import numpy as np
from gym import Space
from copy import copy
from typing import Union, List, Tuple
from tensortrade.features.feature_transformer import FeatureTransformer
[docs]class FractionalDifference(FeatureTransformer):
"""A transformer for differencing values within a feature pipeline by a fractional order."""
[docs] def __init__(self,
columns: Union[List[str], str, None] = None,
difference_order: float = 0.5,
difference_threshold: float = 0.1,
inplace: bool = True):
"""
Arguments:
columns (optional): A list of column names to difference.
difference_order (optional): The fractional difference order. Defaults to 0.5.
difference_threshold (optional): The fractional difference threshold. Defaults to 0.1.
inplace (optional): If `False`, a new column will be added to the output for each input column.
"""
super().__init__(columns=columns, inplace=inplace)
self._difference_order = difference_order
self._difference_threshold = difference_threshold
self.reset()
[docs] def reset(self):
self._history = None
def _difference_weights(self, size: int):
weights = [1.0]
for k in range(1, size):
weight = -weights[-1] / k * (self._difference_order - k + 1)
weights.append(weight)
return np.array(weights[::-1]).reshape(-1, 1)
def _fractional_difference(self, series: pd.Series):
"""Computes fractionally differenced series, with an increasing window width.
Args:
series: A `pandas.Series` to difference by self._difference_order with self._difference_threshold.
Returns:
The fractionally differenced series.
"""
weights = self._difference_weights(len(series))
weight_sums = np.cumsum(abs(weights))
weight_sums /= weight_sums[-1]
skip_weights = len(weight_sums[weight_sums > self._difference_threshold])
curr_series = series.dropna()
diff_series = pd.Series(index=series.index)
for current_index in range(skip_weights, curr_series.shape[0]):
index = curr_series.index[current_index]
if not np.isfinite(curr_series.loc[index]):
continue
diff_series[index] = np.dot(
weights[-(current_index + 1):, :].T, curr_series.loc[:index])[0]
return diff_series.fillna(method='bfill').fillna(0)