# Source code for evalml.pipelines.components.transformers.preprocessing.polynomial_decomposer

```
"""Component that removes trends from time series by fitting a polynomial to the data."""
from __future__ import annotations
import logging
import pandas as pd
from skopt.space import Integer
from sktime.forecasting.base._fh import ForecastingHorizon
from statsmodels.tsa.seasonal import seasonal_decompose
from statsmodels.tsa.tsatools import freq_to_period
from evalml.pipelines.components.transformers.preprocessing import Decomposer
from evalml.utils import import_or_raise, infer_feature_types
[docs]class PolynomialDecomposer(Decomposer):
"""Removes trends and seasonality from time series by fitting a polynomial and moving average to the data.
Scikit-learn's PolynomialForecaster is used to generate the additive trend portion of the target data. A polynomial
will be fit to the data during fit. That additive polynomial trend will be removed during fit so that statsmodel's
seasonal_decompose can determine the addititve seasonality of the data by using rolling averages over the series'
inferred periodicity.
For example, daily time series data will generate rolling averages over the first week of data, normalize
out the mean and return those 7 averages repeated over the entire length of the given series. Those seven
averages, repeated as many times as necessary to match the length of the given target data, will be used
as the seasonal signal of the data.
Args:
time_index (str): Specifies the name of the column in X that provides the datetime objects. Defaults to None.
degree (int): Degree for the polynomial. If 1, linear model is fit to the data.
If 2, quadratic model is fit, etc. Defaults to 1.
period (int): The number of entries in the time series data that corresponds to one period of a
cyclic signal. For instance, if data is known to possess a weekly seasonal signal, and if the data
is daily data, period should be 7. For daily data with a yearly seasonal signal, period
should be 365. Defaults to -1, which uses the statsmodels libarary's freq_to_period function.
https://github.com/statsmodels/statsmodels/blob/main/statsmodels/tsa/tsatools.py
random_seed (int): Seed for the random number generator. Defaults to 0.
"""
name = "Polynomial Decomposer"
hyperparameter_ranges = {"degree": Integer(1, 3)}
"""{
"degree": Integer(1, 3)
}"""
modifies_features = False
modifies_target = True
def __init__(
self,
time_index: str = None,
degree: int = 1,
period: int = -1,
random_seed: int = 0,
**kwargs,
):
self.logger = logging.getLogger(__name__)
error_msg = "sktime is not installed. Please install using 'pip install sktime'"
trend = import_or_raise("sktime.forecasting.trend", error_msg=error_msg)
detrend = import_or_raise(
"sktime.transformations.series.detrend",
error_msg=error_msg,
)
decomposer = detrend.Detrender(trend.PolynomialTrendForecaster(degree=degree))
super().__init__(
component_obj=decomposer,
random_seed=random_seed,
degree=degree,
period=period,
time_index=time_index,
**kwargs,
)
[docs] def fit(self, X: pd.DataFrame, y: pd.Series = None) -> PolynomialDecomposer:
"""Fits the PolynomialDecomposer and determine the seasonal signal.
Currently only fits the polynomial detrender. The seasonality is determined by removing
the trend from the signal and using statsmodels' seasonal_decompose(). Both the trend
and seasonality are currently assumed to be additive.
Args:
X (pd.DataFrame, optional): Conditionally used to build datetime index.
y (pd.Series): Target variable to detrend and deseasonalize.
Returns:
self
Raises:
NotImplementedError: If the input data has a frequency of "month-begin". This isn't supported by statsmodels decompose
as the freqstr "MS" is misinterpreted as milliseconds.
ValueError: If y is None.
ValueError: If target data doesn't have DatetimeIndex AND no Datetime features in features data
"""
self.original_index = y.index if y is not None else None
X, y = self._check_target(X, y)
self._map_dt_to_integer(self.original_index, y.index)
if y.index.freqstr == "MS":
raise NotImplementedError(
"statsmodels decompose does not handle datasets with month-begin (e.g. 10/01/2000, 11/01/2000)"
"datetime data. These values are incorrectly interpreted as milliseconds.",
)
# Copying y as we might modify its index
y_orig = infer_feature_types(y).copy()
self._component_obj.fit(y_orig)
y_detrended_with_time_index = self._component_obj.transform(y_orig)
# Save the frequency of the fitted series for checking against transform data.
self.frequency = y_detrended_with_time_index.index.freqstr
# statsmodel's seasonal_decompose() repeats the seasonal signal over the length of
# the given array. We'll extract the first iteration and save it for use in .transform()
# TODO: Resolve with https://github.com/alteryx/evalml/issues/3708
if self.period == -1:
self.period = freq_to_period(self.frequency)
self.seasonal = seasonal_decompose(
y_detrended_with_time_index,
period=self.period,
).seasonal
self.seasonality = self.seasonal[0 : self.period]
self.trend = y - (y_detrended_with_time_index - self.seasonal) - self.seasonal
return self
[docs] def transform(
self,
X: pd.DataFrame,
y: pd.Series = None,
) -> tuple[pd.DataFrame, pd.Series]:
"""Transforms the target data by removing the polynomial trend and rolling average seasonality.
Applies the fit polynomial detrender to the target data, removing the additive polynomial trend. Then,
utilizes the first period's worth of seasonal data determined in the .fit() function to extrapolate
the seasonal signal of the data to be transformed. This seasonal signal is also assumed to be additive
and is removed.
Args:
X (pd.DataFrame, optional): Conditionally used to build datetime index.
y (pd.Series): Target variable to detrend and deseasonalize.
Returns:
tuple of pd.DataFrame, pd.Series: The input features are returned without modification. The target
variable y is detrended and deseasonalized.
Raises:
ValueError: If target data doesn't have DatetimeIndex AND no Datetime features in features data
"""
if y is None:
return X, y
original_index = y.index
X, y = self._check_target(X, y)
self._check_oos_past(y)
# Give the internal target signal a datetime index built from X
y = y.copy()
# Remove polynomial trend then seasonality of detrended signal
y_ww = infer_feature_types(y)
y_detrended = self._component_obj.transform(y_ww)
seasonal = self._project_seasonal(
y,
self.seasonality,
self.period,
self.frequency,
)
y_t = pd.Series(y_detrended - seasonal)
y_t.ww.init(logical_type="double")
y_t.index = original_index
return X, y_t
[docs] def inverse_transform(self, y_t: pd.Series) -> tuple[pd.DataFrame, pd.Series]:
"""Adds back fitted trend and seasonality to target variable.
The polynomial trend is added back into the signal, calling the detrender's inverse_transform().
Then, the seasonality is projected forward to and added back into the signal.
Args:
y_t (pd.Series): Target variable.
Returns:
tuple of pd.DataFrame, pd.Series: The first element are the input features returned without modification.
The second element is the target variable y with the trend and seasonality added back in.
Raises:
ValueError: If y is None.
"""
if y_t is None:
raise ValueError("y_t cannot be None for Decomposer!")
original_index = y_t.index
y_t = infer_feature_types(y_t).copy()
self._check_oos_past(y_t)
index = self._choose_proper_index(y_t)
y_in_sample = pd.Series([])
y_out_of_sample = pd.Series([])
# For partially and wholly in-sample data, retrieve stored results.
if index[0] <= y_t.index[0] <= index[-1]:
left_index = y_t.index[0]
right_index = min(y_t.index[-1], index[-1])
if isinstance(y_t.index, pd.RangeIndex) or y_t.index.is_numeric():
y_t_ind = pd.RangeIndex(
start=left_index,
stop=right_index + 1,
) # stop value is not inclusive
elif isinstance(y_t.index, pd.DatetimeIndex):
y_t_ind = pd.DatetimeIndex(
pd.date_range(left_index, end=right_index),
) # end value is inclusive
# Build index
y_t_in_sample = y_t[y_t_ind]
# Convert y_t to datetime index to use the built in component
if isinstance(y_t.index, pd.RangeIndex) or y_t.index.is_numeric():
y_t_dt_ind = self._convert_int_index_to_dt_index(y_t_in_sample.index)
elif isinstance(y_t.index, pd.DatetimeIndex):
y_t_dt_ind = y_t_ind
trend = self._component_obj.inverse_transform(
y_t_in_sample.set_axis(y_t_dt_ind),
)
# self.seasonal will always have a datetime index
seasonal = self.seasonal[y_t_dt_ind].set_axis(y_t_dt_ind)
y_in_sample = trend + seasonal
y_in_sample = y_in_sample.dropna()
# For out of sample data....
if y_t.index[-1] > index[-1]:
try:
# ...that is partially out of sample and partially in sample.
truncated_y_t = y_t[y_t.index.get_loc(index[-1]) + 1 :]
except KeyError:
# ...that is entirely out of sample.
truncated_y_t = y_t
projected_seasonality = self._project_seasonal(
truncated_y_t,
self.seasonality,
self.period,
self.frequency,
)
if (
isinstance(truncated_y_t.index, pd.RangeIndex)
or truncated_y_t.index.is_numeric()
):
dt_index = self._convert_int_index_to_dt_index(truncated_y_t.index)
truncated_y_t.index = dt_index
projected_seasonality.index = dt_index
retrended_y = self._component_obj.inverse_transform(truncated_y_t)
y_out_of_sample = infer_feature_types(
pd.Series(
retrended_y + projected_seasonality,
index=truncated_y_t.index,
),
)
y = y_in_sample.append(y_out_of_sample)
y.index = original_index
return y
[docs] def get_trend_dataframe(self, X: pd.DataFrame, y: pd.Series) -> list[pd.DataFrame]:
"""Return a list of dataframes with 4 columns: signal, trend, seasonality, residual.
Scikit-learn's PolynomialForecaster is used to generate the trend portion of the target data. statsmodel's
seasonal_decompose is used to generate the seasonality of the data.
Args:
X (pd.DataFrame): Input data with time series data in index.
y (pd.Series or pd.DataFrame): Target variable data provided as a Series for univariate problems or
a DataFrame for multivariate problems.
Returns:
list of pd.DataFrame: Each DataFrame contains the columns "signal", "trend", "seasonality" and "residual,"
with the latter 3 column values being the decomposed elements of the target data. The "signal" column
is simply the input target signal but reindexed with a datetime index to match the input features.
Raises:
TypeError: If X does not have time-series data in the index.
ValueError: If time series index of X does not have an inferred frequency.
ValueError: If the forecaster associated with the detrender has not been fit yet.
TypeError: If y is not provided as a pandas Series or DataFrame.
"""
X = infer_feature_types(X)
if not isinstance(X.index, pd.DatetimeIndex):
raise TypeError("Provided X should have datetimes in the index.")
if X.index.freq is None:
raise ValueError(
"Provided DatetimeIndex of X should have an inferred frequency.",
)
# Change the y index to a matching datetimeindex or else we get a failure
# in ForecastingHorizon during decomposition.
if not isinstance(y.index, pd.DatetimeIndex):
y = self._set_time_index(X, y)
fh = ForecastingHorizon(X.index, is_relative=False)
result_dfs = []
def _decompose_target(X, y, fh):
"""Function to generate a single DataFrame with trend, seasonality and residual components."""
forecaster = (
self._component_obj.forecaster_
) # the .forecaster attribute is an unfitted version
trend = forecaster.predict(fh=fh, X=y)
if not isinstance(trend, pd.Series):
trend = pd.Series(trend.iloc[:, 0])
seasonality = seasonal_decompose(
y - trend,
period=self.period,
).seasonal
residual = y - trend - seasonality
return pd.DataFrame(
{
"signal": y,
"trend": trend,
"seasonality": seasonality,
"residual": residual,
},
)
if isinstance(y, pd.Series):
result_dfs.append(_decompose_target(X, y, fh))
elif isinstance(y, pd.DataFrame):
for colname in y.columns:
result_dfs.append(_decompose_target(X, y[colname], fh))
return result_dfs
```