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import datetime
from functools import partial
from textwrap import dedent
from typing import TYPE_CHECKING, Optional, Union
import numpy as np
from pandas._libs.tslibs import Timedelta
import pandas._libs.window.aggregations as window_aggregations
from pandas._typing import FrameOrSeries, TimedeltaConvertibleTypes
from pandas.compat.numpy import function as nv
from pandas.util._decorators import Appender, Substitution, doc
from pandas.core.dtypes.common import is_datetime64_ns_dtype
import pandas.core.common as common
from pandas.core.util.numba_ import maybe_use_numba
from pandas.core.window.common import (
_doc_template,
_shared_docs,
flex_binary_moment,
zsqrt,
)
from pandas.core.window.indexers import (
BaseIndexer,
ExponentialMovingWindowIndexer,
GroupbyIndexer,
)
from pandas.core.window.numba_ import generate_numba_groupby_ewma_func
from pandas.core.window.rolling import BaseWindow, BaseWindowGroupby, dispatch
if TYPE_CHECKING:
from pandas import Series
_bias_template = """
Parameters
----------
bias : bool, default False
Use a standard estimation bias correction.
*args, **kwargs
Arguments and keyword arguments to be passed into func.
"""
def get_center_of_mass(
comass: Optional[float],
span: Optional[float],
halflife: Optional[float],
alpha: Optional[float],
) -> float:
valid_count = common.count_not_none(comass, span, halflife, alpha)
if valid_count > 1:
raise ValueError("comass, span, halflife, and alpha are mutually exclusive")
# Convert to center of mass; domain checks ensure 0 < alpha <= 1
if comass is not None:
if comass < 0:
raise ValueError("comass must satisfy: comass >= 0")
elif span is not None:
if span < 1:
raise ValueError("span must satisfy: span >= 1")
comass = (span - 1) / 2.0
elif halflife is not None:
if halflife <= 0:
raise ValueError("halflife must satisfy: halflife > 0")
decay = 1 - np.exp(np.log(0.5) / halflife)
comass = 1 / decay - 1
elif alpha is not None:
if alpha <= 0 or alpha > 1:
raise ValueError("alpha must satisfy: 0 < alpha <= 1")
comass = (1.0 - alpha) / alpha
else:
raise ValueError("Must pass one of comass, span, halflife, or alpha")
return float(comass)
def wrap_result(obj: "Series", result: np.ndarray) -> "Series":
"""
Wrap a single 1D result.
"""
obj = obj._selected_obj
return obj._constructor(result, obj.index, name=obj.name)
class ExponentialMovingWindow(BaseWindow):
r"""
Provide exponential weighted (EW) functions.
Available EW functions: ``mean()``, ``var()``, ``std()``, ``corr()``, ``cov()``.
Exactly one parameter: ``com``, ``span``, ``halflife``, or ``alpha`` must be
provided.
Parameters
----------
com : float, optional
Specify decay in terms of center of mass,
:math:`\alpha = 1 / (1 + com)`, for :math:`com \geq 0`.
span : float, optional
Specify decay in terms of span,
:math:`\alpha = 2 / (span + 1)`, for :math:`span \geq 1`.
halflife : float, str, timedelta, optional
Specify decay in terms of half-life,
:math:`\alpha = 1 - \exp\left(-\ln(2) / halflife\right)`, for
:math:`halflife > 0`.
If ``times`` is specified, the time unit (str or timedelta) over which an
observation decays to half its value. Only applicable to ``mean()``
and halflife value will not apply to the other functions.
.. versionadded:: 1.1.0
alpha : float, optional
Specify smoothing factor :math:`\alpha` directly,
:math:`0 < \alpha \leq 1`.
min_periods : int, default 0
Minimum number of observations in window required to have a value
(otherwise result is NA).
adjust : bool, default True
Divide by decaying adjustment factor in beginning periods to account
for imbalance in relative weightings (viewing EWMA as a moving average).
- When ``adjust=True`` (default), the EW function is calculated using weights
:math:`w_i = (1 - \alpha)^i`. For example, the EW moving average of the series
[:math:`x_0, x_1, ..., x_t`] would be:
.. math::
y_t = \frac{x_t + (1 - \alpha)x_{t-1} + (1 - \alpha)^2 x_{t-2} + ... + (1 -
\alpha)^t x_0}{1 + (1 - \alpha) + (1 - \alpha)^2 + ... + (1 - \alpha)^t}
- When ``adjust=False``, the exponentially weighted function is calculated
recursively:
.. math::
\begin{split}
y_0 &= x_0\\
y_t &= (1 - \alpha) y_{t-1} + \alpha x_t,
\end{split}
ignore_na : bool, default False
Ignore missing values when calculating weights; specify ``True`` to reproduce
pre-0.15.0 behavior.
- When ``ignore_na=False`` (default), weights are based on absolute positions.
For example, the weights of :math:`x_0` and :math:`x_2` used in calculating
the final weighted average of [:math:`x_0`, None, :math:`x_2`] are
:math:`(1-\alpha)^2` and :math:`1` if ``adjust=True``, and
:math:`(1-\alpha)^2` and :math:`\alpha` if ``adjust=False``.
- When ``ignore_na=True`` (reproducing pre-0.15.0 behavior), weights are based
on relative positions. For example, the weights of :math:`x_0` and :math:`x_2`
used in calculating the final weighted average of
[:math:`x_0`, None, :math:`x_2`] are :math:`1-\alpha` and :math:`1` if
``adjust=True``, and :math:`1-\alpha` and :math:`\alpha` if ``adjust=False``.
axis : {0, 1}, default 0
The axis to use. The value 0 identifies the rows, and 1
identifies the columns.
times : str, np.ndarray, Series, default None
.. versionadded:: 1.1.0
Times corresponding to the observations. Must be monotonically increasing and
``datetime64[ns]`` dtype.
If str, the name of the column in the DataFrame representing the times.
If 1-D array like, a sequence with the same shape as the observations.
Only applicable to ``mean()``.
Returns
-------
DataFrame
A Window sub-classed for the particular operation.
See Also
--------
rolling : Provides rolling window calculations.
expanding : Provides expanding transformations.
Notes
-----
More details can be found at:
:ref:`Exponentially weighted windows <window.exponentially_weighted>`.
Examples
--------
>>> df = pd.DataFrame({'B': [0, 1, 2, np.nan, 4]})
>>> df
B
0 0.0
1 1.0
2 2.0
3 NaN
4 4.0
>>> df.ewm(com=0.5).mean()
B
0 0.000000
1 0.750000
2 1.615385
3 1.615385
4 3.670213
Specifying ``times`` with a timedelta ``halflife`` when computing mean.
>>> times = ['2020-01-01', '2020-01-03', '2020-01-10', '2020-01-15', '2020-01-17']
>>> df.ewm(halflife='4 days', times=pd.DatetimeIndex(times)).mean()
B
0 0.000000
1 0.585786
2 1.523889
3 1.523889
4 3.233686
"""
_attributes = ["com", "min_periods", "adjust", "ignore_na", "axis"]
def __init__(
self,
obj,
com: Optional[float] = None,
span: Optional[float] = None,
halflife: Optional[Union[float, TimedeltaConvertibleTypes]] = None,
alpha: Optional[float] = None,
min_periods: int = 0,
adjust: bool = True,
ignore_na: bool = False,
axis: int = 0,
times: Optional[Union[str, np.ndarray, FrameOrSeries]] = None,
**kwargs,
):
self.obj = obj
self.min_periods = max(int(min_periods), 1)
self.adjust = adjust
self.ignore_na = ignore_na
self.axis = axis
self.on = None
self.center = False
self.closed = None
if times is not None:
if isinstance(times, str):
times = self._selected_obj[times]
if not is_datetime64_ns_dtype(times):
raise ValueError("times must be datetime64[ns] dtype.")
if len(times) != len(obj):
raise ValueError("times must be the same length as the object.")
if not isinstance(halflife, (str, datetime.timedelta)):
raise ValueError(
"halflife must be a string or datetime.timedelta object"
)
self.times = np.asarray(times.astype(np.int64))
self.halflife = Timedelta(halflife).value
# Halflife is no longer applicable when calculating COM
# But allow COM to still be calculated if the user passes other decay args
if common.count_not_none(com, span, alpha) > 0:
self.com = get_center_of_mass(com, span, None, alpha)
else:
self.com = 0.0
else:
if halflife is not None and isinstance(halflife, (str, datetime.timedelta)):
raise ValueError(
"halflife can only be a timedelta convertible argument if "
"times is not None."
)
self.times = None
self.halflife = None
self.com = get_center_of_mass(com, span, halflife, alpha)
@property
def _constructor(self):
return ExponentialMovingWindow
def _get_window_indexer(self) -> BaseIndexer:
"""
Return an indexer class that will compute the window start and end bounds
"""
return ExponentialMovingWindowIndexer()
_agg_see_also_doc = dedent(
"""
See Also
--------
pandas.DataFrame.rolling.aggregate
"""
)
_agg_examples_doc = dedent(
"""
Examples
--------
>>> df = pd.DataFrame({"A": [1, 2, 3], "B": [4, 5, 6], "C": [7, 8, 9]})
>>> df
A B C
0 1 4 7
1 2 5 8
2 3 6 9
>>> df.ewm(alpha=0.5).mean()
A B C
0 1.000000 4.000000 7.000000
1 1.666667 4.666667 7.666667
2 2.428571 5.428571 8.428571
"""
)
@doc(
_shared_docs["aggregate"],
see_also=_agg_see_also_doc,
examples=_agg_examples_doc,
klass="Series/Dataframe",
axis="",
)
def aggregate(self, func, *args, **kwargs):
return super().aggregate(func, *args, **kwargs)
agg = aggregate
@Substitution(name="ewm", func_name="mean")
@Appender(_doc_template)
def mean(self, *args, **kwargs):
"""
Exponential weighted moving average.
Parameters
----------
*args, **kwargs
Arguments and keyword arguments to be passed into func.
"""
nv.validate_window_func("mean", args, kwargs)
if self.times is not None:
window_func = self._get_roll_func("ewma_time")
window_func = partial(
window_func,
times=self.times,
halflife=self.halflife,
)
else:
window_func = self._get_roll_func("ewma")
window_func = partial(
window_func,
com=self.com,
adjust=self.adjust,
ignore_na=self.ignore_na,
)
return self._apply(window_func)
@Substitution(name="ewm", func_name="std")
@Appender(_doc_template)
@Appender(_bias_template)
def std(self, bias: bool = False, *args, **kwargs):
"""
Exponential weighted moving stddev.
"""
nv.validate_window_func("std", args, kwargs)
return zsqrt(self.var(bias=bias, **kwargs))
vol = std
@Substitution(name="ewm", func_name="var")
@Appender(_doc_template)
@Appender(_bias_template)
def var(self, bias: bool = False, *args, **kwargs):
"""
Exponential weighted moving variance.
"""
nv.validate_window_func("var", args, kwargs)
window_func = self._get_roll_func("ewmcov")
window_func = partial(
window_func,
com=self.com,
adjust=self.adjust,
ignore_na=self.ignore_na,
bias=bias,
)
def var_func(values, begin, end, min_periods):
return window_func(values, begin, end, min_periods, values)
return self._apply(var_func)
@Substitution(name="ewm", func_name="cov")
@Appender(_doc_template)
def cov(
self,
other: Optional[Union[np.ndarray, FrameOrSeries]] = None,
pairwise: Optional[bool] = None,
bias: bool = False,
**kwargs,
):
"""
Exponential weighted sample covariance.
Parameters
----------
other : Series, DataFrame, or ndarray, optional
If not supplied then will default to self and produce pairwise
output.
pairwise : bool, default None
If False then only matching columns between self and other will be
used and the output will be a DataFrame.
If True then all pairwise combinations will be calculated and the
output will be a MultiIndex DataFrame in the case of DataFrame
inputs. In the case of missing elements, only complete pairwise
observations will be used.
bias : bool, default False
Use a standard estimation bias correction.
**kwargs
Keyword arguments to be passed into func.
"""
if other is None:
other = self._selected_obj
# only default unset
pairwise = True if pairwise is None else pairwise
other = self._shallow_copy(other)
def _get_cov(X, Y):
X = self._shallow_copy(X)
Y = self._shallow_copy(Y)
cov = window_aggregations.ewmcov(
X._prep_values(),
np.array([0], dtype=np.int64),
np.array([0], dtype=np.int64),
self.min_periods,
Y._prep_values(),
self.com,
self.adjust,
self.ignore_na,
bias,
)
return wrap_result(X, cov)
return flex_binary_moment(
self._selected_obj, other._selected_obj, _get_cov, pairwise=bool(pairwise)
)
@Substitution(name="ewm", func_name="corr")
@Appender(_doc_template)
def corr(
self,
other: Optional[Union[np.ndarray, FrameOrSeries]] = None,
pairwise: Optional[bool] = None,
**kwargs,
):
"""
Exponential weighted sample correlation.
Parameters
----------
other : Series, DataFrame, or ndarray, optional
If not supplied then will default to self and produce pairwise
output.
pairwise : bool, default None
If False then only matching columns between self and other will be
used and the output will be a DataFrame.
If True then all pairwise combinations will be calculated and the
output will be a MultiIndex DataFrame in the case of DataFrame
inputs. In the case of missing elements, only complete pairwise
observations will be used.
**kwargs
Keyword arguments to be passed into func.
"""
if other is None:
other = self._selected_obj
# only default unset
pairwise = True if pairwise is None else pairwise
other = self._shallow_copy(other)
def _get_corr(X, Y):
X = self._shallow_copy(X)
Y = self._shallow_copy(Y)
def _cov(x, y):
return window_aggregations.ewmcov(
x,
np.array([0], dtype=np.int64),
np.array([0], dtype=np.int64),
self.min_periods,
y,
self.com,
self.adjust,
self.ignore_na,
1,
)
x_values = X._prep_values()
y_values = Y._prep_values()
with np.errstate(all="ignore"):
cov = _cov(x_values, y_values)
x_var = _cov(x_values, x_values)
y_var = _cov(y_values, y_values)
corr = cov / zsqrt(x_var * y_var)
return wrap_result(X, corr)
return flex_binary_moment(
self._selected_obj, other._selected_obj, _get_corr, pairwise=bool(pairwise)
)
class ExponentialMovingWindowGroupby(BaseWindowGroupby, ExponentialMovingWindow):
"""
Provide an exponential moving window groupby implementation.
"""
def _get_window_indexer(self) -> GroupbyIndexer:
"""
Return an indexer class that will compute the window start and end bounds
Returns
-------
GroupbyIndexer
"""
window_indexer = GroupbyIndexer(
groupby_indicies=self._groupby.indices,
window_indexer=ExponentialMovingWindowIndexer,
)
return window_indexer
var = dispatch("var", bias=False)
std = dispatch("std", bias=False)
cov = dispatch("cov", other=None, pairwise=None, bias=False)
corr = dispatch("corr", other=None, pairwise=None)
def mean(self, engine=None, engine_kwargs=None):
"""
Parameters
----------
engine : str, default None
* ``'cython'`` : Runs mean through C-extensions from cython.
* ``'numba'`` : Runs mean through JIT compiled code from numba.
Only available when ``raw`` is set to ``True``.
* ``None`` : Defaults to ``'cython'`` or globally setting
``compute.use_numba``
.. versionadded:: 1.2.0
engine_kwargs : dict, default None
* For ``'cython'`` engine, there are no accepted ``engine_kwargs``
* For ``'numba'`` engine, the engine can accept ``nopython``, ``nogil``
and ``parallel`` dictionary keys. The values must either be ``True`` or
``False``. The default ``engine_kwargs`` for the ``'numba'`` engine is
``{'nopython': True, 'nogil': False, 'parallel': False}``.
.. versionadded:: 1.2.0
Returns
-------
Series or DataFrame
Return type is determined by the caller.
"""
if maybe_use_numba(engine):
groupby_ewma_func = generate_numba_groupby_ewma_func(
engine_kwargs,
self.com,
self.adjust,
self.ignore_na,
)
return self._apply(
groupby_ewma_func,
numba_cache_key=(lambda x: x, "groupby_ewma"),
)
elif engine in ("cython", None):
if engine_kwargs is not None:
raise ValueError("cython engine does not accept engine_kwargs")
def f(x):
x = self._shallow_copy(x, groupby=self._groupby)
return x.mean()
return self._groupby.apply(f)
else:
raise ValueError("engine must be either 'numba' or 'cython'")