Pandas: Series - ewm() function

Last update on September 15 2022 12:54:02 (UTC/GMT +8 hours)

Exponential weighted functions in Pandas

The ewm() function is used to provide exponential weighted functions.

Syntax:

Series.ewm(self, com=None, span=None, halflife=None, alpha=None, min_periods=0, adjust=True, ignore_na=False, axis=0)

Parameters:

Name	Description	Type/Default Value	Required / Optional
com	Specify decay in terms of center of mass, α=1/(1+com), for com≥0.	float	Optional
span	Specify decay in terms of span, α=2/(span+1), for span≥1.	float	Optional
halflife	Specify decay in terms of half-life, α=1−exp(log(0.5)/halflife),forhalflife>0.	float	Optional
alpha	Specify smoothing factor α directly, 0<α≤1	float	Optional
min_periods	Minimum number of observations in window required to have a value (otherwise result is NA).	int Default Value: 0	Required
adjust	Divide by decaying adjustment factor in beginning periods to account for imbalance in relative weightings (viewing EWMA as a moving average)	bool Default Value: True	Required
ignore_na	Ignore missing values when calculating weights; specify True to reproduce pre-0.15.0 behavior.	bool Default Value: False	Required
axis	The axis to use. The value 0 identifies the rows, and 1 identifies the columns.	{0 or ‘index’, 1 or ‘columns’} Default Value: 0	Required

Returns: DataFrame
A Window sub-classed for the particular operation.

Notes: Exactly one of center of mass, span, half-life, and alpha must be provided. Allowed values and relationship between the parameters are specified in the parameter descriptions above; see the link at the end of this section for a detailed explanation.
When adjust is True (default), weighted averages are calculated using weights (1-alpha)**(n-1), (1-alpha)**(n-2), …, 1-alpha, 1.
When adjust is False, weighted averages are calculated recursively as:
weighted_average[0] = arg[0]; weighted_average[i] = (1-alpha)*weighted_average[i-1] + alpha*arg[i].
When ignore_na is False (default), weights are based on absolute positions. For example, the weights of x and y used in calculating the final weighted average of [x, None, y] are (1-alpha)**2 and 1 (if adjust is True), and (1-alpha)**2 and alpha (if adjust is False).
When ignore_na is True (reproducing pre-0.15.0 behavior), weights are based on relative positions. For example, the weights of x and y used in calculating the final weighted average of [x, None, y] are 1-alpha and 1 (if adjust is True), and 1-alpha and alpha (if adjust is False).

Example:

Python-Pandas Code:

import numpy as np
import pandas as pd
df = pd.DataFrame({'Q': [0, 2, 4, np.nan, 6]})
df

Output:

    Q
0	0.0
1	2.0
2	4.0
3	NaN
4	6.0

Python-Pandas Code:

import numpy as np
import pandas as pd
df = pd.DataFrame({'Q': [0, 2, 4, np.nan, 6]})
df.ewm(com=0.3).mean()

Output:

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