pandas.Series.ewm

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

Provide exponential weighted functions.

New in version 0.18.0.

Parameters:

com : float, optional

Specify decay in terms of center of mass, \(\alpha = 1 / (1 + com),\text{ for } com \geq 0\).

span : float, optional

Specify decay in terms of span, \(\alpha = 2 / (span + 1),\text{ for } span \geq 1\).

halflife : float, optional

Specify decay in terms of half-life, \(\alpha = 1 - exp(log(0.5) / halflife),\text{for} halflife > 0\).

alpha : float, optional

Specify smoothing factor \(\alpha\) directly, \(0 < \alpha \leq 1\).

New in version 0.18.0.

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).

ignore_na : bool, default False

Ignore missing values when calculating weights; specify True to reproduce pre-0.15.0 behavior.

axis : {0 or ‘index’, 1 or ‘columns’}, default 0

The axis to use. The value 0 identifies the rows, and 1 identifies the columns.

Returns:

DataFrame

A Window sub-classed for the particular operation.

See also

rolling

Provides rolling window calculations.

expanding

Provides expanding transformations.

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).

More details can be found at http://pandas.pydata.org/pandas-docs/stable/user_guide/computation.html#exponentially-weighted-windows

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