pandas.Series.ewm

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

Provides 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).

freq : None or string alias / date offset object, default=None (DEPRECATED)

Frequency to conform to before computing statistic

adjust : boolean, 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 : boolean, default False

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

Returns:

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.

The freq keyword is used to conform time series data to a specified frequency by resampling the data. This is done with the default parameters of resample() (i.e. using the mean).

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/computation.html#exponentially-weighted-windows

Examples

>>> df = DataFrame({'B': [0, 1, 2, np.nan, 4]})
     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