Series.
ewm
Provide exponential weighted functions.
Specify decay in terms of center of mass, \(\alpha = 1 / (1 + com),\text{ for } com \geq 0\).
Specify decay in terms of span, \(\alpha = 2 / (span + 1),\text{ for } span \geq 1\).
Specify decay in terms of half-life, \(\alpha = 1 - exp(log(0.5) / halflife),\text{for} halflife > 0\).
Specify smoothing factor \(\alpha\) directly, \(0 < \alpha \leq 1\).
Minimum number of observations in window required to have a value (otherwise result is NA).
Divide by decaying adjustment factor in beginning periods to account for imbalance in relative weightings (viewing EWMA as a moving average).
Ignore missing values when calculating weights; specify True to reproduce pre-0.15.0 behavior.
The axis to use. The value 0 identifies the rows, and 1 identifies the columns.
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.
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 https://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