polars.Series.ewm_mean#

Series.ewm_mean(
*,
com: float | None = None,
span: float | None = None,
half_life: float | None = None,
alpha: float | None = None,
adjust: bool = True,
min_periods: int = 1,
ignore_nulls: bool = False,
) → Series[source]#

Exponentially-weighted moving average.

Parameters:
com

Specify decay in terms of center of mass, \(\gamma\), with

\[\alpha = \frac{1}{1 + \gamma} \; \forall \; \gamma \geq 0\]
span

Specify decay in terms of span, \(\theta\), with

\[\alpha = \frac{2}{\theta + 1} \; \forall \; \theta \geq 1\]
half_life

Specify decay in terms of half-life, \(\lambda\), with

\[\alpha = 1 - \exp \left\{ \frac{ -\ln(2) }{ \lambda } \right\} \; \forall \; \lambda > 0\]
alpha

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

adjust

Divide by decaying adjustment factor in beginning periods to account for imbalance in relative weightings

  • When adjust=True (the default) the EW function is calculated using weights \(w_i = (1 - \alpha)^i\)

  • When adjust=False the EW function is calculated recursively by

    \[\begin{split}y_0 &= x_0 \\ y_t &= (1 - \alpha)y_{t - 1} + \alpha x_t\end{split}\]
min_periods

Minimum number of observations in window required to have a value (otherwise result is null).

ignore_nulls

Ignore missing values when calculating weights.

  • When ignore_nulls=False (default), weights are based on absolute positions. For example, the weights of \(x_0\) and \(x_2\) used in calculating the final weighted average of [\(x_0\), None, \(x_2\)] are \((1-\alpha)^2\) and \(1\) if adjust=True, and \((1-\alpha)^2\) and \(\alpha\) if adjust=False.

  • When ignore_nulls=True, weights are based on relative positions. For example, the weights of \(x_0\) and \(x_2\) used in calculating the final weighted average of [\(x_0\), None, \(x_2\)] are \(1-\alpha\) and \(1\) if adjust=True, and \(1-\alpha\) and \(\alpha\) if adjust=False.

Examples

>>> s = pl.Series([1, 2, 3])
>>> s.ewm_mean(com=1, ignore_nulls=False)
shape: (3,)
Series: '' [f64]
[
        1.0
        1.666667
        2.428571
]