polars.Expr.ewm_mean#
- Expr.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,
Compute 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, \(\tau\), with
\[\alpha = 1 - \exp \left\{ \frac{ -\ln(2) }{ \tau } \right\} \; \forall \; \tau > 0\]- 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 \(1\) ifadjust=True
, and \((1-\alpha)^2\) and \(\alpha\) ifadjust=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 \(1\) ifadjust=True
, and \(1-\alpha\) and \(\alpha\) ifadjust=False
.
Examples
>>> df = pl.DataFrame({"a": [1, 2, 3]}) >>> df.select(pl.col("a").ewm_mean(com=1, ignore_nulls=False)) shape: (3, 1) ┌──────────┐ │ a │ │ --- │ │ f64 │ ╞══════════╡ │ 1.0 │ │ 1.666667 │ │ 2.428571 │ └──────────┘