polars.Expr.ewm_var#

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

Exponentially-weighted moving variance.

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 EW function is calculated using weights \(w_i = (1 - \alpha)^i\)

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

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

When bias=False, apply a correction to make the estimate statistically unbiased.

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

>>> df = pl.DataFrame({"a": [1, 2, 3]})
>>> df.select(pl.col("a").ewm_var(com=1))
shape: (3, 1)
┌──────────┐
│ a        │
│ ---      │
│ f64      │
╞══════════╡
│ 0.0      │
│ 0.5      │
│ 0.928571 │
└──────────┘