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

Exponentially-weighted moving variance.

Parameters:

com

Specify decay in terms of center of mass, $\gamma$, with

$$\alpha =\frac{1}{1+\gamma }\mathrm{\forall }\gamma \ge 0$$

span

Specify decay in terms of span, $\theta$, with

$$\alpha =\frac{2}{\theta +1}\mathrm{\forall }\theta \ge 1$$

half_life

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

$$\alpha =1-\exp \left\{\frac{-\ln (2)}{\lambda }\right\}\mathrm{\forall }\lambda >0$$

alpha

Specify smoothing factor alpha directly, $0<\alpha \le 1$.

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

  $$\begin{array}{rl}{y}_0& =x_0\\ y_t& =(1-\alpha )y_{t-1}+\alpha x_t\end{array}$$

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 │
└──────────┘