Document

ewm(self, com: 'float | None' = None, span: 'float | None' = None, halflife: 'float | TimedeltaConvertibleTypes | None' = None, alpha: 'float | None' = None, min_periods: 'int | None' = 0, adjust: 'bool_t' = True, ignore_na: 'bool_t' = False, axis: 'Axis' = 0, times: 'str | np.ndarray | DataFrame | Series | None' = None, method: 'str' = 'single') -> 'ExponentialMovingWindow'

Exactly one parameter: com , span , halflife , or alpha must be provided.

Notes

See Windowing Operations <window.exponentially_weighted> for further usage details and examples.

Parameters

com : float, optional

Specify decay in terms of center of mass

$\alpha = 1 / (1 + com)$ , for $com \geq 0$ .

span : float, optional

Specify decay in terms of span

$\alpha = 2 / (span + 1)$ , for $span \geq 1$ .

halflife : float, str, timedelta, optional

Specify decay in terms of half-life

$\alpha = 1 - \exp\left(-\ln(2) / halflife\right)$ , for $halflife > 0$ .

If times is specified, the time unit (str or timedelta) over which an observation decays to half its value. Only applicable to mean() , and halflife value will not apply to the other functions.

versionadded

alpha : float, optional

Specify smoothing factor $\alpha$ directly

$0 < \alpha \leq 1$ .

min_periods : int, default 0

Minimum number of observations in window required to have a value; otherwise, result is np.nan .

adjust : bool, default True

Divide by decaying adjustment factor in beginning periods to account for imbalance in relative weightings (viewing EWMA as a moving average).

When adjust=True (default), the EW function is calculated using weights $w_i = (1 - \alpha)^i$ . For example, the EW moving average of the series [:math:None:None:`x_0, x_1, ..., x_t`] would be:

$$y_t = \frac{x_t + (1 - \alpha)x_{t-1} + (1 - \alpha)^2 x_{t-2} + ... + (1 - \alpha)^t x_0}{1 + (1 - \alpha) + (1 - \alpha)^2 + ... + (1 - \alpha)^t}$$

When adjust=False , the exponentially weighted function is calculated recursively:

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

ignore_na : bool, default False

Ignore missing values when calculating weights.

When ignore_na=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 [:math:`x_0`, None, :math:`x_2`] are $(1-\alpha)^2$ and $1$ if adjust=True , and $(1-\alpha)^2$ and $\alpha$ if adjust=False .
When ignore_na=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 [:math:`x_0`, None, :math:`x_2`] are :math:`1-\alpha` and :math:`1` if adjust=True , and $1-\alpha$ and $\alpha$ if adjust=False .

axis : {0, 1}, default 0

If 0 or 'index' , calculate across the rows.

If 1 or 'columns' , calculate across the columns.

times : str, np.ndarray, Series, default None

versionadded

Only applicable to mean() .

Times corresponding to the observations. Must be monotonically increasing and datetime64[ns] dtype.

If 1-D array like, a sequence with the same shape as the observations.

deprecated

If str, the name of the column in the DataFrame representing the times.

method : str {'single', 'table'}, default 'single'

versionadded

Execute the rolling operation per single column or row ( 'single' ) or over the entire object ( 'table' ).

This argument is only implemented when specifying engine='numba' in the method call.

Only applicable to mean()