pandas.DataFrame.ewm#

DataFrame.ewm(com=None,span=None,halflife=None,alpha=None,min_periods=0,adjust=True,ignore_na=False,axis=<no_default>,times=None,method='single')[source]#

Provide exponentially weighted (EW) calculations.

Exactly one ofcom,span,halflife, oralpha must beprovided iftimes is not provided. Iftimes is provided,halflife and one ofcom,span oralpha may be provided.

Parameters:

comfloat, optional

Specify decay in terms of center of mass

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

spanfloat, optional

Specify decay in terms of span

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

halflifefloat, str, timedelta, optional

Specify decay in terms of half-life

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

Iftimes is specified, a timedelta convertible unit over which anobservation decays to half its value. Only applicable tomean(),and halflife value will not apply to the other functions.

alphafloat, optional

Specify smoothing factor\(\alpha\) directly

\(0 < \alpha \leq 1\).

min_periodsint, default 0

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

adjustbool, default True

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

• Whenadjust=True (default), the EW function is calculated using weights\(w_i = (1 - \alpha)^i\). For example, the EW moving average of the series[\(x_0, x_1, ..., x_t\)] would be:

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

• Whenadjust=False, the exponentially weighted function is calculatedrecursively:

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

ignore_nabool, default False

Ignore missing values when calculating weights.

• Whenignore_na=False (default), weights are based on absolute positions.For example, the weights of\(x_0\) and\(x_2\) used in calculatingthe 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.

• Whenignore_na=True, weights are basedon 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.

axis{0, 1}, default 0

If0 or'index', calculate across the rows.

If1 or'columns', calculate across the columns.

ForSeries this parameter is unused and defaults to 0.

timesnp.ndarray, Series, default None

Only applicable tomean().

Times corresponding to the observations. Must be monotonically increasing anddatetime64[ns] dtype.

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

methodstr {‘single’, ‘table’}, default ‘single’

Added in version 1.4.0.

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

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

Only applicable tomean()

Returns:

pandas.api.typing.ExponentialMovingWindow

See also

rolling

Provides rolling window calculations.

expanding

Provides expanding transformations.

Notes

SeeWindowing Operationsfor further usage details and examples.

Examples

>>>df=pd.DataFrame({'B':[0,1,2,np.nan,4]})>>>df     B0  0.01  1.02  2.03  NaN4  4.0

>>>df.ewm(com=0.5).mean()          B0  0.0000001  0.7500002  1.6153853  1.6153854  3.670213>>>df.ewm(alpha=2/3).mean()          B0  0.0000001  0.7500002  1.6153853  1.6153854  3.670213

adjust

>>>df.ewm(com=0.5,adjust=True).mean()          B0  0.0000001  0.7500002  1.6153853  1.6153854  3.670213>>>df.ewm(com=0.5,adjust=False).mean()          B0  0.0000001  0.6666672  1.5555563  1.5555564  3.650794

ignore_na

>>>df.ewm(com=0.5,ignore_na=True).mean()          B0  0.0000001  0.7500002  1.6153853  1.6153854  3.225000>>>df.ewm(com=0.5,ignore_na=False).mean()          B0  0.0000001  0.7500002  1.6153853  1.6153854  3.670213

times

Exponentially weighted mean with weights calculated with a timedeltahalfliferelative totimes.

>>>times=['2020-01-01','2020-01-03','2020-01-10','2020-01-15','2020-01-17']>>>df.ewm(halflife='4 days',times=pd.DatetimeIndex(times)).mean()          B0  0.0000001  0.5857862  1.5238893  1.5238894  3.233686