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# pandas.Series.ewm

Series.ewm(com=None, span=None, halflife=None, alpha=None, min_periods=0, adjust=True, ignore_na=False, times=None, method='single')

  Provide exponentially weighted (EW) calculations.

  Exactly one of `com`, `span`, `halflife`, or `alpha` must be provided if `times` is not provided. If `times` is provided and `adjust=True`, `halflife` and one of `com`, `span` or `alpha` may be provided. If `times` is provided and `adjust=False`, `halflife` must be the only provided decay-specification parameter.

  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, a timedelta convertible unit over which an observation decays to half its value. Only applicable to `mean()`, and halflife value will not apply to the other functions.

    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 [\(x_0, x_1, ..., x_t\)] 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:

      \[\begin{split}\begin{split} y_0 &= x_0\\ y_t &= (1 - \alpha) y_{t-1} + \alpha x_t, \end{split}\end{split}\]
    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 [\(x_0\), None, \(x_2\)] are \((1-\alpha)^2\) and \(1\) if `adjust=True`, and \((1-\alpha)^2\) and \(\alpha\) if `adjust=False`.

      - When `ignore_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 [\(x_0\), None, \(x_2\)] are \(1-\alpha\) and \(1\) if `adjust=True`, and \(1-\alpha\) and \(\alpha\) if `adjust=False`.

    times np.ndarray, Series, default None

      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.

    method str {‘single’, ‘table’}, default ‘single’

      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()`

  Returns:
    pandas.api.typing.ExponentialMovingWindow

      An instance of ExponentialMovingWindow for further exponentially weighted (EW) calculations, e.g. using the `mean` method.

  See also

  `rolling`

    Provides rolling window calculations.

  `expanding`

    Provides expanding transformations.

  Notes

  See Windowing Operations for further usage details and examples.

  Examples

      >>> df = pd.DataFrame({'B': [0, 1, 2, np.nan, 4]})
      >>> df
           B
      0  0.0
      1  1.0
      2  2.0
      3  NaN
      4  4.0

      >>> df.ewm(com=0.5).mean()
                B
      0  0.000000
      1  0.750000
      2  1.615385
      3  1.615385
      4  3.670213
      >>> df.ewm(alpha=2 / 3).mean()
                B
      0  0.000000
      1  0.750000
      2  1.615385
      3  1.615385
      4  3.670213

  adjust

      >>> df.ewm(com=0.5, adjust=True).mean()
                B
      0  0.000000
      1  0.750000
      2  1.615385
      3  1.615385
      4  3.670213
      >>> df.ewm(com=0.5, adjust=False).mean()
                B
      0  0.000000
      1  0.666667
      2  1.555556
      3  1.555556
      4  3.650794

  ignore_na

      >>> df.ewm(com=0.5, ignore_na=True).mean()
                B
      0  0.000000
      1  0.750000
      2  1.615385
      3  1.615385
      4  3.225000
      >>> df.ewm(com=0.5, ignore_na=False).mean()
                B
      0  0.000000
      1  0.750000
      2  1.615385
      3  1.615385
      4  3.670213

  times

  Exponentially weighted mean with weights calculated with a timedelta `halflife` relative to `times`.

      >>> 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()
                B
      0  0.000000
      1  0.585786
      2  1.523889
      3  1.523889
      4  3.233686