pandas.Series.ewm   Series.ewm(com=None, span=None, halflife=None, alpha=None, min_periods=0, adjust=True, ignore_na=False, axis=0, times=None, method='single')[source]
 
Provide exponentially weighted (EW) calculations. Exactly one parameter: com, span, halflife, or alpha must be provided.  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.  New in version 1.1.0.   
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.   
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


 New in version 1.1.0.  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 since version 1.4.0: If str, the name of the column in the DataFrame representing the times.   
method:str {‘single’, ‘table’}, default ‘single’


 New 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 specifying engine='numba' in the method call. Only applicable to mean()    Returns 
 
ExponentialMovingWindow subclass
    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