fynance.features.momentums.emstd

fynance.features.momentums.emstd(X, alpha=0.94, w=None, axis=0, dtype=None)

Compute exponential moving standard deviation(s) for each X’ series.

\[emstd^{\alpha}_t(X) = \sqrt{\alpha\times emstd^{\alpha}_{t-1}^2 + (1-\alpha) \times X_t^2}\]

Parameters:

X : np.ndarray[dtype, ndim=1 or 2]

Elements to compute the moving standard deviation.

alpha : float, optional

These coefficient represents the degree of weighting decrease, default is 0.94 corresponding at 20 lags memory.

w : int, optional

Size of the lagged window of the moving average, must be strictly positive. If w is None the window is ignored and the parameter alpha is used. Default is None.

axis : {0, 1}, optional

Axis along wich the computation is done. Default is 0.

dtype : np.dtype, optional

The type of the output array. If dtype is not given, infer the data type from X input.

Returns:

np.ndarray[dtype, ndim=1 or 2]

Exponential moving standard deviation of each series.

See also

ema, smstd, wmstd

Notes

If the lagged window w is specified \(\alpha\) is overwritten by \(\alpha = 1 - \frac{2}{1 + w}\)

Examples

>>> X = np.array([60, 100, 80, 120, 160, 80])
>>> emstd(X, w=3, dtype=np.float64)
array([ 0.        , 14.14213562, 10.        , 15.8113883 , 23.97915762,
       24.49489743])
>>> emstd(X.reshape([6, 1]), w=3, dtype=np.float64).flatten()
array([ 0.        , 14.14213562, 10.        , 15.8113883 , 23.97915762,
       24.49489743])
>>> emstd(X, alpha=0.5, dtype=np.float64)
array([ 0.        , 14.14213562, 10.        , 15.8113883 , 23.97915762,
       24.49489743])