roll_z_score¶

Defined in fynance.features.metrics

roll_z_score(X, w=None, kind='s', axis=0, dtype=None)[source]

Compute vector of rolling/moving Z-score function.

Parameters:

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

Series of index, prices or returns.

wint, optional

Size of the lagged window of the moving averages, must be positive. If w is None or w=0, then w=X.shape[axis]. Default is None.

kind{‘e’, ‘s’, ‘w’}

If ‘e’ then use exponential moving average, see ema for details.
If ‘s’ (default) then use simple moving average, see sma for details.
If ‘w’ then use weighted moving average, see wma for details.

axis{0, 1}, optional

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

dtypenp.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]: Vector of Z-score at each period.

See also

z_score, roll_mdd, roll_calmar, roll_mad, roll_sharpe

Notes

Compute for each observation the z-score function for a specific moving average function such that \(\forall t \in [1:T]\):

\[z_t = \frac{X_t - \mu_t}{\sigma_t}\]

Where \(\mu_t\) is the moving average and \(\sigma_t\) is the moving standard deviation.

Examples

>>> X = np.array([70, 100, 80, 120, 160, 80]).astype(np.float64)
>>> roll_z_score(X, w=3, kind='e')
array([ 0.        ,  1.41421356, -0.32444284,  1.30806216,  1.27096675,
       -1.04435741])
>>> roll_z_score(X, w=3)
array([ 0.        ,  1.        , -0.26726124,  1.22474487,  1.22474487,
       -1.22474487])