ema

Defined in fynance.features.momentums

ema(X, alpha=0.94, w=None, axis=0, dtype=None)

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

Geometrically decaying weighted average that gives more importance to recent observations. Reacts faster than sma to regime changes; smaller alpha (or smaller equivalent window w) increases reactivity at the cost of more noise. The recursive formulation makes computation O(T) per series, with no need to store the full window.

Either alpha (smoothing factor in [0, 1]) or w (window size mapped to alpha = 1 - 2 / (1 + w)) can be specified.

\[ema^{\apha}_t(X) = \alpha \times ema^{\alpha}_{t-1} + (1-\alpha) \times X_t\]

Parameters:

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

Elements to compute the moving average.

alphafloat, optional

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

wint, 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.

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]

Exponential moving average of each series.

See also

sma, wma, emstd

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])
>>> ema(X, w=3, dtype=np.float64)
array([ 60.,  80.,  80., 100., 130., 105.])
>>> ema(X, alpha=0.5, dtype=np.float64)
array([ 60.,  80.,  80., 100., 130., 105.])