Momentums module

Some tools to compute moving statistic momentums.

fynance.tools.momentums.ema(series[, alpha, …])	Exponential moving average along k lags.
fynance.tools.momentums.emstd(series[, …])	Exponential moving standard deviation along k lags.
fynance.tools.momentums.sma(series[, lags])	Simple moving average along k lags.
fynance.tools.momentums.smstd(series[, lags])	Simple moving standard deviation along k lags.
fynance.tools.momentums.wma(series[, lags])	Weighted moving average along k lags.
fynance.tools.momentums.wmstd(series[, lags])	Weighted moving standard deviation along k lags.

Moving averages

fynance.tools.momentums.ema(series, alpha=0.94, lags=None)

Exponential moving average along k lags.

\[ema_t = \alpha \times ema_{t-1} + (1-\alpha) \times series_t\]

Parameters:

series : np.ndarray[dtype=np.float64, ndim=1]

Index or returns.

alpha : float, optional

Multiplier, default is 0.94 corresponding at 20 lags memory.

lags : int, optional

Number of days.

Returns:

np.ndarray[dtype=np.float64, ndim=1]

Moving average of series.

See also

sma, wma

Notes

If lags is specified \(\alpha = 1 - \frac{2}{1 + k}\)

Examples

>>> series = np.array([60, 100, 80, 120, 160, 80])
>>> ema(series, lags=3)
array([ 60.,  80.,  80., 100., 130., 105.])
>>> ema(series, alpha=0.5)
array([ 60.,  80.,  80., 100., 130., 105.])

fynance.tools.momentums.sma(series, lags=21)

Simple moving average along k lags.

\[sma_t = \frac{1}{k} \sum^{k-1}_{i=0} series_{t-i}\]

Parameters:

series : np.ndarray[dtype=np.float64, ndim=1]

Index or returns.

lags : int, optional

Number of lags for ma, default is 21.

Returns:

np.ndarray[dtype=np.float64, ndim=1]

Vector of moving average of series.

See also

wma, ema

Examples

>>> series = np.array([60, 100, 80, 120, 160, 80])
>>> sma(series, lags=3)
array([ 60.,  80.,  80., 100., 120., 120.])

fynance.tools.momentums.wma(series, lags=21)

Weighted moving average along k lags.

\[wma_t = \frac{2}{k (k-1)} \sum^{k-1}_{i=0} (k-i) \times series_{t-i}\]

Parameters:

series : np.ndarray[dtype=np.float64, ndim=1]

Index or returns.

lags : int, optional

Number of lags for ma, default is 21.

Returns:

np.ndarray[dtype=np.float64, ndim=1]

Moving average of series.

See also

sma, ema

Examples

>>> series = np.array([60, 100, 80, 120, 160, 80])
>>> wma(series, lags=3)
array([ 60.        ,  86.66666667,  83.33333333, 103.33333333,
       133.33333333, 113.33333333])

Moving standard deviation

fynance.tools.momentums.emstd(series, alpha=0.94, lags=None)

Exponential moving standard deviation along k lags.

\[emstd_t = \sqrt{\alpha\times emstd_{t-1}^2+(1-\alpha)\times series_t^2}\]

Parameters:

series : np.ndarray[dtype=np.float64, ndim=1]

Index or returns.

alpha : float, optional

Multiplier, default is 0.94 corresponding at 20 lags memory.

lags : int, optional

Number of days.

Returns:

np.ndarray[dtype=np.float64, ndim=1]

Moving standard deviation of series.

See also

smstd, wmstd

Notes

If lags is specified \(\alpha = 1 - \frac{2}{1 + k}\)

Examples

>>> series = np.array([60, 100, 80, 120, 160, 80])
>>> emstd(series, lags=3)
array([ 0.        , 28.28427125, 20.        , 31.6227766 , 47.95831523,
       48.98979486])

fynance.tools.momentums.smstd(series, lags=21)

Simple moving standard deviation along k lags.

\[smstd_t = \sqrt{\frac{1}{k} \sum^{k-1}_{i=0} (p_{t-i} - sma_t)^2}\]

Parameters:

series : np.ndarray[dtype=np.float64, ndim=1]

Index or returns.

lags : int, optional

Number of lags for ma, default is 21.

Returns:

np.ndarray[dtype=np.float64, ndim=1]

Moving standard deviation of series.

See also

wmstd, emstd

Examples

>>> series = np.array([60, 100, 80, 120, 160, 80])
>>> smstd(series, lags=3)
array([ 0.        , 20.        , 16.32993162, 16.32993162, 32.65986324,
       32.65986324])

fynance.tools.momentums.wmstd(series, lags=21)

Weighted moving standard deviation along k lags.

\[ \begin{align}\begin{aligned}wma_t = \frac{2}{k (k-1)} \sum^{k-1}_{i=0} (k-i) \times series_{t-i}\\wmstd_t = \sqrt{\frac{2}{k(k-1)} \sum^{k-1}_{i=0} (k-i) \times (series_{t-i} - wma_t)^2}\end{aligned}\end{align} \]

Parameters:

series : np.ndarray[dtype=np.float64, ndim=1]

Series of prices, index or returns.

lags : int, optional

Number of days, default is 21.

Returns:

np.ndarray[dtype=np.float64, ndim=1]

Moving standard deviation of series.

See also

smstd, emstd

Examples

>>> series = np.array([60, 100, 80, 120, 160, 80])
>>> wmstd(series, lags=3)
array([ 0.        , 18.85618083, 13.74368542, 17.95054936, 29.8142397 ,
       35.90109871])