gs_quant.timeseries.statistics.std

std(x, w=<gs_quant.timeseries.helper.Window object>)

Rolling standard deviation of series over given window

Parameters:

• x (Series) – series: timeseries

• w (Union[Window, int, str]) – Window or int: size of window and ramp up to use. e.g. Window(22, 10) where 22 is the window size and 10 the ramp up value. If w is a string, it should be a relative date like ‘1m’, ‘1d’, etc. Window size defaults to length of series.

Return type:

Series

Returns:

timeseries of standard deviation

Usage

Provides unbiased estimator of sample standard deviation over a rolling window:

\(R_t = \sqrt{\frac{1}{N-1} \sum_{i=t-w+1}^t (X_i - \overline{X_t})^2}\)

where \(N\) is the number of observations in each rolling window, \(w\), and \(\overline{X_t}\) is the mean value over the same window:

\(\overline{X_t} = \frac{\sum_{i=t-w+1}^{t} X_i}{N}\)

If window is not provided, computes standard deviation over the full series

Examples

Generate price series and compute standard deviation of returns over \(22\) observations

>>> prices = generate_series(100)
>>> std(returns(prices), 22)

See also

sum() mean() var()