gs_quant.timeseries.statistics.cov

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

Rolling co-variance of series over given window

Parameters:

• x (Series) – series: timeseries

• y (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 covariance

Usage

Provides unbiased estimator of sample co-variance over a rolling window:

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

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

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

If window is not provided, computes variance over the full series

Examples

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

>>> prices_x = generate_series(100)
>>> prices_y = generate_series(100)
>>> cov(returns(prices_x) returns(prices_y), 22)

See also

sum() mean() var()