var

var(x, w=Window(w=None, r=0))[source]

Rolling variance of series over given window

Parameters
  • x (Series) – series: timeseries

  • w (Union[Window, int]) – 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. Window size defaults to length of series.

Return type

Series

Returns

timeseries of variance

Usage

Provides unbiased estimator of sample variance over a rolling window:

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

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 variance over the full series

Examples

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

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

See also

var() mean() std()