covar

covar(dt, z1, z2, axis=0, **kwargs)[source]

Return the covariance spectrum at successive lags.

Parameters

  • dt (float or array-like) – The timestep or regularly-spaced time coordinates.

  • z1 (array-like) – The input data.

  • z2 (array-like, optional) – The second input data. Must be same shape as z1.

  • axis (int, optional) – Axis along which covariance is taken.

  • lag (int, optional) – Return covariance at the single lag lag.

  • nlag (int, optional) – Return lagged covariance from 0 timesteps up to nlag timesteps.

Returns

  • lags (array-like) – The lags.

  • result (array-like) – The covariance as a function of lag.

Note

This function uses the following formula to estimate covariance at lag \(k\):

\[\dfrac{\sum_{i=0}^{n-k}\left(x_t - \overline{x}\right)\left(y_{t+k} - \overline{y}\right)}{n - k}\]

where \(\overline{x}\) and \(\overline{y}\) are the sample means.