autocovar

autocovar(dt, z, axis=0, **kwargs)[source]

Return the autocovariance spectrum at successive lags.

Parameters

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

  • z (array-like) – The input data.

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

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

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

Returns

  • lags (array-like) – The lags.

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

Note

This function uses the following formula to estimate autocovariance 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.