autocovar¶

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

Return the autocovariance spectrum at a single lag or successive lags. Default behavior returns the lag-0 autocovariance.

Parameters

dt (float or array-like, optional) – The timestep or time series (from which the timestep is inferred).
z (array-like) – The input data.
axis (int, optional) – Axis along which autocovariance is taken.
lag (float, optional) – Return autocovariance for the single lag lag (must be divisible by dt).
ilag (int, optional) – As with lag but specifies the index instead of the physical time.
maxlag (float, optional) – Return lagged autocovariance up to the lag maxlag (must be divisible by dt).
imaxlag (int, optional) – As with maxlag but specifies the index instead of the physical time.

Returns

Notes

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.