corr¶
- corr(dt, z1, z2, axis=0, **kwargs)[source]¶
Return the correlation spectrum at a single lag or successive lags. Default behavior returns the lag-0 correlation.
- Parameters
dt (float or array-like, optional) – The timestep or time series (from which the timestep is inferred).
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 correlation is taken.
lag (float, optional) – Return correlation for the single lag
lag
(must be divisible bydt
).ilag (int, optional) – As with
lag
but specifies the index instead of the physical time.maxlag (float, optional) – Return lagged correlation up to the lag
maxlag
(must be divisible bydt
).imaxlag (int, optional) – As with
maxlag
but specifies the index instead of the physical time.
- Returns
lags (array-like) – The lags.
result (array-like) – The correlation as a function of lag.
Notes
This function uses the following formula to estimate correlation at lag \(k\):
\[\dfrac{% \sum_{i=0}^{n-k} \left(x_t - \overline{x}\right) \left(y_{t+k} - \overline{y}\right) }{% (n - k) s_x s_y }\]where \(\overline{x}\) and \(\overline{y}\) are the sample means and \(s_x\) and \(s_y\) are the sample standard deviations.