pandas.plotting.autocorrelation_plot

pandas.plotting.autocorrelation_plot(series, ax=None, **kwargs)

Autocorrelation plot for time series.

This method generates an autocorrelation plot for a given time series, which helps to identify any periodic structure or correlation within the data across various lags. It shows the correlation of a time series with a delayed copy of itself as a function of delay. Autocorrelation plots are useful for checking randomness in a data set. If the data are random, the autocorrelations should be near zero for any and all time-lag separations. If the data are not random, then one or more of the autocorrelations will be significantly non-zero.

Parameters:

seriesSeries

The time series to visualize.

axMatplotlib axis object, optional

The matplotlib axis object to use.

**kwargs

Options to pass to matplotlib plotting method.

Returns:

matplotlib.axes.Axes

The matplotlib axes containing the autocorrelation plot.

See also

Series.autocorr

Compute the lag-N autocorrelation for a Series.

plotting.lag_plot

Lag plot for time series.

Notes

The autocorrelation at lag h is computed using the mean and variance of the whole series:

\[r_h = \frac{\sum_{t=1}^{n-h} (x_t - \bar{x})(x_{t+h} - \bar{x})} {\sum_{t=1}^{n} (x_t - \bar{x})^2}\]

This differs from autocorr(), which computes the Pearson correlation between the overlapping portions of the series and its lagged copy, so the two can give different values for the same lag.

Examples

The horizontal lines in the plot correspond to 95% and 99% confidence bands.

The dashed line is 99% confidence band.

>>> spacing = np.linspace(-9 * np.pi, 9 * np.pi, num=1000)
>>> rng = np.random.default_rng(42)
>>> s = pd.Series(0.7 * rng.random(1000) + 0.3 * np.sin(spacing))
>>> pd.plotting.autocorrelation_plot(s)