pmdarima.utils.acf

pmdarima.utils.acf(x, unbiased=False, nlags=40, qstat=False, fft=False, alpha=None, missing='none')

Calculate the autocorrelation function.

Parameters:

x : array_like

The time series data.

unbiased : bool

If True, then denominators for autocovariance are n-k, otherwise n.

nlags : int, optional

Number of lags to return autocorrelation for.

qstat : bool, optional

If True, returns the Ljung-Box q statistic for each autocorrelation coefficient. See q_stat for more information.

fft : bool, optional

If True, computes the ACF via FFT.

alpha : scalar, optional

If a number is given, the confidence intervals for the given level are returned. For instance if alpha=.05, 95 % confidence intervals are returned where the standard deviation is computed according to Bartlett’s formula.

missing : str, optional

A string in [‘none’, ‘raise’, ‘conservative’, ‘drop’] specifying how the NaNs are to be treated.

Returns:

acf : ndarray

The autocorrelation function.

confint : ndarray, optional

Confidence intervals for the ACF. Returned if alpha is not None.

qstat : ndarray, optional

The Ljung-Box Q-Statistic. Returned if q_stat is True.

pvalues : ndarray, optional

The p-values associated with the Q-statistics. Returned if q_stat is True.

Notes

The acf at lag 0 (ie., 1) is returned.

For very long time series it is recommended to use fft convolution instead. When fft is False uses a simple, direct estimator of the autocovariances that only computes the first nlag + 1 values. This can be much faster when the time series is long and only a small number of autocovariances are needed.

If unbiased is true, the denominator for the autocovariance is adjusted but the autocorrelation is not an unbiased estimator.

References

[R91]

Parzen, E., 1963. On spectral analysis with missing observations and amplitude modulation. Sankhya: The Indian Journal of Statistics, Series A, pp.383-392.