statsmodels.tsa.stattools.acf(x, unbiased=False, nlags=40, qstat=False, fft=None, alpha=None, missing='none')[source]

Calculate the autocorrelation function.


The time series data.


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

nlagsint, optional

Number of lags to return autocorrelation for.

qstatbool, optional

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

fftbool, optional

If True, computes the ACF via FFT.

alphascalar, 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.

missingstr, optional

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


The autocorrelation function.

confintndarray, optional

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

qstatndarray, optional

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

pvaluesndarray, optional

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


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.



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