7.8.1.2. statsmodels.tsa.stattools.acf¶

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

Autocorrelation function for 1d arrays.

Parameters:

x : array 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.

Returns:

acf : array autocorrelation function confint : array, optional Confidence intervals for the ACF. Returned if confint is not None. qstat : array, optional The Ljung-Box Q-Statistic. Returned if q_stat is True. pvalues : array, 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.

This is based np.correlate which does full convolution. For very long time series it is recommended to use fft convolution instead.

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