statsmodels.tsa.stattools.acovf(x, adjusted=False, demean=True, fft=True, missing='none', nlag=None)[source]

Estimate autocovariances.


Time series data. Must be 1d.

adjustedbool, default False

If True, then denominators is n-k, otherwise n.

demeanbool, default True

If True, then subtract the mean x from each element of x.

fftbool, default True

If True, use FFT convolution. This method should be preferred for long time series.

missingstr, default “none”

A string in [“none”, “raise”, “conservative”, “drop”] specifying how the NaNs are to be treated. “none” performs no checks. “raise” raises an exception if NaN values are found. “drop” removes the missing observations and then estimates the autocovariances treating the non-missing as contiguous. “conservative” computes the autocovariance using nan-ops so that nans are removed when computing the mean and cross-products that are used to estimate the autocovariance. When using “conservative”, n is set to the number of non-missing observations.

nlag{int, None}, default None

Limit the number of autocovariances returned. Size of returned array is nlag + 1. Setting nlag 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.


The estimated autocovariances.



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

Last update: Dec 14, 2023