statsmodels.tsa.stattools.pacf(x, nlags=40, method='ywunbiased', alpha=None)[source]

Partial autocorrelation estimate.


Observations of time series for which pacf is calculated.

nlagsint, optional

The largest lag for which the pacf is returned.

methodstr, optional

Specifies which method for the calculations to use.

  • ‘yw’ or ‘ywunbiased’ : Yule-Walker with bias correction in denominator for acovf. Default.

  • ‘ywm’ or ‘ywmle’ : Yule-Walker without bias correction.

  • ‘ols’ : regression of time series on lags of it and on constant.

  • ‘ols-inefficient’ : regression of time series on lags using a single common sample to estimate all pacf coefficients.

  • ‘ols-unbiased’ : regression of time series on lags with a bias adjustment.

  • ‘ld’ or ‘ldunbiased’ : Levinson-Durbin recursion with bias correction.

  • ‘ldb’ or ‘ldbiased’ : Levinson-Durbin recursion without bias correction.

alphafloat, 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 1/sqrt(len(x)).


Partial autocorrelations, nlags elements, including lag zero.

confintndarray, optional

Confidence intervals for the PACF. Returned if confint is not None.

See also


Estimate the autocorrelation function.


Partial autocorrelation estimation.


Partial autocorrelation estimation using Yule-Walker.


Partial autocorrelation estimation using OLS.


Partial autocorrelation estimation using Burg’s method.


Based on simulation evidence across a range of low-order ARMA models, the best methods based on root MSE are Yule-Walker (MLW), Levinson-Durbin (MLE) and Burg, respectively. The estimators with the lowest bias included included these three in addition to OLS and OLS-unbiased.

Yule-Walker (unbiased) and Levinson-Durbin (unbiased) performed consistently worse than the other options.