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

Partial autocorrelation estimated

x1d array

observations of time series for which pacf is calculated


largest lag for which the pacf is returned


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))

pacf1d array

partial autocorrelations, nlags elements, including lag zero

confintarray, optional

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


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.