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

Partial autocorrelation estimated

  • x (1d array) – observations of time series for which pacf is calculated

  • nlags (int) – largest lag for which the pacf is returned

  • method (str) –

    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

  • alpha (float, 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))


  • pacf (1d array) – partial autocorrelations, nlags elements, including lag zero

  • confint (array, 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.