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

Partial autocorrelation estimate.


Observations of time series for which pacf is calculated.

nlagsint, optional

Number of lags to return autocorrelation for. If not provided, uses min(10 * np.log10(nobs), nobs // 2 - 1). The returned value includes lag 0 (ie., 1) so size of the pacf vector is (nlags + 1,).

methodstr, default “ywunbiased”

Specifies which method for the calculations to use.

  • “yw” or “ywadjusted” : Yule-Walker with sample-size adjustment in denominator for acovf. Default.

  • “ywm” or “ywmle” : Yule-Walker without adjustment.

  • “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-adjusted” : regression of time series on lags with a bias adjustment.

  • “ld” or “ldadjusted” : Levinson-Durbin recursion with bias correction.

  • “ldb” or “ldbiased” : Levinson-Durbin recursion without bias correction.

  • “burg” : Burg”s partial autocorrelation estimator.

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)).


The partial autocorrelations for lags 0, 1, …, nlags. Shape (nlags+1,).

confintndarray, optional

Confidence intervals for the PACF at lags 0, 1, …, nlags. Shape (nlags + 1, 2). Returned if alpha 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-adjusted.

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

Last update: Jul 16, 2024