# statsmodels.tsa.stattools.pacf¶

Partial autocorrelation estimate.

Parameters
xarray_like

Observations of time series for which pacf is calculated.

nlags`int`, `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,).

method`str`, `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.

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)).

Returns
pacf`ndarray`

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

confint`ndarray`, `optional`

Confidence intervals for the PACF at lags 0, 1, …, nlags. Shape (nlags + 1, 2). Returned if alpha is not None.

`statsmodels.tsa.stattools.acf`

Estimate the autocorrelation function.

`statsmodels.tsa.stattools.pacf`

Partial autocorrelation estimation.

`statsmodels.tsa.stattools.pacf_yw`

Partial autocorrelation estimation using Yule-Walker.

`statsmodels.tsa.stattools.pacf_ols`

Partial autocorrelation estimation using OLS.

`statsmodels.tsa.stattools.pacf_burg`

Partial autocorrelation estimation using Burg”s method.

Notes

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.