statsmodels.tsa.stattools.pacf

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

Partial autocorrelation estimate.

Parameters
xarray_like

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).

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.

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)).

Returns
pacfndarray

Partial autocorrelations, nlags elements, including lag zero.

confintndarray, optional

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

See also

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.