pmdarima.utils.pacf

pmdarima.utils.pacf(x, nlags=40, method='ywunbiased', alpha=None)[source][source]

Partial autocorrelation estimate.

Parameters:

x : array_like

Observations of time series for which pacf is calculated.

nlags : int, optional

The largest lag for which the pacf is returned.

method : str, optional

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)).
Returns:

pacf : ndarray

Partial autocorrelations, nlags elements, including lag zero.

confint : ndarray, 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-unbiased.

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