statsmodels.tsa.stattools.pacf¶

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

Partial autocorrelation estimated

Parameters
x1d array

observations of time series for which pacf is calculated

nlagsint

largest lag for which the pacf is returned

methodstr

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

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
pacf1d array

partial autocorrelations, nlags elements, including lag zero

confintarray, optional

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

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.