pmdarima.utils.pacf

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

Partial autocorrelation estimate.

Parameters:

x : array_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.

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.