statsmodels.regression.linear_model.yule_walker

statsmodels.regression.linear_model.yule_walker(x, order=1, method='adjusted', df=None, inv=False, demean=True)[source]

Estimate AR(p) parameters from a sequence using the Yule-Walker equations.

Adjusted or maximum-likelihood estimator (mle)

Parameters:
x : array_like

A 1d array.

order : int, optional

The order of the autoregressive process. Default is 1.

method : str, optional

Method can be ‘adjusted’ or ‘mle’ and this determines denominator in estimate of autocorrelation function (ACF) at lag k. If ‘mle’, the denominator is n=X.shape[0], if ‘adjusted’ the denominator is n-k. The default is adjusted.

df : int, optional

Specifies the degrees of freedom. If df is supplied, then it is assumed the X has df degrees of freedom rather than n. Default is None.

inv : bool

If inv is True the inverse of R is also returned. Default is False.

demean : bool

True, the mean is subtracted from X before estimation.

Returns:

  • rho (ndarray) – AR(p) coefficients computed using the Yule-Walker method.

  • sigma (float) – The estimate of the residual standard deviation.

See also

burg

Burg’s AR estimator.

Notes

See https://en.wikipedia.org/wiki/Autoregressive_moving_average_model for further details.

Examples

>>> import statsmodels.api as sm
>>> from statsmodels.datasets.sunspots import load
>>> data = load()
>>> rho, sigma = sm.regression.yule_walker(data.endog, order=4,
...                                        method="mle")

>>> rho
array([ 1.28310031, -0.45240924, -0.20770299,  0.04794365])
>>> sigma
16.808022730464351