3.9.2.1.4. statsmodels.regression.linear_model.yule_walker¶

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

Estimate AR(p) parameters from a sequence X using Yule-Walker equation.

Unbiased or maximum-likelihood estimator (mle)

See, for example:

http://en.wikipedia.org/wiki/Autoregressive_moving_average_model

Parameters:

X : array-like

1d array

order : integer, optional

The order of the autoregressive process. Default is 1.

method : string, optional

Method can be “unbiased” 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 “unbiased” the denominator is n-k. The default is unbiased.

df : integer, 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

The autoregressive coefficients

sigma

TODO

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