statsmodels.regression.linear_model.yule_walker¶
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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