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statsmodels.regression.linear_model.GLSAR

class statsmodels.regression.linear_model.GLSAR(endog, exog=None, rho=1)[source]

A regression model with an AR(p) covariance structure.

The linear autoregressive process of order p–AR(p)–is defined as:
TODO

Notes

GLSAR is considered to be experimental.

Examples

>>> import statsmodels.api as sm
>>> X = range(1,8)
>>> X = sm.add_constant(X)
>>> Y = [1,3,4,5,8,10,9]
>>> model = sm.GLSAR(Y, X, rho=2)
>>> for i in range(6):
...     results = model.fit()
...     print "AR coefficients:", model.rho
...     rho, sigma = sm.regression.yule_walker(results.resid,
...                                            order=model.order)
...     model = sm.GLSAR(Y, X, rho)
...
AR coefficients: [ 0.  0.]
AR coefficients: [-0.52571491 -0.84496178]
AR coefficients: [-0.6104153  -0.86656458]
AR coefficients: [-0.60439494 -0.857867  ]
AR coefficients: [-0.6048218  -0.85846157]
AR coefficients: [-0.60479146 -0.85841922]
>>> results.params
array([ 1.60850853, -0.66661205])
>>> results.tvalues
array([ 21.8047269 ,  -2.10304127])
>>> print results.t_test([0,1])
<T test: effect=array([-0.66661205]), sd=array([[ 0.31697526]]),
t=array([[-2.10304127]]), p=array([[ 0.06309969]]), df_denom=3>
>>> print(results.f_test(np.identity(2)))
<F test: F=array([[ 1815.23061844]]), p=[[ 0.00002372]], df_denom=3,
                                                         df_num=2>

Or, equivalently

>>> model2 = sm.GLSAR(Y, X, rho=2)
>>> res = model2.iterative_fit(maxiter=6)
>>> model2.rho
array([-0.60479146, -0.85841922])

Methods

fit([method]) Full fit of the model.
hessian(params) The Hessian matrix of the model
information(params) Fisher information matrix of model
initialize()
iterative_fit([maxiter]) Perform an iterative two-stage procedure to estimate a GLS model.
loglike(params) Returns the value of the gaussian loglikelihood function at params.
predict(params[, exog]) Return linear predicted values from a design matrix.
score(params) Score vector of model.
whiten(X) Whiten a series of columns according to an AR(p) covariance structure.

Attributes

endog_names
exog_names

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