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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: [-0.620642   -0.88654567]
AR coefficients: [-0.61887622 -0.88137957]
AR coefficients: [-0.61894058 -0.88152761]
AR coefficients: [-0.61893842 -0.88152263]
>>> results.params
array([ 1.58747943, -0.56145497])
>>> results.tvalues
array([ 30.796394  ,  -2.66543144])
>>> print results.t_test([0,1])
<T test: effect=-0.56145497223945595, sd=0.21064318655324663, t=-2.6654314408481032, p=0.022296117189135045, df_denom=5>
>>> import numpy as np
>>> print(results.f_test(np.identity(2)))
<F test: F=2762.4281271616205, p=2.4583312696e-08, df_denom=5, df_num=2>

Or, equivalently

>>> model2 = sm.GLSAR(Y, X, rho=2)
>>> res = model2.iterative_fit(maxiter=6)
>>> model2.rho
array([-0.61893842, -0.88152263])

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)

Attributes

endog_names
exog_names

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