regression.linear_model.GLSAR()

statsmodels.regression.linear_model.GLSAR

class statsmodels.regression.linear_model.GLSAR(endog, exog=None, rho=1, missing='none', **kwargs) [source]

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

Parameters:

endog : array-like 1-d endogenous response variable. The dependent variable. exog : array-like A nobs x k array where nobs is the number of observations and k is the number of regressors. An intercept is not included by default and should be added by the user. See statsmodels.tools.add_constant. rho : int Order of the autoregressive covariance missing : str Available options are ?none?, ?drop?, and ?raise?. If ?none?, no nan checking is done. If ?drop?, any observations with nans are dropped. If ?raise?, an error is raised. Default is ?none.? hasconst : None or bool Indicates whether the RHS includes a user-supplied constant. If True, a constant is not checked for and k_constant is set to 1 and all result statistics are calculated as if a constant is present. If False, a constant is not checked for and k_constant is set to 0.

Notes

GLSAR is considered to be experimental. The linear autoregressive process of order p?AR(p)?is defined as: TODO

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: {0}".format(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([-0.66661205,  1.60850853])
>>> results.tvalues
array([ -2.10304127,  21.8047269 ])
>>> print(results.t_test([1, 0]))
<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, cov_type, cov_kwds, use_t])	Full fit of the model.
fit_regularized([method, maxiter, alpha, ...])	Return a regularized fit to a linear regression model.
from_formula(formula, data[, subset])	Create a Model from a formula and dataframe.
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 log-likelihood 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

df_model	The model degree of freedom, defined as the rank of the regressor matrix minus 1 if a constant is included.
df_resid	The residual degree of freedom, defined as the number of observations minus the rank of the regressor matrix.
endog_names
exog_names