1.2.4. statsmodels.api.GLSAR¶

class statsmodels.api.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])

__init__(endog, exog=None, rho=1, missing='none', **kwargs)[source]¶