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)
>>> 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])
```

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` Names of endogenous variables `exog_names` Names of exogenous variables

Methods

 `fit`([method, cov_type, cov_kwds, use_t]) Full fit of the model. `from_formula`(formula, data[, subset, drop_cols]) Create a Model from a formula and dataframe. `get_distribution`(params, scale[, exog, ...]) Returns a random number generator for the predictive distribution. `hessian`(params) The Hessian matrix of the model `information`(params) Fisher information matrix of model `initialize`() `iterative_fit`([maxiter, rtol]) 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.

Methods

 `fit`([method, cov_type, cov_kwds, use_t]) Full fit of the model. `from_formula`(formula, data[, subset, drop_cols]) Create a Model from a formula and dataframe. `get_distribution`(params, scale[, exog, ...]) Returns a random number generator for the predictive distribution. `hessian`(params) The Hessian matrix of the model `information`(params) Fisher information matrix of model `initialize`() `iterative_fit`([maxiter, rtol]) 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` Names of endogenous variables `exog_names` Names of exogenous variables