statsmodels.regression.linear_model.GLSAR#

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

Generalized Least Squares with AR covariance structure

Parameters:

endogarray_like

A 1-d endogenous response variable. The dependent variable.

exogarray_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.

rhoint or array_like

If an integer is provided, it specifies the order of the autoregressive process. The AR coefficients are initialized to zero and estimated during iterative fitting.

If an array is provided, it specifies initial values for the autoregressive coefficients. The length of the array determines the AR order.

missingstr

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’.

hasconstNone 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.

**kwargs

Extra arguments that are used to set model properties when using the formula interface.

Attributes:

df_model: The model degree of freedom.
df_resid: The residual degree of freedom.
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.
`fit_regularized`([method, alpha, L1_wt, ...])	Return a regularized fit to a linear regression model
`from_formula`(formula, data[, subset, drop_cols])	Create a Model from a formula and dataframe
`get_distribution`(params, scale[, exog, ...])	Construct a random number generator for the predictive distribution.
`hessian`(params)	The Hessian matrix of the model
`hessian_factor`(params[, scale, observed])	Compute weights for calculating Hessian.
`information`(params)	Fisher information matrix of model
`initialize`()	Initialize model components
`iterative_fit`([maxiter, rtol])	Perform an iterative two-stage procedure to estimate a GLS model.
`loglike`(params)	Compute 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)	For an AR(p) process, the errors are modeled as

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, alpha, L1_wt, ...])	Return a regularized fit to a linear regression model
`from_formula`(formula, data[, subset, drop_cols])	Create a Model from a formula and dataframe
`get_distribution`(params, scale[, exog, ...])	Construct a random number generator for the predictive distribution.
`hessian`(params)	The Hessian matrix of the model
`hessian_factor`(params[, scale, observed])	Compute weights for calculating Hessian.
`information`(params)	Fisher information matrix of model
`initialize`()	Initialize model components
`iterative_fit`([maxiter, rtol])	Perform an iterative two-stage procedure to estimate a GLS model.
`loglike`(params)	Compute 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)	For an AR(p) process, the errors are modeled as

Properties

`df_model`	The model degree of freedom.
`df_resid`	The residual degree of freedom.
`endog_names`	Names of endogenous variables
`exog_names`	Names of exogenous variables