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
.- rho
int
The 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.
- **kwargs
Extra arguments that are used to set model properties when using the formula interface.
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 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)Whiten a series of columns according to an AR(p) covariance structure.
Properties
The model degree of freedom.
The residual degree of freedom.
Names of endogenous variables.
Names of exogenous variables.