statsmodels.tsa.ar_model.ARResults

class statsmodels.tsa.ar_model.ARResults(model, params, normalized_cov_params=None, scale=1.0)

Class to hold results from fitting an AR model.

Parameters:

model : AR Model instance

Reference to the model that is fit.

params : array

The fitted parameters from the AR Model.

normalized_cov_params : array

inv(dot(X.T,X)) where X is the lagged values.

scale : float, optional

An estimate of the scale of the model.

Returns:

**Attributes** :

aic : float

Akaike Information Criterion using Lutkephol’s definition. log(sigma) + 2*(1 + k_ar + k_trend)/nobs

bic : float

Bayes Information Criterion \log(\sigma) + (1 + k_ar + k_trend)*\log(nobs)/nobs

bse : array

The standard errors of the estimated parameters. If method is ‘cmle’, then the standard errors that are returned are the OLS standard errors of the coefficients. If the method is ‘mle’ then they are computed using the numerical Hessian.

fittedvalues : array

The in-sample predicted values of the fitted AR model. The k_ar initial values are computed via the Kalman Filter if the model is fit by mle.

fpe : float

Final prediction error using Lutkepohl’s definition ((n_totobs+k_trend)/(n_totobs-k_ar-k_trend))*sigma

hqic : float

Hannan-Quinn Information Criterion.

k_ar : float

Lag length. Sometimes used as p in the docs.

k_trend : float

The number of trend terms included. ‘nc’=0, ‘c’=1.

llf : float

The loglikelihood of the model evaluated at params. See AR.loglike

model : AR model instance

A reference to the fitted AR model.

nobs : float

The number of available observations nobs - k_ar

n_totobs : float

The number of total observations in endog. Sometimes n in the docs.

params : array

The fitted parameters of the model.

pvalues : array

The p values associated with the standard errors.

resid : array

The residuals of the model. If the model is fit by ‘mle’ then the pre-sample residuals are calculated using fittedvalues from the Kalman Filter.

roots : array

The roots of the AR process are the solution to (1 - arparams[0]*z - arparams[1]*z**2 -...- arparams[p-1]*z**k_ar) = 0 Stability requires that the roots in modulus lie outside the unit circle.

scale : float

Same as sigma2

sigma2 : float

The variance of the innovations (residuals).

trendorder : int

The polynomial order of the trend. ‘nc’ = None, ‘c’ or ‘t’ = 0, ‘ct’ = 1, etc.

tvalues : array

The t-values associated with params.

Methods

aic()
bic()
bse()
conf_int([alpha, cols, method])	Returns the confidence interval of the fitted parameters.
cov_params([r_matrix, column, scale, cov_p, ...])	Returns the variance/covariance matrix.
f_test(r_matrix[, cov_p, scale, invcov])	Compute the F-test for a joint linear hypothesis.
fittedvalues()
fpe()
hqic()
initialize(model, params, **kwd)
llf()
load(fname)	load a pickle, (class method)
normalized_cov_params()
predict([start, end, dynamic])	Returns in-sample and out-of-sample prediction.
pvalues()
remove_data()	remove data arrays, all nobs arrays from result and model
resid()
roots()
save(fname[, remove_data])	save a pickle of this instance
scale()
sigma2()
t_test(r_matrix[, cov_p, scale, use_t])	Compute a t-test for a each linear hypothesis of the form Rb = q
tvalues()	Return the t-statistic for a given parameter estimate.
wald_test(r_matrix[, cov_p, scale, invcov, ...])	Compute a Wald-test for a joint linear hypothesis.

Attributes

extra_doc
preddoc
use_t