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

modelAR Model instance

Reference to the model that is fit.

paramsarray

The fitted parameters from the AR Model.

normalized_cov_paramsarray

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

scalefloat, optional

An estimate of the scale of the model.

Attributes

aicfloat

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

bicfloat

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

bsearray

The standard errors of the parameter estimates.

fittedvaluesarray

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.

fpefloat

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

hqicfloat

Hannan-Quinn Information Criterion.

k_arfloat

Lag length. Sometimes used as p in the docs.

k_trendfloat

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

llffloat

Log-likelihood of model

modelAR model instance

A reference to the fitted AR model.

nobsfloat

The number of available observations nobs - k_ar

n_totobsfloat

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

paramsarray

The fitted parameters of the model.

pvaluesarray

The two-tailed p values for the t-stats of the params.

residarray

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.

rootsarray

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.

scalefloat

Same as sigma2

sigma2float

The variance of the innovations (residuals).

trendorderint

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

tvaluesarray

Return the t-statistic for a given parameter estimate.

Methods

bse()	The standard errors of the parameter estimates.
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.
initialize(model, params, **kwd)	Initialize (possibly re-initialize) a Results instance.
llf()	Log-likelihood of model
load(fname)	load a pickle, (class method)
normalized_cov_params()	See specific model class docstring
predict([start, end, dynamic])	Returns in-sample and out-of-sample prediction.
pvalues()	The two-tailed p values for the t-stats of the params.
remove_data()	remove data arrays, all nobs arrays from result and model
save(fname[, remove_data])	save a pickle of this instance
summary()	Summary
t_test(r_matrix[, cov_p, scale, use_t])	Compute a t-test for a each linear hypothesis of the form Rb = q
t_test_pairwise(term_name[, method, alpha, …])	perform pairwise t_test with multiple testing corrected p-values
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.
wald_test_terms([skip_single, …])	Compute a sequence of Wald tests for terms over multiple columns

aic
bic
fittedvalues
fpe
hqic
resid
roots
scale
sigma2