# statsmodels.tsa.ar_model.ARResults¶

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

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. **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 Lütkepohl’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() 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

Attributes

 extra_doc preddoc use_t