# statsmodels.tsa.arima_model.ARMAResults¶

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

Class to hold results from fitting an ARMA model.

Parameters
modelARMA instance

The fitted model instance

paramsndarray

Fitted parameters

normalized_cov_paramsndarray, optional

The normalized variance covariance matrix

scalefloat, optional

Optional argument to scale the variance covariance matrix.

Attributes
aicfloat

Akaike Information Criterion $$-2*llf+2* df_model$$ where df_model includes all AR parameters, MA parameters, constant terms parameters on constant terms and the variance.

arparamsndarray

The parameters associated with the AR coefficients in the model.

arrootsndarray

The roots of the AR coefficients 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.

bicfloat

Bayes Information Criterion -2*llf + log(nobs)*df_model Where if the model is fit using conditional sum of squares, the number of observations nobs does not include the p pre-sample observations.

bsendarray

The standard errors of the parameters. These are computed using the numerical Hessian.

df_modelndarray

The model degrees of freedom = k_exog + k_trend + k_ar + k_ma

df_residndarray

The residual degrees of freedom = nobs - df_model

fittedvaluesndarray

The predicted values of the model.

hqicfloat

Hannan-Quinn Information Criterion -2*llf + 2*(df_model)*log(log(nobs)) Like bic if the model is fit using conditional sum of squares then the k_ar pre-sample observations are not counted in nobs.

k_arint

The number of AR coefficients in the model.

k_exogint

The number of exogenous variables included in the model. Does not include the constant.

k_maint

The number of MA coefficients.

k_trendint

This is 0 for no constant or 1 if a constant is included.

llffloat

The value of the log-likelihood function evaluated at params.

maparamsndarray

The value of the moving average coefficients.

marootsndarray

The roots of the MA coefficients are the solution to (1 + maparams[0]*z + maparams[1]*z**2 + … + maparams[q-1]*z**q) = 0 Stability requires that the roots in modules lie outside the unit circle.

modelARMA instance

A reference to the model that was fit.

nobsfloat

The number of observations used to fit the model. If the model is fit using exact maximum likelihood this is equal to the total number of observations, n_totobs. If the model is fit using conditional maximum likelihood this is equal to n_totobs - k_ar.

n_totobsfloat

The total number of observations for endog. This includes all observations, even pre-sample values if the model is fit using css.

paramsndarray

The parameters of the model. The order of variables is the trend coefficients and the k_exog exogenous coefficients, then the k_ar AR coefficients, and finally the k_ma MA coefficients.

pvaluesndarray

The p-values associated with the t-values of the coefficients. Note that the coefficients are assumed to have a Student’s T distribution.

residndarray

The model residuals. If the model is fit using ‘mle’ then the residuals are created via the Kalman Filter. If the model is fit using ‘css’ then the residuals are obtained via scipy.signal.lfilter adjusted such that the first k_ma residuals are zero. These zero residuals are not returned.

scalefloat

This is currently set to 1.0 and not used by the model or its results.

sigma2float

The variance of the residuals. If the model is fit by ‘css’, sigma2 = ssr/nobs, where ssr is the sum of squared residuals. If the model is fit by ‘mle’, then sigma2 = 1/nobs * sum(v**2 / F) where v is the one-step forecast error and F is the forecast error variance. See nobs for the difference in definitions depending on the fit.

Methods

 conf_int([alpha, cols]) Construct confidence interval for the fitted parameters. cov_params([r_matrix, column, scale, cov_p, …]) Compute the variance/covariance matrix. f_test(r_matrix[, cov_p, scale, invcov]) Compute the F-test for a joint linear hypothesis. forecast([steps, exog, alpha]) Out-of-sample forecasts initialize(model, params, **kwargs) Initialize (possibly re-initialize) a Results instance. load(fname) Load a pickled results instance See specific model class docstring plot_predict([start, end, exog, dynamic, …]) Plot forecasts predict([start, end, exog, dynamic]) ARMA model in-sample and out-of-sample prediction Remove data arrays, all nobs arrays from result and model. save(fname[, remove_data]) Save a pickle of this instance. summary([alpha]) Summarize the Model summary2([title, alpha, float_format]) Experimental summary function for ARIMA Results 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. 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.

Properties

 aic arfreq Returns the frequency of the AR roots. arparams arroots bic bse cov_params_default fittedvalues hqic llf mafreq Returns the frequency of the MA roots. maparams maroots pvalues The two-tailed p values for the t-stats of the params. resid tvalues Return the t-statistic for a given parameter estimate. use_t Flag indicating to use the Student’s distribution in inference.