# 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

paramsarray

Fitted parameters

normalized_cov_paramsarray, 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.

arparamsarray

The parameters associated with the AR coefficients in the model.

arrootsarray

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.

bsearray

The standard errors of the parameter estimates.

df_modelarray

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

df_residarray

The residual degrees of freedom = nobs - df_model

fittedvaluesarray

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

Log-likelihood of model

maparamsarray

The value of the moving average coefficients.

marootsarray

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.

paramsarray

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

pvaluesarray

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

residarray

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

 Returns the frequency of the AR roots. The standard errors of the parameter estimates. conf_int([alpha, cols, method]) Returns the confidence interval of the fitted parameters. Returns 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, **kwd) Initialize (possibly re-initialize) a Results instance. Log-likelihood of model load(fname) load a pickle, (class method) Returns the frequency of the MA roots. 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 The two-tailed p values for the t-stats of the params. 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 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 arparams arroots bic fittedvalues hqic maparams maroots resid