statsmodels.tsa.arima_model.ARMAResults

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

Class to hold results from fitting an ARMA model.

Parameters:

• model (ARMA instance) – The fitted model instance
• params (array) – Fitted parameters
• normalized_cov_params (array, optional) – The normalized variance covariance matrix
• scale (float, optional) – Optional argument to scale the variance covariance matrix.

Returns:

• **Attributes**
• aic (float) – 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.
• arparams (array) – The parameters associated with the AR coefficients in the model.
• arroots (array) – 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.
• bic (float) – 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.
• bse (array) – The standard errors of the parameters. These are computed using the numerical Hessian.
• df_model (array) – The model degrees of freedom = k_exog + k_trend + k_ar + k_ma
• df_resid (array) – The residual degrees of freedom = nobs - df_model
• fittedvalues (array) – The predicted values of the model.
• hqic (float) – 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_ar (int) – The number of AR coefficients in the model.
• k_exog (int) – The number of exogenous variables included in the model. Does not include the constant.
• k_ma (int) – The number of MA coefficients.
• k_trend (int) – This is 0 for no constant or 1 if a constant is included.
• llf (float) – The value of the log-likelihood function evaluated at params.
• maparams (array) – The value of the moving average coefficients.
• maroots (array) – 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.
• model (ARMA instance) – A reference to the model that was fit.
• nobs (float) – 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_totobs (float) – The total number of observations for endog. This includes all observations, even pre-sample values if the model is fit using css.
• params (array) – 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.
• pvalues (array) – The p-values associated with the t-values of the coefficients. Note that the coefficients are assumed to have a Student’s T distribution.
• resid (array) – 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.
• scale (float) – This is currently set to 1.0 and not used by the model or its results.
• sigma2 (float) – 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

aic()
arfreq()	Returns the frequency of the AR roots.
arparams()
arroots()
bic()
bse()
conf_int([alpha, cols, method])	Returns the confidence interval of the fitted parameters.
cov_params()	Returns the variance/covariance matrix.
f_test(r_matrix[, cov_p, scale, invcov])	Compute the F-test for a joint linear hypothesis.
fittedvalues()
forecast([steps, exog, alpha])	Out-of-sample forecasts
hqic()
initialize(model, params, **kwd)
llf()
load(fname)	load a pickle, (class method)
mafreq()	Returns the frequency of the MA roots.
maparams()
maroots()
normalized_cov_params()
plot_predict([start, end, exog, dynamic, …])	Plot forecasts
predict([start, end, exog, dynamic])	ARMA model in-sample and out-of-sample prediction
pvalues()
remove_data()	remove data arrays, all nobs arrays from result and model
resid()
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
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

use_t