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
- 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
ndarray The parameters associated with the AR coefficients in the model.
- arroots
ndarray 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
ndarray The standard errors of the parameters. These are computed using the numerical Hessian.
- df_model
ndarray The model degrees of freedom = k_exog + k_trend + k_ar + k_ma
- df_resid
ndarray The residual degrees of freedom = nobs - df_model
- fittedvalues
ndarray 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
ndarray The value of the moving average coefficients.
- maroots
ndarray 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
ARMAinstance 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
ndarray 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.
- pvalues
ndarray 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
ndarray 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.
- aic
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.
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
Returns the frequency of the AR roots.
Returns the frequency of the MA roots.
The two-tailed p values for the t-stats of the params.
Return the t-statistic for a given parameter estimate.
Flag indicating to use the Student’s distribution in inference.