statsmodels.tsa.ar_model.AutoRegResults

class statsmodels.tsa.ar_model.AutoRegResults(model, params, cov_params, normalized_cov_params=None, scale=1.0)

Class to hold results from fitting an AutoReg model.

Parameters

modelAutoReg

Reference to the model that is fit.

paramsndarray

The fitted parameters from the AR Model.

cov_paramsndarray

The estimated covariance matrix of the model parameters.

normalized_cov_paramsndarray

The array inv(dot(x.T,x)) where x contains the regressors in the model.

scalefloat, optional

An estimate of the scale of the model.

Attributes

aic

Akaike Information Criterion using Lutkepohl’s definition.

\(log(sigma) + 2*(1 + df_model) / nobs\)

ar_lags

The autoregressive lags included in the model

arfreq

Returns the frequency of the AR roots.

This is the solution, x, to z = abs(z)*exp(2j*np.pi*x) where z are the roots.

bic

Bayes Information Criterion

\(\ln(\sigma) + (1 + df_{model}) \ln(nobs)/nobs\)

bse

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.

df_model

The degrees of freedom consumed by the model.

df_resid

The remaining degrees of freedom in the residuals.

fittedvalues

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

Final prediction error using Lütkepohl’s definition.

((n_totobs+k_trend)/(n_totobs-k_ar-k_trend))*sigma

hqic

Hannan-Quinn Information Criterion using Lutkepohl’s definition.

\(\ln(\sigma) + (1 + df_{model}) 2 \ln(\ln(nobs))/nobs\)

llf

Log-likelihood of model

nobs

The number of observations after adjusting for losses due to lags.

params

The estimated parameters.

pvalues

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

resid

The residuals of the model.

roots

The roots of the AR process.

The roots 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.

tvalues

Return the t-statistic for a given parameter estimate.

use_t

Flag indicating to use the Student’s distribution in inference.

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.
diagnostic_summary()	Returns a summary containing standard model diagnostic tests
f_test(r_matrix[, cov_p, scale, invcov])	Compute the F-test for a joint linear hypothesis.
forecast([steps, exog])	Out-of-sample forecasts
get_prediction([start, end, dynamic, exog, …])	Predictions and prediction intervals
initialize(model, params, **kwargs)	Initialize (possibly re-initialize) a Results instance.
load(fname)	Load a pickled results instance
normalized_cov_params()	See specific model class docstring
plot_diagnostics([lags, fig, figsize])	Diagnostic plots for standardized residuals
plot_predict([start, end, dynamic, exog, …])	Plot in- and out-of-sample predictions
predict([start, end, dynamic, exog, exog_oos])	In-sample prediction and out-of-sample forecasting.
remove_data()	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
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.
test_heteroskedasticity([lags])	ARCH-LM test of residual heteroskedasticity
test_normality()	Test for normality of standardized residuals.
test_serial_correlation([lags, model_df])	Ljung-Box test for residual serial correlation
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.

scale
sigma2

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.
diagnostic_summary()	Returns a summary containing standard model diagnostic tests
f_test(r_matrix[, cov_p, scale, invcov])	Compute the F-test for a joint linear hypothesis.
forecast([steps, exog])	Out-of-sample forecasts
get_prediction([start, end, dynamic, exog, …])	Predictions and prediction intervals
initialize(model, params, **kwargs)	Initialize (possibly re-initialize) a Results instance.
load(fname)	Load a pickled results instance
normalized_cov_params()	See specific model class docstring
plot_diagnostics([lags, fig, figsize])	Diagnostic plots for standardized residuals
plot_predict([start, end, dynamic, exog, …])	Plot in- and out-of-sample predictions
predict([start, end, dynamic, exog, exog_oos])	In-sample prediction and out-of-sample forecasting.
remove_data()	Remove data arrays, all nobs arrays from result and model.
save(fname[, remove_data])	Save a pickle of this instance.
scale()
sigma2()
summary([alpha])	Summarize the Model
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.
test_heteroskedasticity([lags])	ARCH-LM test of residual heteroskedasticity
test_normality()	Test for normality of standardized residuals.
test_serial_correlation([lags, model_df])	Ljung-Box test for residual serial correlation
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	Akaike Information Criterion using Lutkepohl’s definition.
ar_lags	The autoregressive lags included in the model
arfreq	Returns the frequency of the AR roots.
bic	Bayes Information Criterion
bse	The standard errors of the estimated parameters.
df_model	The degrees of freedom consumed by the model.
df_resid	The remaining degrees of freedom in the residuals.
fittedvalues	The in-sample predicted values of the fitted AR model.
fpe	Final prediction error using Lütkepohl’s definition.
hqic	Hannan-Quinn Information Criterion using Lutkepohl’s definition.
llf	Log-likelihood of model
nobs	The number of observations after adjusting for losses due to lags.
params	The estimated parameters.
pvalues	The two-tailed p values for the t-stats of the params.
resid	The residuals of the model.
roots	The roots of the AR process.
tvalues	Return the t-statistic for a given parameter estimate.
use_t	Flag indicating to use the Student’s distribution in inference.