statsmodels.tsa.ar_model.AutoRegResults

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

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.

use_tbool, optional

Whether use_t was set in fit

summary_textstr, optional

Additional text to append to results summary

Attributes:

aic

Akaike Information Criterion using Lutkepohl’s definition

\(-2 llf + \ln(nobs) (1 + df_{model})\)

aicc

Akaike Information Criterion with small sample correction

\(2.0 * df_{model} * nobs / (nobs - df_{model} - 1.0)\)

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

\(-2 llf + \ln(nobs) (1 + df_{model})\)

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.

centered_tss

The total (weighted) sum of squares centered about the mean

df_model

The degrees of freedom consumed by the model

df_resid

The remaining degrees of freedom in the residuals

ess

The explained sum of squares

If a constant is present, the centered total sum of squares minus the sum of squared residuals. If there is no constant, the uncentered total sum of squares is used.

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

\(((nobs+df_{model})/(nobs-df_{model})) \sigma^2\)

hqic

Hannan-Quinn Information Criterion using Lutkepohl’s definition

\(-2 llf + 2 \ln(\ln(nobs)) (1 + df_{model})\)

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.

rsquared

R-squared of the model

This is defined here as 1 - ssr/centered_tss if the constant is included in the model and 1 - ssr/uncentered_tss if the constant is omitted.

ssr

Sum of squared (whitened) residuals

tvalues

Return the t-statistic for a given parameter estimate

uncentered_tss

Uncentered sum of squares

The sum of the squared values of the (whitened) endogenous response variable.

use_t

Flag indicating to use the Student’s distribution in inference

Methods

append(endog[, exog, refit, fit_kwargs])	Append observations to the ones used to fit the model
apply(endog[, exog, refit, fit_kwargs])	Apply the fitted parameters to new data unrelated to the original data
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, 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, use_t])	Compute a t-test for 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, invcov, use_f, ...])	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

append(endog[, exog, refit, fit_kwargs])	Append observations to the ones used to fit the model
apply(endog[, exog, refit, fit_kwargs])	Apply the fitted parameters to new data unrelated to the original data
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, 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, use_t])	Compute a t-test for 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, invcov, use_f, ...])	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
aicc	Akaike Information Criterion with small sample correction
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
centered_tss	The total (weighted) sum of squares centered about the mean
df_model	The degrees of freedom consumed by the model
df_resid	The remaining degrees of freedom in the residuals
ess	The explained sum of squares
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
rsquared	R-squared of the model
ssr	Sum of squared (whitened) residuals
tvalues	Return the t-statistic for a given parameter estimate
uncentered_tss	Uncentered sum of squares
use_t	Flag indicating to use the Student's distribution in inference