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 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()
cov_params()
fittedvalues()
forecast([steps, exog, alpha])	Out-of-sample forecasts
hqic()
llf()
mafreq()	Returns the frequency of the MA roots.
maparams()
maroots()
plot_predict([start, end, exog, dynamic, ...])	Plot forecasts
predict([start, end, exog, dynamic])	ARMA model in-sample and out-of-sample prediction
pvalues()
resid()
summary([alpha])	Summarize the Model
summary2([title, alpha, float_format])	Experimental summary function for ARIMA Results

Attributes

use_t