summarize

Display estimation results of conditional variance model

Syntax

summarize(Mdl)

results = summarize(Mdl)

Description

summarize(Mdl) displays a summary of the conditional variance model Mdl.

• If Mdl is an estimated model returned by estimate, then summarize prints estimation results to the MATLAB^® Command Window. The display includes an estimation summary and a table of parameter estimates with corresponding standard errors, t statistics, and p-values. The estimation summary includes fit statistics, such as the Akaike Information Criterion (AIC).

• If Mdl is an unestimated model returned by garch, egarch, or gjr, then summarize prints the standard object display (the same display printed during model creation).

results = summarize(Mdl) returns one of the following variables and does not print to the Command Window.

• If Mdl is an estimated model, then results is a structure containing estimation results.

• If Mdl is an unestimated model, then results is a garch, egarch, or gjr model object that is equal to Mdl.

Examples

Display Estimation Results

Print the results from estimating a GARCH model using simulated data.

Simulate data from a GARCH(1,1) model with known parameter values.

Mdl0 = garch('Constant',0.01,'GARCH',0.8,'ARCH',0.14);
rng 'default'; % For reproducibility
[V,Y] = simulate(Mdl0,100);

Fit a GARCH(1,1) model to the simulated data. Suppress the estimation display.

Mdl = garch(1,1);
EstMdl = estimate(Mdl,Y,'Display','off');

Display an estimation summary.

summarize(EstMdl)

 
   GARCH(1,1) Conditional Variance Model (Gaussian Distribution)
 
    Effective Sample Size: 100
    Number of Estimated Parameters: 3
    LogLikelihood: -96.5255
    AIC: 199.051
    BIC: 206.866
 
                 Value     StandardError    TStatistic      PValue  
                _______    _____________    __________    __________

    Constant     0.0167      0.016508         1.0117         0.31169
    GARCH{1}    0.77263       0.07769          9.945      2.6523e-23
    ARCH{1}     0.19169      0.075068         2.5535        0.010664

 

Extract Estimation Results from Estimated Model

Estimate several models by passing an EGARCH model template and data to estimate. Vary the number of ARCH and GARCH lags among the models. Extract the AIC from the estimation results, and choose the model that minimizes the fit statistic.

Simulate data from an EGARCH(0,1) model with known parameter values.

Mdl0 = egarch('Constant',0.01,'ARCH',0.75,'Leverage',-0.1);
rng(2); % For reproducibility
[~,Y] = simulate(Mdl0,100);

To determine the number of ARCH and GARCH lags, create and estimate multiple EGARCH models. Vary the number of GARCH and ARCH lags (p and q, respectively) among the models from 0 to 1 lag. Exclude the case where p = 1 and q = 0 because the presence of GARCH lags requires the presence of ARCH lags. Suppress all estimation displays. Extract the AIC from the estimation results structure. The field AIC stores the AIC.

pq = [0 0; 0 1; 1 1];
AIC = zeros(size(pq,1),1); % Preallocation

for j = 1:size(pq,1)
    Mdl = egarch(pq(j,1),pq(j,2));
    EstMdl = estimate(Mdl,Y,'Display','off');
    results = summarize(EstMdl);
    AIC(j) = results.AIC;
end

Compare the AIC values among the models.

[minAIC,bestidx] = min(AIC,[],1);
bestPQ = pq(bestidx,:)

bestPQ = 1×2

     0     1

The best fitting model is the EGARCH(0,1) model because its corresponding AIC is the lowest. This model also has the structure of the model used to simulate the data.

Input Arguments

Mdl — Conditional variance model

garch model object | egarch model object | gjr model object

Conditional variance model, specified as a garch, egarch, or gjr model object returned by estimate, garch, egarch, or gjr.

Output Arguments

results — Model summary

structure array | garch model object | egarch model object | gjr model object

Model summary, returned as a structure array or a garch, egarch, or gjr model object.

• If Mdl is an estimated model, then results is a structure array containing the fields in this table.

  Field	Description
  Description	Model summary description (string)
  SampleSize	Effective sample size (numeric scalar)
  NumEstimatedParameters	Number of estimated parameters (numeric scalar)
  LogLikelihood	Optimized loglikelihood value (numeric scalar)
  AIC	Akaike Information Criterion (numeric scalar)
  BIC	Bayesian Information Criterion (numeric scalar)
  Table	Maximum likelihood estimates of the model parameters with corresponding standard errors, t statistics (estimate divided by standard error), and p-values (assuming normality); a table with rows corresponding to model parameters

• If Mdl is an unestimated model, then results is a conditional variance model object that is equal to Mdl.

Version History

Introduced in R2012a