Documentation

# summarize

Display estimation results of conditional variance model

## Syntax

``summarize(Mdl)``
``results = summarize(Mdl)``

## Description

example

````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). ```

example

````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

collapse all

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

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

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

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

```ToEstMdl = garch(1,1); EstMdl = estimate(ToEstMdl,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 2.6522e-23 ARCH{1} 0.19169 0.075068 2.5535 0.010664 ```

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.

```Mdl = egarch('Constant',0.01,'ARCH',0.75,'Leverage',-0.1); rng(2); % For reproducibility [~,Y] = simulate(Mdl,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) ToEstMdl = egarch(pq(j,1),pq(j,2)); EstMdl = estimate(ToEstMdl,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

collapse all

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

## Output Arguments

collapse all

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.

FieldDescription
`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`.