# Documentation

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# print

Display parameter estimation results for conditional variance models

## Syntax

``print(Mdl,EstParamCov)``

## Description

example

````print(Mdl,EstParamCov)` displays parameter estimates, standard errors, and t statistics for the fitted conditional variance model `Mdl`, with estimated parameter variance-covariance matrix `EstParamCov`. `Mdl` can be a `garch`, `egarch`, or `gjr` model.```

## Examples

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

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

`modSim = garch('Constant',0.01,'GARCH',0.8,'ARCH',0.14)`
```modSim = GARCH(1,1) Conditional Variance Model: -------------------------------------- Distribution: Name = 'Gaussian' P: 1 Q: 1 Constant: 0.01 GARCH: {0.8} at Lags [1] ARCH: {0.14} at Lags [1] ```
```rng 'default'; [V,Y] = simulate(modSim,100);```

Fit a GARCH(1,1) model to the simulated data, turning off the print display.

```model = garch(1,1); [fit,VarCov] = estimate(model,Y,'print',false);```

Print the estimation results.

`print(fit,VarCov)`
``` GARCH(1,1) Conditional Variance Model: ---------------------------------------- Conditional Probability Distribution: Gaussian Standard t Parameter Value Error Statistic ----------- ----------- ------------ ----------- Constant 0.0167004 0.0165077 1.01167 GARCH{1} 0.77263 0.0776905 9.94498 ARCH{1} 0.191686 0.0750675 2.55351 ```

Print the results from estimating an EGARCH model using simulated data.

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

```modSim = egarch('Constant',0.01,'GARCH',0.8,'ARCH',0.14,... 'Leverage',-0.1); rng 'default'; [V,Y] = simulate(modSim,100);```

Fit an EGARCH(1,1) model to the simulated data, turning off the print display.

```model = egarch(1,1); [fit,VarCov] = estimate(model,Y,'print',false);```

Print the estimation results.

`print(fit,VarCov)`
``` EGARCH(1,1) Conditional Variance Model: -------------------------------------- Conditional Probability Distribution: Gaussian Standard t Parameter Value Error Statistic ----------- ----------- ------------ ----------- Constant 0.0654887 0.0746315 0.877494 GARCH{1} 0.85807 0.154361 5.55886 ARCH{1} 0.27702 0.171036 1.61966 Leverage{1} -0.179034 0.125057 -1.43162 ```

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

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

```modSim = gjr('Constant',0.01,'GARCH',0.8,'ARCH',0.14,... 'Leverage',0.1); rng 'default'; [V,Y] = simulate(modSim,100);```

Fit a GJR(1,1) model to the simulated data, turning off the print display.

```model = gjr(1,1); [fit,VarCov] = estimate(model,Y,'print',false);```

Print the estimation results.

`print(fit,VarCov)`
``` GJR(1,1) Conditional Variance Model: -------------------------------------- Conditional Probability Distribution: Gaussian Standard t Parameter Value Error Statistic ----------- ----------- ------------ ----------- Constant 0.194785 0.254199 0.766271 GARCH{1} 0.69954 0.11266 6.20928 ARCH{1} 0.192966 0.0931335 2.07192 Leverage{1} 0.214988 0.223923 0.960101 ```

## Input Arguments

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Conditional variance model without any unknown parameters, specified as a `garch`, `egarch`, or `gjr` model object.

`Mdl` is usually the estimated conditional variance model returned by `estimate`.

Estimated parameter variance-covariance matrix, returned as a numeric matrix.

`EstParamCov` is usually the estimated conditional variance model returned by `estimate`.

The rows and columns associated with any parameters contain the covariances. The standard errors of the parameter estimates are the square root of the entries along the main diagonal.

The rows and columns associated with any parameters held fixed as equality constraints during estimation contain `0`s.

The order of the parameters in `EstParamCov` must be:

• Constant

• Nonzero GARCH coefficients at positive lags

• Nonzero ARCH coefficients at positive lags

• For EGARCH and GJR models, nonzero leverage coefficients at positive lags

• Degrees of freedom (t innovation distribution only)

• Offset (models with nonzero offset only)

Data Types: `double`