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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 0s.

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

Introduced in R2012a

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