The ARCH/GARCH(Multivariate) operation on the Statistics menu estimates multivariate ARCH and GARCH models. The Wizard will generate the appropriate GARCH instruction based on the information you enter. Note that the GARCH command offers several additional options not available using the Wizard, such as an option to input the mean model using the MODEL option.

Selecting the Wizard brings up the following dialog box:

Header Items

Dependent Variable(s)

Use this field to enter or select the dependent variable(s) for your model. You can either type in a list of variables, separating them with at least one blank space, or click on the series list button to select from a list of the series available in memory with a Select Variables dialog box.

Sample Start and End

Use these fields to set a specific starting and/or ending date for the estimation.

GARCH Model Tab

Lagged U^2 (q)

Lagged Variance (p) Terms

Use these fields to specify the order of the ARCH(q) or GARCH(p,q) model, by entering the number of lags of the squared residuals (Q) and variances (P).

I-GARCH

For certain models, you can use this field to select an I-GARCH. Your choices are No, With Drift and Without Drift.

Model Type

This chooses the overall multivariate model type: choose from Simple(Diagonal VECH), BEKK, CC (Constant Correlation), DCC (Dynamic Conditional), Asymmetric DCC, Triangular BEKK, Diagonal BEKK, Cholesky, Full VECH, Diagonal and EWMA (Exponential Weighted Moving Average).

Univariate Models

If the Model Type is CC, DCC, Asymmetric DCC, Cholesky or Diagonal, RATS will display the Univariate Models field, which you use to select the form of the individual univariate models in the system. This generates a VARIANCES option on the GARCH instruction. You can choose from Simple, VARMA, Exponential, Spillover and Koutmos.

Asymmetric Effects

Select this checkbox to include asymmetric effects.

Distribution

Choose the conditional distribution for the residuals. The choices are Normal, Student t, and GED. If you choose Student t or GED, the Shape Box is added to the dialog

Mean Model Tab

Mean Model Variables(s)

Use this field to choose the variables in the "mean model" for the equations. The same variables are included in eachâ€”you need to use the MODEL option on GARCH to get mean equations with different explanatory variables. By default, this is just the CONSTANT. If you want to estimate a model with a forced zero mean, just erase the content of the text box. For a different set, you can either type in a list of explanatory variables in Regression Format, separating variables with at least one blank space, or click on the series list button to select from a list of the series available in memory with a Select Regressors dialog box.

Variance Shifts Tab

Variance Shift Variable(s)

Use this field to add exogenous variables to the variance equation(s). You can either type in a list of explanatory variables in Regression Format, separating variables with at least one blank space, or click on the series list button to select from a list of the series available in memory with a Select Regressors dialog box.

Estimation Tab

Estimation Method,Iterations

(Preliminary) Estimation Methods,Iterations

Use the Estimation Method fields to select the main estimation method that will be used and the maximum number of iterations that will be performed (200 is the default for GARCH). Use the corresponding (Preliminary) Estimation Method fields if you want RATS to use a different estimation method for a specified number of iterations to refine the initial parameter values, before switching to the main estimation routine. A common choice would be to use 5 or 10 iterations of Simplex as a preliminary estimation method.

Robust (HAC) Standard Errors

Lags/Bandwidth

Lag Window Type

These correspond to the ROBUSTERRORS, LAGS, and LWINDOW options. See Robust Error Calculations for details.

Output Tab

Residuals to

Variances to

These respectively generate the RVECTORS option, which saves a SERIES[VECTOR] with the residuals and HMATRICES option, which saves a SERIES[SYMMETRIC] with the covariances. You have to type a variable name into a field in order to save the corresponding information.

Standard Residuals To/Standardization Method

This generates the STDRESIDS option, which saves a VECT[SERIES] with the jointly standardized residualsâ€”residuals which should be jointly serially uncorrelated in the first and second moments if the model is correct. There are many ways to achieve such a standardization; the Standardization Method popup menu chooses between a Cholesky factorization and an eigen decomposition.

Show Standard Output

Clear this checkbox if you want to suppress the output from the regression (this adds a NOPRINT option to the estimation instruction).

Show VCV of Coefficients

Select this to display the estimated variance/covariance matrix of the coefficients (adds a VCV option).