RATS 10.1
RATS 10.1

The Restricted Covariance Models all use GARCH models for the individual variances, but generate the covariances in a more restricted fashion. This allows them to be applied to larger sets of variables. Note, however, that the restrictions they impose generally only work with variables that are closely related: such as a set of exchange rates, or a set of stock returns.

 

There are several choices for modeling the variances, which are discussed in "VARIANCES option". The detailed descriptions of most of these are in separate topics, linked in the short descriptions below.

MV=DIAG

The simplest of the restricted models is MV=DIAG. This estimates separate univariate GARCH models on each dependent variable. The “model” for the covariances between variables is that they are all zero. This allows you to do “two-step” procedures, which model the correlations based upon the standardized residuals from the univariate models. Using GARCH to handle all the variables simultaneously (rather than doing separate univariate GARCH instructions) ensures that they are estimated over a common range. Other than that, it has relatively little use, since there is typically quite a bit of contemporaneous correlation among the residuals, which this ignores.

MV=CC (Constant Correlation)

 

The next step up in complexity is the Constant Correlation specification, which you can estimate with the option MV=CC. This assumes that the conditional correlations are fixed across time.

MV=DCC (Dynamic Conditional Correlation)

 

The DCC (Dynamic Conditional Correlation) model was proposed by Engle(2002) to allow for conditional correlations which can evolve over time. (CC is generally far too restrictive). Engle's original proposal was for a "two-step" process, where individual GARCH models are fit to the variables and their standardized residuals are used to make a separate estimate of the parameters governing DCC. However, RATS estimates the unified model, which is more efficient statistically, plus it allows for a wider range of variance recursions.

MV=ADCC

is a variant of DCC which allows for asymmetric effects in the DCC model.

 

MV=CHOLESKY

The Cholesky model is a rarely used model which adopts some ideas from the structural VAR literature. Note that the model is sensitive to the ordering of the variables, unlike any models above.

 

 


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