Explain the curse of dimensionality.

Explain the concept of positive-definiteness and why it is important in multivariate volatility forecasting.

Suppose you have two stocks, \(A\) and \(B\). Write down the EWMA model for forecasting the covariance matrix for the two stocks.

What is the main empirical issue that arises with the EWMA model in the last question above and beyond what would arise in a univariate model?

What are the two main downsides of the EWMA model?

Consider an univariate GARCH model. Suppose you extend this model to forecasting the covariance matrix of both stocks. That means you need to forecast the two variances and the covariance. Furthermore, you believe that the equations for each of these two variances and covariance include the lagged variances, squared returns and covariance. How many parameters would such a model have and what is the main difficulty in estimating the model?

For most applications in covariance forecasting the DCC model represents the best compromise for the various considerations one needs to take in account.

Write down the DCC model.

Outline how you would estimate the DCC model.

Why is the DCC model usually preferred over the alternatives?

Explain how does the PCA approach allow us to create the covariance matrix in the OGARCH model?

Briefly explain the process of orthogonalizing covariance in the orthogonal GARCH model

What are the main advantages of orthogonal GARCH model?

Consider CCC model:

Briefly explain the CCC approach

What are the main advantages and disadvantages of the CCC model?

Consider the BEKK model:

Briefly explain the BEKK model.

What are the useful features of the BEKK model? What is the drawback of the BEKK model?