Let rt be a k 1 vector of daily log stock returns. Assume that rt N(0,Ht), where Ht is the conditional variance-covariance matrix.

Let it be a k x 1 vector of daily log stock returns. Further assume that It ~ N(0, Ht), where H4 is the conditional variance-covariance matrix. (a) Write down the diagonal VGARCH model and the BEKK model in matrix notation, i.e., H = .... What are the main disadvantages of the diagonal VGARCH model compared to the BEKK model? (b) (C) Calculate the number of parameters in the BEKK model and in the full VGARCH model (both with one lag) as a function of the number of assets K. Discuss the "curse of dimensionality" for multivariate volatility mod- els. Do the BEKK and VGARCH models suffer from the curse of dimensionality? Explain your answer. (d) Discuss whether the DCC model suffers from the curse of dimensionality. (e) Write down the likelihood function for the DCC model and demonstrate how it can be decomposed such that the estimation of the model can be done in two steps. (f) | Briefly discuss other approaches to deal with the curse of dimensionality in the context of multivariate volatility models. Let it be a k x 1 vector of daily log stock returns. Further assume that It ~ N(0, Ht), where H4 is the conditional variance-covariance matrix. (a) Write down the diagonal VGARCH model and the BEKK model in matrix notation, i.e., H = .... What are the main disadvantages of the diagonal VGARCH model compared to the BEKK model? (b) (C) Calculate the number of parameters in the BEKK model and in the full VGARCH model (both with one lag) as a function of the number of assets K. Discuss the "curse of dimensionality" for multivariate volatility mod- els. Do the BEKK and VGARCH models suffer from the curse of dimensionality? Explain your answer. (d) Discuss whether the DCC model suffers from the curse of dimensionality. (e) Write down the likelihood function for the DCC model and demonstrate how it can be decomposed such that the estimation of the model can be done in two steps. (f) | Briefly discuss other approaches to deal with the curse of dimensionality in the context of multivariate volatility models