Instability of Correlations: Multivariate GARCH

Question 1

3 issues in multivariate modelling of CH covariances

Answer 1

1) need very long time series as many parameters
2) difficult to guarantee that Var(R_t+1) is pd matrix
3) Many Ch models over-parameterized and low saturation ratio.

E.g.: GARCH not good for stock-bond covariances (pd matrix issue)

Question 2

VECH GARCH. Concept and appropriate restrictions

Answer 2

vector half converts uniqie upper triangular elements of symmetric matrix into column vector that removes duplicates.

Possible restriction: diagonal (prevents detection of any causality in variance, i.e. past shocks to some variable forecasr variances of others=

Question 3

BEKK GARCH

Answer 3

variables are sandwiched by coefficients. -> sigma guaranteed to be pd.
3 attractive properties: 1) decomposition 2) pd-ness ensured 3) invariant to linear compination (if some returns follow BEKK, then a ptf of these returns follow BEKK)

Question 4

DCC/CCC

Answer 4

are estimated by QMLE