Let's say we have two series and estimate a BEKK-MGARCH model.
Normally, researchers study the volatility spillover effect (from series 2 to series 1) by checking the coefficients A21.
However, I think the A21 shows four relationships
1) How the square of lagged second shock affects the first variance
2) How the cross product of lagged shocks affect the first variance
3) How the lagged second shock affects the covariance
4) How the cross product of lagged shocks affect the covariance
Because the A21 coefficient appear four times in the first variance equation and the covariance equation.
It seems to me that this A21 has multiple meanings.
Most articles just focus on the first relationship stated above.
I am not sure whether I miss something here. Please advise.