If the subject knows what ARCH or GARCH model is, then MGARCH model is multivariable. BEKK's idea is to put all parameters into the model in quadratic form to ensure that all variances are positive. This is mainly used for fluctuation spillover effect. As the name implies, it is to see whether there is correlation between the variance of variance.

Related introduction:

The full name of ARCH (Autoregressive Conditional Heteroscedasticity Model) is "Autoregressive Conditional Heteroscedasticity Model", which solves the problems brought by the second hypothesis (variance unchanged) of time series variables in traditional econometrics. This model is one of the econometric achievements that won the Nobel Prize in Economics in 2003.

The second assumption of traditional econometrics on time series variables: it is unrealistic to assume that the fluctuation range (variance) of time series variables is fixed. For example, people have long found that the fluctuation range of stock returns changes with time, not constant. This makes the traditional time series analysis ineffective for practical problems.

In a paper published in Econometrics 1982, Robert Engel proposed an ARCH model to solve the problem of time series fluctuation. At that time, he studied the fluctuation of inflation rate in Britain.