  Study of instantaneous dependence among several variable is important in many
of the high-dimensional sciences. Multivariate GARCH models are as a standard
approach for modelling time-varying covariance matrix such phenomena. Cholesky
GARCH is one of these approaches where the time-varying covariance matrix can
be written parsimoniously, containing variance components through a diagonal
matrix and dependency components through a unit lower triangular matrix with
regression coefficients as entries. In this paper, we proposed a stochastic
structure for dependency components in Cholesky GARCH model by considering
linear regression model as a state-space model and using kalman filtering for
estimating regression coefficients. We find that the MSE of stochastic Cholesky
GARCH model is smaller than the MSE of other models also show that the
stochastic Cholesky GARCH has better performance in compare to another models
based on MAE and MSE criterions for the real data.
