8.2 Vector Autoregressive Models
A simple vector model useful in modeling asset returns is the vector autoregressive (VAR) model. A multivariate time series is a VAR process of order 1, or VAR(1) for short, if it follows the model
where is a k-dimensional vector, is a k × k matrix, and is a sequence of serially uncorrelated random vectors with mean zero and covariance matrix . In application, the covariance matrix is required to be positive definite; otherwise, the dimension of can be reduced. In the literature, it is often assumed that is multivariate normal.
Consider the bivariate ...