University of Nottingham
Publication details: Nottingham University Statistics Research Report 98-13. 1998.
The problem of formulating covariance structures between two random variables or random vectors arises in many fields. One way to specify a covariance structure for a set of random variables defined at each point on a product space is by a Kronecker product form. Then the specification requires only a covariance structure on each of the component spaces. This note proves that a simple Markov-like assumption on the random variables implies that their covariance structure must, apart from an arbitrary scaling, follow a Kronecker product form. When a more restricted version of the Markov property is assumed, an autoregressive or Ornstein-Uhlenbeck form arises.
Keywords: Autoregressive models; Covariance structures; Kronecker product; Ornstein-Uhlenbeck process; Space-time modelling