University of Sheffield

Tony O'Hagan - Academic pages - Abstracts


A Markov property for covariance structures

A. O'Hagan

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

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Updated: 8 March 2000
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