Bayesian forecasts in markets with overlapping structures

This paper defines a new class of multivariate state space models which combine the power steady model of Smith (Smith, J.Q., 1981, The multiparameter steady model, Journal of the Royal Statistical Society, Series B, 43, 255-260; 1990, Non-linear state-space models with partially specified distributions on states, Journal of Forecasting, 9, 137-149; 1992, A comparison of the characteristics of some Bayesian forecasting models, International Statistical Review, 60(1), 75-87) with models of Queen (Queen, C.M., 1991, Bayesian Graphical Forecasting Models for Business Time Series (Ph.D. Thesis, University of Warwick)) and Smith and Queen (Smith, J.Q. and C.M. Queen, 1993, Bayesian models for conditional probabilities in a bivariate mass function with many zeros (Warwick University Statistics Department Research Report No 252. Copies obtainable from the Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK)) and can be used to forecast time series of shares in markets which have overlapping structures. Although these models as yet cannot accommodate all possible overlapping structures, they do provide an initial attempt to integrate market information directly into the forecasting process. It is shown how the market structure can be represented by a graph, which not only provides a useful pictorial representation of the structure, but can also play an important part in defining the new model.