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The theory of state-dependent models was developed by Priestley (1980), and a few simple applications were given in Priestley (1981). In this paper, an extensive study of the application of state-dependent models to a wide variety of non-linear time series data is carried out. Both real and simulated data are used in the study, and the problems encountered are highlighted. The method is demonstrated to be successful in practice in many cases, and suggestions for the further development of the algorithm are also given.

The estimation of subset autoregressive time series models has been a difficult problem because of the large number of possible alternative models involved. However, with the advent of model selection criteria based on the maximum likelihood, subset model fitting has become feasible. Using an efficient technique for evaluating the residual variance of all possible subset models, a method is proposed for the fitting of subset autoregressive models. The application of the method is illustrated by means of real and simulated data.

The transfer function mat.rj x of a large mult.i-m put.jrrmlt.i-out.put. linear st.ochnst.ic time-invariant control system may be computationally difficult to estimate und, further, may not provide a good interpretation of the underlying structure of the system. Priest.ley, Ran and Tong (\Ui3) have suggested a method, using information theoretic and statistical criteria, for reducing the dimensions of such a system, and thus. to some extent, overcoming these difficult.ics. The authors have undertaken a computational study of t.hc application of this t.hcory, illuminating the problems encountered, and demonstrating the feasibility of the method in practice.