Structure Selection of Stochastic Dynamic Systems

Part 1 Preliminaries: a brief history of information criteria; discrete-time multivariable linear models; introduction to predictive modelling. Part 2 Asymptotic theory for discrete-time models: Bayesian framework for information criteria; modelling by the principle of the shortest data description; stochastic complexity and its relation to the Bayesian estimation; strong consistency of the complexity criterion for ARMA processes; structurally recursive two-stage methods based on covariance estimates. Part 3 Model structure validation: short review of methods; invariance principle of likelihood ratios for ARMA methods; lagrange multiplier test for predictive models. Part 4 Simulational comparison of methods: relations of some methods for parameter estimation; structure selection for heavy-tailed infinite order AR processes; structure selection of finite order AR processes; structure selection of MA and ARMA processes; spectrum and transfer function estimation for ARMAX processes; comparison of the likelihood ratio and lagrange multiplier tests. Part 5 Continuous time linear models: diffusional canonical representation of Gaussian processes; radon nikodym derivatives for multivariable processes; on the loss of information when sampling continuous time processes; structural change between continuous time and sampled models. Appendices: some results on Martingale convergence; some simple Pascal routines; demonstration programmes.