The role of Skorokhod space in the development of the econometric analysis of time series

This paper discusses the fundamental role played by Skorokhod space, through its underpinning of functional central limit theory, in the development of the paradigm of unit roots and co-integration. This paradigm has fundamentally affected the way economists approach economic time series as was recognized by the award of the Nobel Memorial Prize in Economic Sciences to Robert F. Engle and Clive W.J. Granger in 2003. Here, we focus on how P.C.B. Phillips and others used the Skorokhod topology to establish a limiting distribution theory that underpinned and facilitated the development of methods of estimation and testing of single equations and systems of equations with possibly integrated regressors. This approach has spawned a large body of work that can be traced back to Skorokhod's conception of fifty years ago. Much of this work is surprisingly confined to the econometrics literature.Skorokhod space, functional central limit theorems, non-stationary time series, unit roots and co-integration, Wiener functionals, econometrics.

Bayesian Learning and Predictability in a Stochastic Nonlinear Dynamical Model

Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple nonlinear marine biogeochemical model. A novel approach is proposed to the formulation of the stochastic process model, in which ecophysiological properties of plankton communities are represented by autoregressive stochastic processes. This approach captures the effects of changes in plankton communities over time, and it allows the incorporation of literature metadata on individual species into prior distributions for process model parameters. The approach is applied to a case study at Ocean Station Papa, using Particle Markov chain Monte Carlo computational techniques. The results suggest that, by drawing on objective prior information, it is possible to extract useful information about model state and a subset of parameters, and even to make useful long-term forecasts, based on sparse and noisy observations