Founding body: EPSRC
Duration: January 1997 -- December 1998
Grant Holders: Howell Tong and Qiwei Yao
This grant was to support research in dynamical system approach to multi-input-output nonlinear stochastic systems for a period of 2 years. Dr Cees Diks was appointed as the RA for the whole grant period. Together with our collaborators, we have finished over thirty papers, twelve of which have already been published (or accepted for publication) in refereed journals. One book by Dr Diks has been published. Our results have been presented at international conferences/workshops on nine occasions since 1997.
The main research achievements are:
(a) We have developed a method for control nonlinear chaotic maps with a bounded stochastic signal. We have found a way of stabilising the fixed point of noisy logistic maps numerically and observed that the control gives rise to an intermittent type of behaviour. By identifying some common structure in a panel of short time series through a bootstrap test, we have used nonlinear multi-input-output statistical models to model biological population dynamics, paying particular attention to food-chain-interactions between predators and preys.
(b) We have proposed an adaptive varying-coefficient linear model to approximate any unknown smooth multivariate function. This class of models includes the threshold autoregressive models and the functional-coefficient autoregressive models as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better post-sample forecasting performance. By searching indices through a one-step-iteration type algorithm, we can fit high-dimensional data through one- or two-dimensional smoothers. The proposed methodology is data-analytic and is of such appreciable flexibility that we can analyse complex and multivariate nonlinear structures without suffering from the "curse of dimensionality".
(c) We have explored nonparametric techniques in many areas of nonlinear time series analysis, which include ratios of noise-to-signal, conditional variances, conditional distribution functions and conditional minimum volume predictors, testing for symmetry, conditional symmetry, serial independence, linearity and some simple structure in a general nonparametric regression setting.