The topic of time-series prediction has been very well researched in studies of dynamic systems. However, most studies in the field have focused more on predicting movement of a single time-series only, whilst prediction of multiple time-series based on the dynamics of interactions between variables has received little attention. This PhD study is concerned with advances in the analysis, modelling and prediction of dynamic systems with respect to multiple time-series.

The main objective of this thesis is to develop novel adaptive methods to discover and model dynamic pattern of interactions in multiple time-series to not only predict their future values but also to extract knowledge about their joint movement. Being able to adaptively model dynamic pattern of interactions between multiple variables is expected to lead to a better understanding of the dynamic system under evaluation. Additionally, as new patterns of interaction emerge intermittently, the models to be developed are also required to have the ability to evolve and learn incrementally.

To realise these objectives three distinct methods of multiple time-series analysis are developed based on different concepts of learning (inductive and transductive reasoning) which are capable of modelling the dynamics of interaction between variables in a specific setting. As each approach addresses the problem of multiple time-series analysis and modelling from a different perspective and since each has its own predictive power, an integrated multi-model framework that incorporates the different approaches through a dynamic contribution adjustment function is also proposed.

In this study, the proposed methods have been applied for the analysis, modelling and prediction of two real world case studies: (1) multiple interactive stock markets in the Asia Pacific region and (2) weather conditions at different locations in New Zealand. Results from the two case studies suggest that (a) the proposed methods are capable of modelling dynamic pattern of interactions between variables and (b) that the idea of including the nature and strength of relationship between a collection of time sensitive variables (which are related to each other) into a prediction model appears to be beneficial to the problem of multiple time-series prediction.

The research is based on three main information processing principles proposed by Prof. Kasabov in the period of 1998-2011: (1) The principle of evolving, adaptive connectionist systems; (2) The principle of integrated global, local and personalised modelling; and (3) The principle of dynamic interaction network. Using these three principles 3 new computational methods are proposed and tested on both synthetic and real data for adaptive incremental learning and knowledge discovery from multiple time-series data. A software system was developed to implement the methods. Solutions to two specific case study problems are proposed and tested - financial time-series prediction; climate events prediction.