Causality analysis advancements and applications by subspace-based techniques.

Abstract

Causality analysis remains a fundamental research question and the ultimate objective for many scientific studies. Alongside the increasing speed of data science and technological advancements, as well as the overwhelming existence of complex systems in social science and economics studies, causality analysis has become more complex than ever. The drawbacks of the existing empirical methods (parametric and limited nonparametric approaches) are gradually revealed through implementations. There are increasing number of proofs that the existing methods are limited and fail to catch up the rapid progress of the causality analysis study. Therefore, it is both crucial and time-sensitive to establish the advancements of causality analysis methods by embracing the advanced time series analysis techniques. Subspace-based techniques adopted in this thesis include Singular Value Decomposition (SVD), Singular Spectrum Analysis (SSA) and Convergent CrossMapping (CCM). These subspace-based techniques have been proved powerful nonparametric time series analysis techniques with promising performances on various fields, for instance, time series denoising, filtering, forecasting, signal extraction, image processing, etc. This thesis aims to expand the multivariate extension of subspace-based techniques on causality analysis and brings novel contributions to not only the theoretical advancements of causality analysis methods but also broadening the horizon of the corresponding applications in complex systems like climate change, economics and genetic science. This research project focuses on, but is not limited to the causality detection test. In particular, the thesis initially proposed four novel multivariate analysis methods based on the study of subspace-based techniques: the similarity measure based on eigenvalue distribution; the mutual association measure based on eigenvalue-based criterion; the causality detection method based on multivariate SSA forecasting accuracy; the hybrid causality detection approach by combining SSA and CCM. Moreover, this thesis also introduces CCM in details and expands its implementations in climate change, oil-tourism study, and gene regulatory role detection. The advantages of these methods are that they are nonparametric approaches, assumption free, only two key variables needed, no limitations to nonlinearity or complex dynamics, signal and noise together as a whole as the research object. Both simulations and a number of successful implementations are conducted for the critical evaluation of the proposed advancements with promising robust performances. Specifically, the novel similarity measure overcomes the difficulties of empirical similarity measures through identifying the comparable criterion, and it is proved robust among various types of series. The novel mutual association measure has no restriction on non- linearity, it performs well with various generated linear and nonlinear association patterns, as well as real data from oil-stock market and oil-tourism studies. SSA causality test, CCM causality and the SSA-CCM hybrid causality tests are comprehensively evaluated by comparing with empirical Granger approaches respectively and with two key variables considered, the results of applications significantly reflect their advantages on nonlinear dynamics and causality detection in complex systems. In general, this thesis contributes on offering novel solutions to the crucial question of causality analysis. However, causality analysis contains a broad range of integrated disciplines, and it has the characteristics of cross discipline, strong practicality and intimate connection with other academic fields. It is such a broad subject that no study can independently comprise all. Therefore, this research attempts to provide evidence of successful applications in a possibly wide range of subjects rather than one subject only so to initially evident on the applicability of these novel methods. The applications have covered studies of climate change, oil-stock market, oil-tourism relationship, gene regulatory role detection to date and more future works are in progress. These novel approaches are self-contained to address the corresponding advancements, therefore, they are not comparable between each other, but all contribute differently to the development of causality analysis in a broad sense. These newly proposed approaches offer the interested parties a different angle to resolve the causality analysis questions in a reduced form, data-oriented perspective. It is also expected to open up the research opportunities of nonparametric multivariate analysis through the advanced, inclusive subspace-based techniques that show strong adaptability and capability in the study of complex systems.