Abstract
Most real-world time series data is produced by complex systems. For example, the economy is a social system which produces time series of stocks, bonds, and foreign exchange rates whereas the human body is a biological system which produces time series of heart rate variations, brain activity, and rate of blood circulation. Complex systems exhibit great variety and complexity and so does the time series emanating from these systems. However, universal principles and tools seem to govern our understanding of highly complex phenomena, processes, and dynamics. It has been argued that one of the universal properties of complex systems and time series produced by complex systems is 'scaling'. The multiscale wavelet analysis shows promise to systematically elucidate complex dynamics in time series data at various timescales. In this research we investigate whether the wavelet analysis can be used as a universal tool to study the universal property of scaling in complex systems. We have developed and evaluated a wavelet time series analysis framework for automatically assessing the state and behaviour of complex systems such as the economy and the human body. Our results are good and support the hypothesis that 'scaling' is indeed a universal property of complex systems and that the wavelet analysis can be used as a universal tool to study it. We conclude that a system based on universal principles (e.g. 'scaling') and tools (e.g. wavelet analysis) is not only robust but also renders itself useful in diverse environments. Key words: Complex systems, scaling, time series analysis, wavelet analysis.