Discovery of Structures and Processes in Temporal Data

Beyond any doubt, natural and man-made phenomena change over time and space. In our natural environment, temperature, rainfall, cloud cover, ice cover, water level of a lake, river channel morphology, surface temperature of the ocean, to name but a few examples, all exhibit dynamic changes over time. In terms of human activities, we have witnessed the change of birth rate, death rate, migration rate, population concentration, unemployment, and economic productivity throughout our history. In our interacting with the environment, we have experienced the time varying concentration of various pollutants, usage of natural resource, and global warming. For natural disasters, the occurrence of typhoon, flood, drought, earthquake, and sand storm are all dynamic in time. All of these changes might be seasonal, cyclical, randomly fluctuating, or trend oriented in a local or global scale. To have a better understanding of and to improve our knowledge about these dynamic phenomena occurring in natural and human systems, we generally make a sequence of observations ordered by a time parameter within certain temporal domain. Time series are a special kind of realization of such variations. They measure changes of variables at points in time. The objectives of time series analysis are essentially the description, explanation, prediction, and perhaps control of the time varying processes. With respect to data mining and knowledge discovery, we are primarily interested in the unraveling of the generating structures or processes of time series data. Our aim is to discover and characterize the underlying dynamics, deterministic or stochastic, that generate the time varying phenomena manifested in chronologically recorded data.