Ever since Granger first proposed the idea of quantitatively testing the causal relationship between data streams, the endeavor of accurately inferring the causality in data and using that information to predict the future has not stopped. Artificial Intelligence (AI), by utilizing the massive amounts of data, helps to solve complex problems, whether they include the diagnosis and detection of disease through medical imaging, email spam detection, or self-driving vehicles. Perhaps, this thesis will be trivial in ten years from now. AI has pushed humankind to reach the next technological level in technology. Nowadays, among most machine leaning inquiries, statistical relationships are determined using correlation measures. By feeding data into machine learning algorithms, computers update the algorithm’s parameters iteratively by extracting and mapping features to learning targets until the correlation increases to a significant level to cease the training process. However, with the increasing developments of powerful AI, there is really a shortage of exploring causality in data. It is almost self-evident that ”correlation is not causality." Sometimes, the strong correlation established between variables through machine learning can be absurd and meaningless. Providing insight into causality information through data, which most of the machine learning methods fall short to do, is of paramount importance. The subsequent chapters detail the four endeavors of studying causality in financial markets, earthquakes, animal/human brain signals, the predictivity of data sets. In Chapter 2, we further developed the concept of causality networks into a higher-order causality network. We applied these to financial data and tested their validity and ability to capture the system’s causal relationship. In next Chapter 3, We examined another type of time series-earthquakes. Violent seismic activities decimate people's lives and destroy entire cities and areas. This begs us to understand how earthquakes work and help us make reliably and evacuation-actionable predictions. The causal relationships of seismic activities in different areas are studied and established. Biological data, specifically brain signals, are time-series data and their causal pattern are explored and studied. Different human and mice brain signals are analyzed and clustered in Chapter 4 using their unique causal pattern to understand different brain cell activity. Finally, we realized that the causal pattern in the time series can be used to compress data. A causal compression ratio is invented and used as the data stream’s predictivity index. We describe this in Chapter 5.

Athlete preparation and performance continue to increase in complexity and costs. Modern coaches are shifting from reliance on personal memory, experience, and opinion to evidence from collected training-load data. Training-load monitoring may hold vital information for developing systems of monitoring that follow the training process with such precision that both performance prediction and day-to-day management of training become adjuncts to preparation and performance. Time-series data collection and analyses in sport are still in their infancy, with considerable efforts being applied in "big data" analytics, models of the appropriate variables to monitor, and methods for doing so. Training monitoring has already garnered important applications but lacks a theoretical framework from which to develop further. As such, we propose a framework involving the following: analyses of individuals, trend analyses, rules-based analysis, and statistical process control.

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