The analysis of a time series is a problem well known to statisticians. Neural networks form the basis of an entirely non-linear approach to the analysis of time series. It has been widely used in pattern recognition, classification and prediction. Recently, reviews from a statistical perspective were done by Cheng and Titterington (1994) and Ripley (1993). One of the most important properties of a neural network is its ability to learn. In neural network methodology, the data set is divided in three different sets, namely a training set, a cross-validation set, and a test set. The training set is used for training the network with the various available learning (optimisation) algorithms. Different algorithms will perform best on different problems. The advantages and limitations of different algorithms in respect of all training problems are discussed. In this dissertation the method of neural networks and that of ARlMA. models are discussed. The procedures of identification, estimation and evaluation of both models are investigated. Many of the standard techniques in statistics can be compared with neural network methodology, especially in applications with large data sets. Additional information available on two discs stored at the Africana section, Merensky Library. / Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2007. / Statistics / unrestricted

Global forests are experiencing a variety of stresses in response to climate change and human activities. The broad objective of this dissertation is to improve understanding of how temperate and boreal forests are changing by using remote sensing to develop new techniques for detecting change in forest ecosystems and to use these techniques to investigate patterns of change in North American forests. First, I developed and applied a temporal segmentation algorithm to an 11-year time series of MODIS data for a region in the Pacific Northwest of the USA. Through comparison with an existing forest disturbance map, I characterized how the severity and spatial scale of disturbances affect the ability of MODIS to detect these events. Results from these analyses showed that most disturbances occupying more than one-third of a MODIS pixel can be detected but that prior disturbance history and gridding artifacts complicate the signature of forest disturbance events in MODIS data. Second, I focused on boreal forests of Canada, where recent studies have used remote sensing to infer decreases in forest productivity. To investigate these trends, I collected 28 years of Landsat TM and ETM+ data for 11 sites spanning Canada's boreal forests. Using these data, I analyzed how sensor geometry and intra- and inter-sensor calibration influence detection of trends from Landsat time series. Results showed systematic patterns in Landsat time series that reflect sensor geometry and subtle issues related to inter-sensor calibration, including consistently higher red band reflectance values from TM data relative to ETM+ data. In the final chapter, I extended the analyses from my second chapter to explore patterns of change in Landsat time series at an expanded set of 46 sites. Trends in peak-summer values of vegetation indices from Landsat were summarized at the scale of MODIS pixels. Results showed that the magnitude and slope of observed trends reflect patterns in disturbance and land cover and that undisturbed forests in eastern sites showed subtle, but detectable, differences from patterns observed in western sites. Drier forests in western Canada show declining trends, while mostly increasing trends are observed for wetter eastern forests.

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.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.