I apply the GMTS approach to graphical modelling of time series to data sets from economics, ecology and environmental science. This approach improves on traditional approaches to modelling insofar as it selects the most parsimonius model. I improve on this approach by removing some redundancies in the GMTS approach. However, a bias in terms of which links are selected means that it is unlikely that this model will select the best causal model.

This thesis considers an approach to evaluate the effectiveness of risk communications for prescription drugs by performing interrupted time series analysis of prescription drug volumes prior to and after the risk communication date. The paper presents methods for detecting change in the presence of autocorrelation and techniques to reduce bias in estimation. Statistical results and data plots are presented for 63 data series. Size and power of the statistical techniques are considered, and a correspondence analysis between these statistical techniques and a small group of physicians is performed. The methods considered in this thesis correspond weakly with physician sentiment, and exhibit inflated type I errors in the presence of significant autocorrelation.

This thesis focuses on various aspects of community mobility and lifespace. Mobility is of particular interest to those working with the elderly population or patients affected by neurological diseases, such as Alzheimer's and Parkinson's diseases. One aspect of mobility is the number of “hotspots" in a person's daily (or weekly) trajectory, which represent the locations at which an individual remains for a minimum predetermined length of time. The individual demonstrates potential limited mobility if there is only one identified hotspot; the individual is more mobile if there are multiple identified hotspots. Based on GPS time series, we can use cluster analysis to identify hotspots. However, existing clustering algorithms such as k-means and trimmed k-means do not take into account the time dependencies between the location points in the series, and require knowing the number of clusters ahead of time. Thus, the resulting clusters do not represent the subjects' activity centres well. In this thesis we have developed a robust time-dependent clustering criterion that works very well to find clusters. Another aspect of mobility is the total distance travelled. The total distance computed from the original GPS data is inflated as there is noise in the data. Due to the particular characteristics of noise specific to GPS time series, we have investigated the identification of noisy segments of data as well as smoothing techniques. The average amplitude of acceleration is proposed as an appropriate method to identify the large noise that occurs in GPS data. A multi-level trimmed means smoother is proposed as an appropriate method to filter the identified large noise. Three methods were investigated to determine an ellipse that identifies the spatial area an individual purposely moves through in daily life. The classical and robust 95% ellipses contain 95% of the points, but do not necessarily capture the distinct shape of the data. The minimum spanning ellipse over the series with all points in each identified cluster reduced to each cluster's central value captures the shape of the data very well and is proposed as the most appropriate lifespace ellipse. Results are obtained and presented for the subjects available in the mobility study for the total distance travelled and a meaningful lower bound, the number of hotspots, the proportion of time spent in the hotspots, as well as the area of the classical 95% ellipse, robust 95% ellipse and minimum spanning ellipse. In the processing of the data, other problems that had to be addressed include obtaining appropriate estimates for the missing values and translating time series from degrees of longitude and latitude to metres in the Cartesian (x,y) plane. / Graduate / 0463 / lauramor@uvic.ca

No description available.

This thesis is an analysis of convergence results on Fourier series. Convergence of Fourier series is studied in two ways in this thesis. The first way is in the context of Banach spaces, where the set of functions is restricted to a certain Banach space. Then the problem is in determining whether the Fourier series of a function can be represented as an element of that Banach space. The second way is in the context of pointwise convergence. Here, the problem is in determining what conditions need to be placed on an arbitrary function for its Fourier series to converge at a point.

I examine the extent to which accounting information is reflected in market prices at different points in time. The efficient market hypothesis implies that price always reflects (value-relevant) accounting information, based on the assumptions of rational investors and costless arbitrage. I examine the time-series relation between price and value in two studies which are motivated by potential shortcomings of these assumptions. First, there is significant debate regarding the rationality of equity investors during the late 1990s. I therefore contrast the historical time-series relation between price and value with that of the 1990s, and show that the historical tendency of price to converge towards value breaks down during this period. Second, I examine the impact of the lack of close substitutes - an arbitrage cost - on the time-series relation between price and value. I find some evidence of a positive association between this arbitrage cost and both the level and the duration of the disparity between price and value. My results provide empirical support for the hypothesis that price requires time to reflect (accounting) information and has implications for research that assumes that prices are measured without error.

Time series datasets are useful in a wide range of diverse real world applications. Retrieving or querying from a collection of time series is a fundamental task, with a key example being the similarity query. A similarity query returns all time series from the collection that are similar to a given reference time series. This type of query is particularly useful in prediction and forecasting applications. / A key challenge for similarity queries is efficiency and for large datasets, it is important to develop efficient indexing techniques. Existing approaches in this area are mainly based on the Generic Multimedia Indexing Method (GEMINI), which is a framework that uses spatial indexes such as the R-tree to index reduced time series. For processing a similarity query, the index is first used to prune candidate time series using a lower bounding distance. Then, all remaining time series are compared using the original similarity measure, to derive the query result. Performance within this framework depends on the tightness of the lower bounding distance with respect to the similarity measure. Indeed much work has been focused on representation and dimensionality reduction, in order to provide a tighter lower bounding distance. / Existing work, however, has not used employed dimensionality reduction in a flexible way, requiring all time series to be reduced to have the same dimension. In contrast, in this thesis, we investigate the possibility of allowing a variable dimension reduction. To this end, we develop a new and more flexible tree based indexing structure called the Multi-Resolution Index (MR-Index), which allows dimensionality to vary across different levels of the tree. We provide efficient algorithms for querying, building and maintaining this structure. Through an experimental analysis, we show that the MR-Index can deliver improved query efficiency compared to the traditional R-tree index, using both the Euclidean and dynamic time warping similarity measures.

Time series datasets are useful in a wide range of diverse real world applications. Retrieving or querying from a collection of time series is a fundamental task, with a key example being the similarity query. A similarity query returns all time series from the collection that are similar to a given reference time series. This type of query is particularly useful in prediction and forecasting applications. / A key challenge for similarity queries is efficiency and for large datasets, it is important to develop efficient indexing techniques. Existing approaches in this area are mainly based on the Generic Multimedia Indexing Method (GEMINI), which is a framework that uses spatial indexes such as the R-tree to index reduced time series. For processing a similarity query, the index is first used to prune candidate time series using a lower bounding distance. Then, all remaining time series are compared using the original similarity measure, to derive the query result. Performance within this framework depends on the tightness of the lower bounding distance with respect to the similarity measure. Indeed much work has been focused on representation and dimensionality reduction, in order to provide a tighter lower bounding distance. / Existing work, however, has not used employed dimensionality reduction in a flexible way, requiring all time series to be reduced to have the same dimension. In contrast, in this thesis, we investigate the possibility of allowing a variable dimension reduction. To this end, we develop a new and more flexible tree based indexing structure called the Multi-Resolution Index (MR-Index), which allows dimensionality to vary across different levels of the tree. We provide efficient algorithms for querying, building and maintaining this structure. Through an experimental analysis, we show that the MR-Index can deliver improved query efficiency compared to the traditional R-tree index, using both the Euclidean and dynamic time warping similarity measures.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (leaves 81-87).

Thesis (M.S.)--Ohio University, June, 1987. / Title from PDF t.p.