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Full-Text Articles in Physical Sciences and Mathematics
Data Visualization, Dimensionality Reduction, And Data Alignment Via Manifold Learning, Andrés Felipe Duque Correa
Data Visualization, Dimensionality Reduction, And Data Alignment Via Manifold Learning, Andrés Felipe Duque Correa
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
The high dimensionality of modern data introduces significant challenges in descriptive and exploratory data analysis. These challenges gave rise to extensive work on dimensionality reduction and manifold learning aiming to provide low dimensional representations that preserve or uncover intrinsic patterns and structures in the data. In this thesis, we expand the current literature in manifold learning developing two methods called DIG (Dynamical Information Geometry) and GRAE (Geometry Regularized Autoencoders). DIG is a method capable of finding low-dimensional representations of high-frequency multivariate time series data, especially suited for visualization. GRAE is a general framework which splices the well-established machinery from kernel …
Feasibility Of Multi-Year Forecast For The Colorado River Water Supply: Time Series Modeling, Brian Plucinski, Yan Sun, Shih-Yu (Simon) Wang, Robert R. Gilies, James Eklund, Chih-Chia Wang
Feasibility Of Multi-Year Forecast For The Colorado River Water Supply: Time Series Modeling, Brian Plucinski, Yan Sun, Shih-Yu (Simon) Wang, Robert R. Gilies, James Eklund, Chih-Chia Wang
Mathematics and Statistics Faculty Publications
The future of the Colorado River water supply (WS) affects millions of people and the US economy. A recent study suggested a cross-basin correlation between the Colorado River and its neighboring Great Salt Lake (GSL). Following that study, the feasibility of using the previously developed multi-year prediction of the GSL water level to forecast the Colorado River WS was tested. Time-series models were developed to predict the changes in WS out to 10 years. Regressive methods and the GSL water level data were used for the depiction of decadal variability of the Colorado River WS. Various time-series models suggest a …
Regime Switching In Cointegrated Time Series, Bradley David Zynda Ii
Regime Switching In Cointegrated Time Series, Bradley David Zynda Ii
Undergraduate Honors Capstone Projects
Volatile commodities and markets can often be difficult to model and forecast given significant breaks in trends through time. To account such breaks, regime switching methods allow for models to accommodate abrupt changes in behavior of the data. However, the difficulty often arises in beginning the process of choosing a model and its associated parameters with which to represent the data and the objects of interest. To improve model selection for these volatile markets, this research examines time series with regime switching components and argues that a synthesis of vector error correction models with regime switching models with ameliorate financial …
A Comparison Of Prediction Methods Of Functional Autoregressive Time Series, Devin Didericksen
A Comparison Of Prediction Methods Of Functional Autoregressive Time Series, Devin Didericksen
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Functional data analysis (FDA) is a relatively new branch of statistics that has seen a lot of expansion recently. With the advent of computer processing power and more efficient software packages we have entered the beginning stages of applying FDA methodology and techniques to data. Part of this undertaking should include an empirical assessment of the effectiveness of some of the tools of FDA, which are sound on theoretical grounds. In a small way, this project helps advance this objective.
This work begins by introducing FDA, scalar prediction techniques, and the functional autoregressive model of order one - FAR(1). Two …
Wavelet Techniques In Time Series Analysis With An Application To Space Physics, Agnieszka Jach
Wavelet Techniques In Time Series Analysis With An Application To Space Physics, Agnieszka Jach
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Several wavelet techniques in the analysis of time series are developed and applied to real data sets.
Methods for long-memory models include wavelet-based confidence intervals for the self-similarity parameter in potentially heavy-tailed observations. Empirical coverage probabilities are used to assess the procedures by applying them to Linear Fractional Stable Motion with many choices of parameters. Asymptotic confidence intervals provide empirical coverage often much lower than nominal and it is recommended to use subsampling confidence intervals. A procedure for monitoring the constancy of the self-similarity parameter is proposed and applied to Ethernet data sets.
A test to distinguish a weakly dependent …