Dissertation
DATA ANALYTICS METHODOLOGIES FOR BUSINESS PRINCIPLES
Washington State University
Doctor of Philosophy (PhD), Washington State University
01/2021
DOI:
https://doi.org/10.7273/000005397
Handle:
https://hdl.handle.net/2376/119072
Abstract
The first part of this thesis analyzes inhomogeneous time series data caused by the presence of an unknown change-point. We assume that the time series data are from a gamma distribution and at an unknown point of time, a change in the rate and/or shape parameters occurs. A complete change-point methodology is proposed including change detection based on the likelihood ratio statistic as well as estimation of the unknown change-point by the method of maximum likelihood estimation (mle). Furthermore, we provide the asymptotic distribution of the change-point mle when a change occurs in the rate parameter of the gamma distribution. Extensive simulations have been conducted to show excellent agreement between the distribution of the change-point under finite sample sizes and its asymptotic counterparts. A comparison analysis between known parameters and estimated parameters indicates that the error committed is negligible. Four examples, one from the financial market, another from climatology, one from queueing theory, and the last one from ecology, are analyzed to adequately illustrate the proposed inferential methodology. In the second part, our study revisits the class of multivariate generalized hyperbolic (MGH) distributions for capturing the uncertainty in financial log-returns. Beginning with the Geometric subordinated Brownian motion for asset prices, we first demonstrate that the mean-variance mixing model of the multivariate normal law is natural for log-returns of financial assets. This variance mixing multivariate model forms the basis for deriving the MGH family as a class of distributions for modeling the behavior of log-returns. Theory suggests MGH to be an appropriate family, however empirical considerations must also support such a proposition. From a theoretical perspective, we present an alternative form of the density for the MGH family and its conditionals. Numerical study of the distributional behavior of six stocks in the US market forms the foundation of investigating the suitability of the MGH family and some of its well-known sub-families.
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Details
- Title
- DATA ANALYTICS METHODOLOGIES FOR BUSINESS PRINCIPLES
- Creators
- Alexandros Paparas
- Contributors
- Stergios B. Fotopoulos (Advisor)Stergios B. Fotopoulos (Committee Member)Chuck Munson (Committee Member)Xinchang Wang (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Carson College of Business
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 170
- Identifiers
- 99900592156101842
- Language
- English
- Resource Type
- Dissertation