Dissertation
SUBORDINATED GAUSSIAN PROCESS, FLUCTUATION IDENTITIES, AND THEIR APPLICATIONS TO LOG-RETURNS AND TO CHANGE-POINT ANALYSIS
Doctor of Philosophy (PhD), Washington State University
01/2014
Handle:
https://hdl.handle.net/2376/118021
Abstract
The aim of this thesis is to provide new results concerning the distribution of the first time a process reaches its supremum and also the magnitude of the supremum. We establish these characteristics, when the underlying process is either a linear subordinated Brownian motion (SBM) or when the process is simply a linear Brownian motion with negative drift. For reasons of applicability and confirmation of the distributional behavior of the supremum and its position, extensive simulations are conducted and we find, as we expected, that there is a strong close relationship between the theoretical distributional results. Upon seeing that the simulation investigation and theoretical derivations are at a coincide level, we apply our work to three USA indices from which various inferences are mined. In conclusion, the SBM appears to be a strong candidate for modeling log returns of asset price movements, which in turn the geometric subordinated Brownian motion is a possible candidate to model asset prices. From a statistical prospective, we apply our theoretical results to the continuous abrupt change-point problem. It has been shown (Fotopoulos et al 2010) that the key components to analyze the change-point problem and obtain the distribution of the maximum likelihood estimate (mle) of the change point in an abrupt case is the distributional behavior of the maximum of an underlying process and the position at which the maximum occurs. Therefore, our scope here is to reinvent the mle change-point for continuous processes, which includes the purely linear Brownian motions as well as jump processes, i.e., SBM. The problem of multiple change-points has dominated the literature over the last 10 years. This has been done only to case of discrete scenario. In here, an attempt to resolve the continuous case is of significance. Further, to evaluate the best selection procedure we implement four criteria: the dynamic programming, the Lasso methodology, the Lebarbier approach and the Bayesian approach. To understand even further, we apply these methodologies to real data as the global and zonal temperature deviations.
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Details
- Title
- SUBORDINATED GAUSSIAN PROCESS, FLUCTUATION IDENTITIES, AND THEIR APPLICATIONS TO LOG-RETURNS AND TO CHANGE-POINT ANALYSIS
- Creators
- Yuxing Luo
- Contributors
- Stergios B Fotopoulos (Advisor)Venkata K Jandhyala (Committee Member)Gene C Lai (Committee Member)Sung K Ahn (Committee Member)Sheen Liu (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Carson College of Business
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 212
- Identifiers
- 99900581738201842
- Language
- English
- Resource Type
- Dissertation