Inference for cumulative intraday return curves
Date
2018
Authors
Zheng, Ben, author
Kokoszka, Piotr S., advisor
Cooley, Dan, committee member
Miao, Hong, committee member
Zhou, Wen, committee member
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Abstract
The central theme of this dissertation is inference for cumulative intraday return (CIDR) curves computed from high frequency data. Such curves describe how the return on an investment evolves with time over a relatively short period. We introduce a functional factor model to investigate the dependence of cumulative return curves of individual assets on the market and other factors. We propose a new statistical test to determine whether this dependence is the same in two sample periods. The statistical power of the new test is validated by asymptotic theory and a simulation study. We apply this test to study the impact on individual stocks and Sector Exchanged-Traded Funds (ETF) of the recent financial crisis and of trends in the oil price. Our analysis reveals that the functional approach has an information content different from that obtained from scalar factor models for point-to-point returns. Motivated by the risk inherent in intraday investing, we propose several ways of quantifying extremal behavior of a time series of curves. A curve can be extreme if it has shape and/or magnitude much different than the bulk of observed curves. Our approach is at the nexus of Functional Data Analysis and Extreme Value Theory. The risk measures we propose allow us to assess probabilities of observing extreme curves not seen in a historical record. These measures complement risk measures based on point-to-point returns, but have different interpretation and information content. Using our approach, we study how the financial crisis of 2008 impacted the extreme behavior of intraday cumulative return curves. We discover different impacts on shares in important sectors of the US economy. The information our analysis provides is in some cases different from the conclusions based on the extreme value analysis of daily closing price returns. In a different direction, we investigate a large-scale multiple testing problem motivated by a biological study. We introduce mixed models to fit the longitudinal data and incorporate a bootstrap method to construct a false discovery rate (FDR) controlling procedure. A simulation study is implemented to show its effectiveness.
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Subject
extreme value theory
large-scale multiple testing
two sample test
functional data analysis
cumulative intraday return curves
risk analysis