Essays on the Econometrics of Financial Data

This dissertation proposes a methodology for inference in the context of diffusion processes with jumps. There are many applications. For example, in finance, this methodology can be used to study asset pricing. My dissertation consists of two chapters which are closely related. They reveal the relationship between the power of a test, jump height and jump frequency. In the first chapter I construct a likelihood ratio test to test whether a diffusion process has jumps. This test statistic is independent of the distribution of jump height. I show the test is asymptotically optimal when the jump height is O(1/n^alpha) , the jump frequency is O(1/n^beta) where n is sample size, 3alpha+beta=2,alpha>1/2,beta>0. By constructing this optimal test, I derive the asymptotic power envelopes for testing continuous diffusion process against diffusion processes with asymmetric jumps. In recent years, many tests for this problem were proposed. I compare the power of these tests with the envelopes using simulations.In chapter two I test the continuous diffusion process against a diffusion process with symmetric jumps. I show my test statistic is optimal when the jump height is O(1/n^alpha), the jump frequency is O(1/n^beta) where n is sample size, 4alpha+beta=5/2, alpha>2/3, 0<beta<1/12. Comparing this with the first chapter,alpha can take larger values and beta can take lower values. Thus, this test can detect smaller height and lower intensity jump processes. In this sense, the test of symmetric jumps can be more sensitive. As in the first essay, I also derive the asymptotic power envelopes and use simulations to compare the existing tests with the asymptotically optimal power.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Economics

Year dc:date.available

2015

Author dc:creator

• Cao, Yunfei

Contributors dc:contributor

• Werner Ploberger
• George-Levi Gayle, Nan Lin, John Nachbar, Jonathan Weinstein

• Economics

Statement dc:rights

• I have not registered my thesis with the U.S. Copyright Office, and do not intend to.

Language dc:language

English (en)

Identifier

https://openscholarship.wustl.edu/art_sci_etds/425

OAI identifier oai:identifier

oai:openscholarship.wustl.edu:art_sci_etds-1425