FUNCTIONAL DATA BASED INFERENCE FOR HIGH FREQUENCY FINANCIAL DATA

Open Access
Author:
Taoufik, Bahaeddine
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
July 27, 2016
Committee Members:
  • Matthew Logan Reimherr, Dissertation Advisor
  • Matthew Logan Reimherr, Committee Chair
  • Runze Li, Committee Member
  • Zhibiao Zhao, Committee Member
  • John C Liechty, Outside Member
Keywords:
  • Functional Data
  • Nonlinear Functional Regression
  • Cross-section of returns
  • Cumulative intraday returns
  • Reproducing kernel Hilbert spaces
Abstract:
This thesis is concerned with developing new functional data techniques for high frequency financial applications. Chapter 1 of the thesis introduces Functional Data Analysis (FDA) with examples of application to real data. In this chapter, we provide some theoretical foundations for FDA. We also present a general theory and basic properties of reproducing kernel Hilbert spaces (RKHS). Chapter 2 of the thesis explores the relationship between market returns and a number of financial factors by fitting functional regression models. We establish two estimation procedures based on the least squares and generalized least squares methods. We also present four hypothesis testing procedures on the functional regression coefficients based on the squared integral $L^2$ approach and the PCA approach for both least squares and generalized least squares methods. New asymptotic results are established allowing for minor departures from stationarity, to ensure convergence and asymptotic normality of our estimates. Our functional regression model is applied to cross-section returns data. Our data application results indicate a positive correlation between the volatility factor ``FVIX" and the higher returns and a negative correlation between the volatility factor ``FVIX" and the low and middle returns. Chapter 3 of the thesis develops a nonlinear function-on-function model using RKHS for real-valued functions. We establish the minimax rate of convergence of the excess prediction risk. Our simulation studies faced computational challenges due to the complexity of the estimation procedure. We examine the prediction performance accuracy of our model through a simulation study. Our nonlinear function-function model is applied to Cumulative intraday return (CIDR) data in order to investigate the prediction performance of Standard \& Poor's 500 Index (S\&P 500) and the Dow Jones Industrial Average (DJIA) for General Electric Company (GE) and International Business Machines Corp.(IBM) for the three periods defining the crisis: ``Before," `` During," and `` After''.