Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 59. Regression Analysis

SVETLOZAR T. RACHEV, PhD, DrSci

Chair-Professor, Chair of Econometrics, Statistics and Mathematical Finance, School of Economics and Business Engineering, University of Karlsruhe and Department of Statistics and Applied Probability University of California, Santa Barbara

STEFAN MITTNIK, PhD

Professor of Financial Econometrics at the University of Munich, Germany, and Research Director at the Ifo Institute for Economic Research in Munich

FRANK J. FABOZZI, PhD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

SERGIO FOCARDI

Partner, The Intertek Group in Paris, France

TEO JASIC, Dr. rer. pol.

Postdoctoral Research Fellow at the Chair of Statistics, Econometrics and Mathematical Finance at the University of Karlsruhe in the School of Economics and Business Engineering and a partner of an international management consultancy firm in Frankfurt, Germany

Abstract: Regressions are the probabilistic equivalent of functions in the deterministic domain. A regression expresses a functional link between a random variable Y and one or more independent variables X_i called regressors. The variables X_i can be either deterministic or random variables. The regression function is the expectation of the variable Y given the variables X_i. If the variables X_i are deterministic, regressions express the fact that the distribution of the variable Y is indexed by the X_i. If all variables are random variables, regressions express the fact that the joint distribution ...