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
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 Xi called regressors. The variables Xi can be either deterministic or random variables. The regression function is the expectation of the variable Y given the variables Xi. If the variables Xi are deterministic, regressions express the fact that the distribution of the variable Y is indexed by the Xi. If all variables are random variables, regressions express the fact that the joint distribution ...