Bayesian Linear Regression Model

BILIANA S. GüNER, PhD

Assistant Professor of Statistics and Econometrics, Ozyegin University, Turkey

SVETLOZAR T. RACHEV, PhD, Dr Sci

Frey Family Foundation Chair Professor, Department of Applied Mathematics and Statistics, Stony Brook University, and Chief Scientist, FinAnalytica

JOHN S. J. HSU, PhD

Professor of Statistics and Applied Probability, University of California, Santa Barbara

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: Linear regression is the “workhorse” of financial modeling. Cornerstone applications, such as asset pricing models, as well as time series models, are built around linear regression’s methods and tools. Casting the linear regression methodology in a Bayesian setting helps account for estimation uncertainty, allows for integration of prior information, and makes accessible the Bayesian numerical simulation framework.

In this entry, we lay the foundations of Bayesian linear regression estimation. We start with a univariate model with Gaussian innovations and consider two cases for prior distributional assumptions—diffuse and informative. Then, we show how one could incorporate knowledge that the sample is not homogeneous with respect to the variance, for example, due to a structural break. Finally, multivariate regression estimation is discussed.

THE UNIVARIATE LINEAR REGRESSION MODEL

The univariate linear regression model attempts to explain the variability in one variable ...

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