Case Studies in Bayesian Statistical Modelling and Analysis

15

A Bayesian Approach to Multivariate State Space Modelling: A Study of a Fama–French Asset-Pricing Model with Time-Varying Regressors

Christopher M. Strickland¹ and Philip Gharghori²

¹Queensland University of Technology, Brisbane, Australia

²Monash University, Melbourne, Australia

15.1 Introduction

The state space framework provides a generic methodology for modelling time series. Algorithms such as the Kalman filter (Kalman 1960) provide generally applicable tools that facilitate estimation, see Anderson and Moore (1979) and Harvey (1989). Bayesian inference of state space models (SSMs) is currently most commonly undertaken using Markov chain Monte Carlo (MCMC). As MCMC methods typically require the state space algorithms to be used tens of thousands of times, particular care is required with their implementation. This is especially true when dealing with multivariate data. This chapter details a Bayesian approach to the estimation of linear Gaussian multivariate SSMs. The approach is applied to a system analysis of the Fama–French asset-pricing model, with time-varying regressors.

15.2 Case Study: Asset Pricing in Financial Markets

Modelling the behaviour of asset prices is at the core of finance. The first model that quantified the relationship between an asset's risk and return is the capital asset-pricing model (CAPM) of Sharpe (1964), Lintner (1965) and Black (1972). The model suggests that there is a positive relationship between the systematic risk of an asset and its ...