A Class of Multivariate Micromovement Models of Asset Price and Their Bayesian Model Selection via Filtering

Abstract

A filtering model with counting process observations has been recently developed as a reasonable framework for the micromovement of asset price. In this paper, we first highlight such an extension to multivariate case for modeling multi-stocks and related results on Bayes estimation via filtering. For this rich class of multivariate models, we develop the Bayesian model selection using Bayes factor. Based on the unnormalized, Duncan-Mortensen-Zakai-like filtering equation, we derive a system of SPDE characterizing the evolution of the Bayes factors and prove their uniqueness. Furthermore, applying Kushner’s Markov chain approximation method, we propose a numerical scheme to derive recursive algorithms, and we prove the consistency (or robustness) of the recursive algorithms.