Modeling Multivariate Positive-Valued Time Series Using R-INLA

TL;DR

This paper introduces a fast Bayesian approach using R-INLA to model multivariate positive-valued time series, specifically applied to financial volatility data, by combining gamma marginals with a hierarchical correlation structure.

Contribution

It develops a flexible hierarchical model framework for vector positive-valued time series and implements it efficiently with R-INLA for financial data analysis.

Findings

Effective modeling of interdependent volatility measures

Fast Bayesian inference via R-INLA

Hierarchical gamma-based multivariate time series model

Abstract

In this paper we describe fast Bayesian statistical analysis of vector positive-valued time series, with application to interesting financial data streams. We discuss a flexible level correlated model (LCM) framework for building hierarchical models for vector positive-valued time series. The LCM allows us to combine marginal gamma distributions for the positive-valued component responses, while accounting for association among the components at a latent level. We use integrated nested Laplace approximation (INLA) for fast approximate Bayesian modeling via the R-INLA package, building custom functions to handle this setup. We use the proposed method to model interdependencies between realized volatility measures from several stock indexes.