Efficient variational approximations for state space models

TL;DR

This paper introduces a new variational approximation method for state space models that is both accurate and computationally efficient, applicable to models with certain distributional properties, demonstrated on financial and macroeconomic data.

Contribution

The paper presents a novel variational approximation technique that is scalable, accurate, and fast for a broad class of state space models with exponential family distributions.

Findings

Accurately estimates multivariate Skellam stochastic volatility models

Efficiently models time-varying parameter vector autoregressions with stochastic volatility

Demonstrates applicability to high-frequency financial data and macroeconomic variables

Abstract

Variational Bayes methods are a potential scalable estimation approach for state space models. However, existing methods are inaccurate or computationally infeasible for many state space models. This paper proposes a variational approximation that is accurate and fast for any model with a closed-form measurement density function and a state transition distribution within the exponential family of distributions. We show that our method can accurately and quickly estimate a multivariate Skellam stochastic volatility model with high-frequency tick-by-tick discrete price changes of four stocks, and a time-varying parameter vector autoregression with a stochastic volatility model using eight macroeconomic variables.