Filtering and estimation in stochastic volatility models with rationally distributed disturbances

TL;DR

This paper presents an exact filtering approach for stochastic volatility models with rational disturbances, employing state space realizations and truncation techniques, and introduces a moments-based estimator for parameter inference.

Contribution

It introduces a novel exact filtering method for models with rational disturbances and develops a practical approximation using balanced truncation, along with a simple moments estimator.

Findings

Exact filtering achieved for models with rational disturbances.

Balanced truncation effectively approximates high-order rational functions.

Simulation confirms the method's applicability.

Abstract

This paper deals with the filtering problem for a class of discrete time stochastic volatility models in which the disturbances have rational probability density functions. This includes the Cauchy distributions and Student t-distributions with odd number of degrees of freedom. Using state space realizations to represent the rational probability density functions we are able to solve the filtering problem exactly. However the size of the involved state space matrices grows exponentially with each time step of the filter. Therefore we use stochastically balanced truncation techniques to approximate the high order rational functions involved. In a simulation study we show the applicability of this approach. In addition a simple method of moments estimator is derived.