Feasible Inference for Stochastic Volatility in Brownian Semistationary Processes

TL;DR

This paper evaluates the finite sample performance of three feasible estimators for integrated volatility in Brownian semistationary processes, comparing their convergence and asymptotic properties through simulations.

Contribution

It introduces three consistent feasible estimators for integrated volatility in non semi-martingale settings, including two parametric and one non-parametric method.

Findings

Three estimators are consistent for integrated volatility.

Simulation results compare convergence properties of estimators.

Bounds for asymptotic variance of the infeasible estimator are established.

Abstract

This article studies the finite sample behaviour of a number of estimators for the integrated power volatility process of a Brownian semistationary process in the non semi-martingale setting. We establish three consistent feasible estimators for the integrated volatility, two derived from parametric methods and one non-parametrically. We then use a simulation study to compare the convergence properties of the estimators to one another, and to a benchmark of an infeasible estimator. We further establish bounds for the asymptotic variance of the infeasible estimator and assess whether a central limit theorem which holds for the infeasible estimator can be translated into a feasible limit theorem for the non-parametric estimator.