The SIML method without microstructure noise

TL;DR

This paper analyzes the SIML method for estimating integrated volatility, demonstrating its consistency and asymptotic normality in noise-free high-frequency data, and establishing a fast convergence rate similar to the Malliavin--Mancino estimator.

Contribution

The paper proves the consistency and asymptotic normality of the SIML estimator without microstructure noise, extending its theoretical properties under general sampling schemes.

Findings

Proves the SIML estimator is consistent and asymptotically normal.

Establishes fast convergence rate for the SIML estimator.

Extends properties of the Malliavin--Mancino estimator to SIML.

Abstract

The SIML (abbreviation of Separating Information Maximal Likelihood) method, has been introduced by N. Kunitomo and S. Sato and their collaborators to estimate the integrated volatility of high-frequency data that is assumed to be an It\^o process but with so-called microstructure noise. The SIML estimator turned out to share many properties with the estimator introduced by P. Malliavin and M.E. Mancino. The present paper establishes the consistency and the asymptotic normality under a general sampling scheme but without microstructure noise. Specifically, a fast convergence shown for Malliavin--Mancino estimator by E. Clement and A. Gloter is also established for the SIML estimator.