The Fourier estimation method with positive semi-definite estimators

TL;DR

This paper introduces a modified Fourier estimation method for spot volatility that guarantees positive semi-definite estimators, reducing computational costs through factorization.

Contribution

The paper proposes a slight modification to the Fourier estimation method ensuring non-negative definite estimators and improved computational efficiency.

Findings

Estimators are always positive semi-definite.

Factorization reduces computational cost.

Method maintains accuracy of volatility estimation.

Abstract

In this paper we present a slight modification of the Fourier estimation method of the spot volatility (matrix) process of a continuous It\^o semimartingale where the estimators are always non-negative definite. Since the estimators are factorized, computational cost will be saved a lot.