Spectral covolatility estimation from noisy observations using local weights

TL;DR

This paper introduces localized spectral estimators for quadratic covariation and spot covolatility in noisy, discretely observed diffusion processes, demonstrating improved performance over existing methods through theoretical and simulation analysis.

Contribution

It develops a novel localized spectral estimation method that accounts for noise and time variation, with proven asymptotic equivalence to a white noise model.

Findings

Outperforms previous nonparametric estimators in simulations

Proves asymptotic equivalence of models with linear interpolation and local means

Provides finite sample performance analysis

Abstract

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an appropriate estimation for time-varying volatilities stems from an asymptotic equivalence of the underlying statistical model to a white noise model with correlation and volatility processes being constant over small intervals. The asymptotic equivalence of the continuous-time and the discrete-time experiments are proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier nonparametric approaches in the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between the various proposed methods.