Realized wavelet-based estimation of integrated variance and jumps in the presence of noise

TL;DR

This paper presents a wavelet-based method for estimating realized variance and jumps in financial data, effectively handling noise and decomposing volatility across multiple investment horizons, with superior accuracy demonstrated through extensive simulations and real data application.

Contribution

It introduces a novel wavelet-based estimator that decomposes realized variance into multiple horizons and accounts for noise, improving estimation accuracy over existing methods.

Findings

Wavelet-based estimator outperforms other methods in simulation studies.

Estimator effectively decomposes volatility into different investment horizons.

Application to forex futures reveals detailed volatility dynamics during crises.

Abstract

We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the realized variance into several investment horizons and jumps. Basing our estimator in the two-scale realized variance framework, we are able to utilize all available data and get feasible estimator in the presence of microstructure noise as well. The estimator is tested in a large numerical study of the finite sample performance and is compared to other popular realized variation estimators. We use different simulation settings with changing noise as well as jump level in different price processes including long memory fractional stochastic volatility model. The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Our time-frequency estimators not only produce feasible estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. We apply it to study the volatility of forex futures during the recent crisis at several investment horizons and obtain the results which provide us with better understanding of the volatility dynamics.