# Conditionally Gaussian Random Sequences for an Integrated Variance Estimator with Correlation between Noise and Returns

## TL;DR

This paper introduces a new integrated variance estimator that effectively handles correlation between microstructure noise and returns, using a generalized sampling algorithm, and demonstrates improved accuracy on real financial data.

## Contribution

It proposes a novel estimator and a generalized sampling algorithm to account for noise-return correlation, filling a gap in existing financial variance estimation methods.

## Key findings

- Outperforms existing estimators in simulation studies.
- Shows improved accuracy on intra-day Microsoft prices.
- Demonstrates robustness to noise-return dependence.

## Abstract

Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the financial literature are not designed to explicitly handle such a dependence, or handle it only in special settings. We provide an integrated variance estimator that is robust to correlated noise and returns. For this purpose, a generalization of the Forward Filtering Backward Sampling algorithm is proposed, to provide a sampling technique for a latent conditionally Gaussian random sequence. We apply our methodology to intra-day Microsoft prices, and compare it in a simulation study with established alternatives, showing an advantage in terms of root mean square error and dispersion.