Conditionally Gaussian random sequences for an integrated variance estimator with correlation between noise and returns

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 intraday Microsoft prices and compare it in a simulation study with established alternatives, showing an advantage in terms of root‐mean‐square error and dispersion.

A Bayesian Semiparametric Vector Multiplicative Error Model

“…Volatility measurements using intra-daily data were first adopted by Parkinson (1980) for the estimation of the daily range. Since then the literature has significantly expanded: from the realized volatility of Andersen and Bollerslev (1998) and Peluso et al (2019) to realized kernels of Barndorff-Nielsen et al (2008) and realized covariance matrices (Aït-Sahalia et al, 2010;Peluso et al, 2014;Corsi et al, 2015). In parallel to the evolution of these measures, there has been a natural complementary effort to build adequate models to describe their dynamics.…”