Conditionally Gaussian Random Sequences for Robust Integrated Variance Estimation

Conditionally Gaussian random sequences generalize State Space models along two relevant directions: (a) the parameters of the model depend in an arbitrary way from past observations, but once this dependence is realized, the randomness can be expressed in terms of Gaussian random variables, (b) correlation is introduced between the transition and measurement equations, through the presence of a common Brownian motion. Adopting a Bayesian perspective, we propose a general methodology for sampling, a posteriori, the latent stochastic process of a conditionally Gaussian random sequence. The motivating problem is to provide a high-frequency realized variance estimator of the integrated variance that is robust to the presence of correlation between microstructure noise and latent logarithmic returns. The developed algorithm is applied to this financial problem and for modelling noisy normal inverse Gaussian financial returns.