We develop a systematic framework for the joint modelling of returns and multiple daily realised measures. We assume a linear state space representation for the log realised measures, which are noisy and biased estimates of the log integrated variance, at least due to Jensen's inequality. We...

We propose a new methodology for the Bayesian analysis of nonlinear non-Gaussian state space models with a Gaussian time-varying signal, where the signal is a function of a possibly high-dimensional state vector. The novelty of our approach is the development of proposal densities for the joint...