Conditional Gauss-Hermite Filtering with Application to Volatility Estimation

The conditional Gauss-Hermite filter(CGHF) utilizes a decomposition of the filter density p(y1,y2) into the product of the conditional density p(y1Iy2) with the P(y2) where the state vector y is partitioned into (y1,y2). In contrast the usual Gauss-Hermite filter (GHF) it is assumed that the product terms can be approximated by Gaussians. Due to the nonlinear dependence of (y1Iy2) from y2, quite complicated densities can be modelled, but the advantages of the normal distribution are preserved. For example, in stochastic volatility modelsm the joint density stringly derivates from a bivariate Gaussian...