Nonlinear state-space models with state-dependent variances

Nonlinear state-space models with state-dependent variances (SDVs) are commonly used in financial time series. Important examples include stochastic volatility (SV) and affine term structure models. We propose a methodology for state smoothing in this class of models. Our smoothing technique is simulation based and uses an auxiliary mixture model. Key features of the auxiliary mixture model are the use of state-dependent weights and efficient block sampling algorithms to jointly update all unobserved states given latent mixture indicators. Conditional on latent indicator variables, the auxiliary mixture model reduces to a normal dynamic linear model. We illustrate our methodology with two time series applications. First, we show how to construct the auxiliary model for a logarithmic SV model and compare the performance of our methodology with the current literature. Next, we implement a square-root SV model with jumps for short-term interest rates in Hong Kong.