In this paper we provide a methodology for state smoothing in nonlinear state space models with state dependent variance (SDV). This general class of models contains both stochastic volatility (SVOL) and affine term structure models (ATSMs) which are commonly used in financial time series. For our smoothing technique, we use simulation-based methods with an auxiliary mixture model. We illustrate our methodology with three time-series applications. First, we show how to construct the auxiliary model for a logarithmic SVOL model. Second, we implement a stochastic volatility model with jumps for short-term interest rates in Hong Kong. We find strong evidence for jumps and stochastic volatility in the data and we find the smoothing distribution for the jump times, sizes and volatilities. Third, we implement a two-factor affine term structure model for daily U.S. bond yields from 1996-1999. Our methodology uncovers the unobserved state vector and provides sharper estimates of the parameters of the state dynamics than a simple SVOL interest-rate model. Finally, we conclude with directions for future research.

Keywords: State-Space Model, State-Dependent Variance; Nonlinear Time Series; Mixture Model; Smoothing; MCMC; Stochastic Volatility; Affine Term Structure Model.

The manuscript is available in postscript, and pdf format.