Nonlinear State-Space Models with State-Dependent Variances

Jonathan R. Stroud, Peter Müller, Nicholas G. Polson

University of Pennsylvania, MD Anderson Cancer Center, and University of Chicago

Nonlinear state-space models with state-dependent variances (SDV) are commonly used in financial time series. Important examples include stochastic volatility (SV) and affine term structure models. We propose a method 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 the 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 mixture model for a logarithmic SV model and we compare the performance of our methodology with the current literature. Second, we implement a stochastic volatility model with jumps for short-term interest rates in Hong Kong.

The manuscript is available in PDF format.