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.