Concurrent research documents sizeable changes in the volatility of U.S. macroeconomic time series; e.g., see Kim and Nelson (1999), McConnell and Pérez-Quirós (2000), Stock and Watson (2002), and Sensier and van Dijk (2004). Most of the evidence from this literature suggests a sizeable reduction in volatility for many series; many of them used to construct business cycle indicators. With the e...

Suppose we are given a multi-dimensional Itô process, which can be regarded as a model for an underlying asset price together with related stochastic processes, e.g., volatility. The drift and diffusion terms for this Itô process are permitted to be arbitrary adapted processes. We construct a weak solution to a diffusion-type equation that matches the distribution of the Itô process at each fix...