  This paper introduces a local-to-unity/small sigma process for a stationary
time series with strong persistence and non-negligible long run risk. This
process represents the stationary long run component in an unobserved short-
and long-run components model involving different time scales. More
specifically, the short run component evolves in the calendar time and the long
run component evolves in an ultra long time scale. We develop the methods of
estimation and long run prediction for the univariate and multivariate
Structural VAR (SVAR) models with unobserved components and reveal the
impossibility to consistently estimate some of the long run parameters. The
approach is illustrated by a Monte-Carlo study and an application to
macroeconomic data.
