  This paper presents a model for smoothly varying heterogeneous persistence of
economic data. We argue that such dynamics arise naturally from the dynamic
nature of economic shocks with various degree of persistence. The
identification of such dynamics from data is done using localised regressions.
Empirically, we identify rich persistence structures that change smoothly over
time in two important data sets: inflation, which plays a key role in policy
formulation, and stock volatility, which is crucial for risk and market
analysis.

General Finance;General Economics;Economics