Particle Gibbs with Ancestor Sampling Methods for Unobserved Component Time Series Models with Heavy Tails, Serial Dependence and Structural Breaks

Particle Gibbs with ancestor sampling (PG-AS) is a new tool in the family of sequential Monte Carlo methods. We apply PG-AS to the challenging class of unobserved component time series models and demonstrate its flexibility under different circumstances. We also combine discrete structural breaks within the unobserved component model framework. We do this by modeling and forecasting time series characteristics of postwar US inflation using a long memory autoregressive fractionally integrated moving average model with stochastic volatility where we allow for structural breaks in the level, long and short memory parameters contemporaneously with breaks in the level, persistence and the conditional volatility of the volatility of inflation.