This paper develops a new Bayesian algorithm to efficiently estimate non-linear/non-Gaussian state space models with abruptly changing parameters. Within the Particle Gibbs framework developed by Andrieu et al. (2010), the proposed algorithm effectively combines two ideas: ancestor sampling and...

I develop a new method for approximating and estimating nonlinear, non-Gaussian state space models. I show that any such model can be well approximated by a discrete-state Markov process and estimated using techniques developed in Hamilton (1989). Through Monte Carlo simulations, I demonstrate...

Empirical volatility studies have discovered nonstationary, long-memory dynamics in the volatility of the stock market and foreign exchange rates. This highly persistent, infinite variance - but still mean reverting - behavior is commonly found with nonparametric estimates of the fractional...