Essays in sequential Monte Carlo methods for economics and finance

This dissertation focuses on sequential Monte Carlo methods, also known as particle filters, and their application to economic problems. It contains four chapters. The first chapter is a survey of the sequential Monte Carlo field. This chapter describes particle filters and their generalization to sequential Monte Carlo samplers beginning from the basics of state space models and Monte Carlo methods. The remaining three chapters apply sequential Monte Carlo methods to economic problems. In Chapter 2, I compare the particle filter to the Kalman filter on non-Gaussian Levy-driven stochastic volatility models. In Chapter 3, I investigate the relationship between cycles in U.S. macroeconomic times series using a multivariate unobserved components model. The resulting Bayesian posterior distribution of the model is multimodal. I demonstrate how sequential Monte Carlo samplers correctly estimate the posterior distribution of the model. In the final chapter, I build new sequential Monte Carlo algorithms for Bayesian estimation of dynamic stochastic general equilibrium models found in macroeconomics.