Ph.d.-forsvar: Andreas Lund Hetland:On Particle Filter-Based Estimation and Inference for Dynamic Models with Unobserved Variables
This PhD thesis discusses particle filter-based methods for optimal filtering and likelihood-based inference in dynamic models with unobserved variables. It is a general feature of these models that it is not possible to obtain closed-form expressions for the optimal filtering problem and model likelihood. Particle filters constitute a family of simulation-based approximation methods that produce approximations to these intractable quantities. The thesis consists of three self-contained chapters. The first chapter reviews recent induction-based arguments for the asymptotic properties of standard particle filters with multinomial resampling. Specifically, we consider the asymptotic properties of the particle filter-based approximations of the optimal filtering problem and model likelihood when the number of particles tends to infinity and the observations are fixed. The second chapter proposes and studies the hybrid particle filter, which enables optimal filtering and parameter inference for a new class of dynamic factor models with nonlinear non-Gaussian common component. The third chapter proposes and studies the stochastic stationary root model, which is a multivariate nonlinear state space model with a cointegration-like structure and interpretation. Chapter two and three contain simulation studies and empirical illustrations of the proposed methods.