ESSAYS ON ESTIMATION OF NON-LINEAR STATE-SPACE MODELS

The first chapter of my thesis (co-authored with David N. DeJong, Jean-Francois Richard and Roman Liesenfeld) develops a numerical procedure that facilitates efficient likelihood evaluation and filtering in applications involving non-linear and non-Gaussian state-space models. These tasks require the calculation of integrals over unobservable state variables. We introduce an efficient procedure for calculating such integrals: the EIS-Filter. The procedure approximates necessary integrals using continuous approximations of target densities. Construction is achieved via efficient importance sampling, and approximating densities are adapted to fully incorporate current information. Extensive comparisons to the standard particle filter are presented using four diverse examples.The second chapter illustrates the use of copulas to create low-dimensional multivariate importance sampling densities. Copulas enable the problem of multivariate density approximation to be split into a sequence of simpler univariate density approximation problems for the marginals, with the dependence accounted by the copula parameter(s). This separation of the marginals from their dependence allows maximum flexibility in the selection of marginal densities. Combined with the EIS method for refining importance sampling densities, copula densities offer substantial flexibility in creating multivariate importance samplers. In a simulation exercise, we compare the accuracy of the copula-based EIS-Filter to the particle filter in evaluating the likelihood function and in obtaining filtered estimates of the latent variables.Reliability of growth forecasts critically depend on being able to anticipate/recognize shifts of the economy from recessions to expansions or vice versa. It is widely accepted that the processes that govern these shifts could be highly non-linear. In the third chapter (co-authored with David N. DeJong, Jean-Francois Richard and Roman Liesenfeld), we study regime shifts using a non-linear model of GDP growth. The model characterizes growth as following non-linear trajectories that fluctuate stochastically between alternative periods of general acceleration and deceleration. Also, we introduce a non-stochastic rule-based recession-dating method to forecast likely dates for the start of a recession and it length. Results indicate that the model is capable of exhibiting substantially non-linear behavior in its regime-specific latent process and hence is able to anticipate and detect regime-shifts accurately, improving the quality of growth forecasts obtained from it.