BILLIO Monica

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Non-linear state-space models (or dynamic models with latent variables) form a very broad class that includes in particular many models used in economics and finance. However, the development of these models is hampered by the difficulties of calculating the likelihood, which requires the calculation of integrals whose dimension is a multiple of the number of observations. This thesis deals with the use of simulation-based methods, which provide powerful tools to solve this type of problem. After presenting the existing methods in the literature (chapter 1), extensions and new methods are proposed in the four other chapters. Chapter 2 proposes the indirect functional inference approach, which is a very general estimation method based on the principle of indirect inference. This method considers as link functions conditional moments estimated by non-parametric techniques. Chapters 3 and 4 deal with models with regime shifts for which the filter introduced by Hamilton does not allow to compute the likelihood. In chapter 3, a class of simulators, based on the importance function technique, is proposed to approximate the likelihood function in the framework of state-space models with regime changes. Chapter 4 suggests a Bayesian resolution, using partially non-informative laws and hybrid Gibbs sampling, for the estimation of arma models with regime changes. In the last chapter, MCMC type algorithms are used and the simulated likelihood ratio method is proposed to approximate the likelihood function and thus the maximum likelihood estimator. This is a very general approach that has many advantages. In each chapter, the theoretical properties of the estimation method, filtering and smoothing are studied and Monte-Carlo experiments illustrate the good performances of the proposed methods.