Une methode d'inference bayesienne pour les modeles espace-etat affines faiblement identifies appliquee a une strategie d'arbitrage statistique de la dynamique de la structure a terme des taux d'interet.

摘要

The suject of this is thesis is Bayesian inference for affine models of the term structure of interest rates. In particular, it highlights the critical role of normalization for the forecasting performance of Gaussian linear state-space models. Because the likelihood function of these models is invariant with respect to certain transformations of the parameter vector, the maximum likelihood parameter point estimator is not well defined. In general, one addresses transformation invariance by normalizing the parameter space. When this normalization does not provide global parameter identification, it can introduce weak identification problems, which can produce severely biased parameter point estimators. In contrast, Bayesian predictive densities do not rely on parameter point estimators. From a methodological point of view, I propose a novel MCMC sampler.;Finally, I evaluate empirically the usefulness of affine term structure models for statistical arbitrage strategy construction. Statistical arbitrage exploits temporary deviations between market prices and fundamental values given by an economic model. In order to bet on temporary market price deviations from those implied by this model, I consider portfolios that are first-order hedged with respect to latent factors. In spite of obvious misspecification problems, I find that maximizing expected gains can be a profitable strategy for large institutional investors.;Keywords: dynamic term-structure models, Kalman filter, Bayesian forecasts, weak identification, empirical under-identification, normalization.;The thesis also demonstrates how observational error specification affects inference in these models. I show that one popular specification where the error covariance matrix does not have full rank can yield highly persistent residuals. Beyond that extreme particular case, I provide an empirical analysis of other strict restrictions on the covariance matrix and I propose a novel prior distribution for error covariance matrices. This prior allows the econometrician to specify soft restrictions on error cross-correlations and heteroscedasticity on a continuum between arbitrary and restricted covariance matrices.