Dynamic factor model with non-linearities : application to the business cycle analysis.

Summary This thesis is dedicated to a particular class of nonlinear dynamic factor models, the Markovian regime-switching dynamic factor models (MS-DFM). By combining the features of the dynamic factor model and the Markov regime-switching model (i.e. the ability to aggregate massive amounts of information and to track fluctuating processes), this framework has proven to be very useful and suitable for several applications, the most important of which is the analysis of business cycles.The knowledge of the current state of business cycles is crucial in order to monitor economic health and to evaluate the results of economic policies. Nevertheless, this is not an easy task to achieve because, on the one hand, there is no commonly accepted data set and methods to identify turning points, and on the other hand, official institutions announce a new turning point, in countries where such a practice exists, with a structural delay of several months.The MS-DFM is able to solve these problems by providing estimates of the current state of the economy in a fast, transparent and reproducible way based on the common component of macroeconomic indicators characterizing the real sector.This thesis contributes to the vast literature on the identification of turning points of the business cycle in three directions. In Chapter 3, the two MS-DFM estimation techniques, the one-step and the two-step methods, are compared and applied to French data to obtain the timing of business cycle turning points. In Chapter 4, on the basis of Monte Carlo simulations, we study the convergence of the estimators of the chosen technique - the two-step estimation method - and we analyze their behavior in finite sample. In Chapter 5, we propose an extension of MS-DFM - the dynamically influenced MS-DFM (DI-MS-DFM) - that allows us to evaluate the contribution of the financial sector to the dynamics of the business cycle and vice versa, while taking into account the fact that the interaction between them may be dynamic.