Modern approaches for nonlinear data analysis of economic and financial time series.

Summary The main focus of the thesis is on modern nonlinear approaches to the analysis of economic and financial data, with a particular emphasis on business cycles and financial crises. A consensus in the statistical and financial literature has developed around the fact that economic variables behave non-linearly during different phases of the business cycle. As such, nonlinear approaches/models are required to capture the characteristics of the inherently asymmetric data generation mechanism, which linear models are unable to reproduce.In this regard, the thesis proposes a new interdisciplinary and open approach to the analysis of economic and financial systems. The thesis presents approaches robust to extreme values and non-stationarity, applicable to both small and large samples, for both economic and financial time series. The thesis provides step-by-step procedures in the analysis of economic and financial indicators by integrating concepts based on the data substitution method, wavelets, phase embedding space, delay vector variance (DVV) method and plot recurrences. The thesis also highlights transparent methods for identifying and dating turning points and assessing the impacts of economic and financial crises. In particular, the thesis also provides a procedure for anticipating future crises and its consequences.The study shows that the integration of these techniques in learning the structure and interactions within and between economic and financial variables will be very useful in the development of crisis policies, as it facilitates the choice of appropriate treatment methods suggested by the data.In addition, a new procedure for testing linearity and unit root in a nonlinear framework is proposed by introducing a new model - the MT-STAR model - which has similar properties to the ESTAR model but reduces the effects of identification problems and can also represent asymmetry in the adjustment mechanism towards equilibrium. The proposed asymptotic distributions of the unit root test are non-standard and are calculated. The power of the test is evaluated by simulation and some empirical illustrations on real exchange rates show its effectiveness. Finally, the thesis develops multi-variate Self-Exciting Threshold Autoregressive models with exogenous variables (MSETARX) and presents a parametric estimation method. The modeling of MSETARX models and the problems generated by its estimation are briefly discussed.