Indirect inference, TIMA models with contemporaneous skewness, and ARFIMA threshold models: applications in economics and finance.

Summary In this thesis we have been interested in models to characterize long memory in terms of fractional integration and threshold effects. These models allow us to decide whether the observed persistence is best represented by a fractional integration or nonlinearity property. Thus, we were interested in TIMA models with contemporaneous asymmetry that generalize TIMA models with delayed asymmetry. The introduction of a contemporaneous asymmetry implies that the shocks are no longer characterized by a noise according to the usual representation. This type of asymmetry excludes an estimation of the model parameters by standard methods. We have therefore developed an indirect simulated inference method that we have implemented after having studied its performance from simulations. We have also studied ARFIMA threshold models which allow to model simultaneously threshold effects in the fractional integration parameter and the autoregressive parameters. The threshold effect is introduced separately and then jointly in the long memory parameter and in the autoregressive parameters. We have proposed a procedure to test both types of threshold effects simultaneously by showing how tests conducted separately to analyze each of the two types of threshold effect could lead to spurious results. The application of the methodology developed in our thesis shows that the joint test is decisive to validate the presence of threshold effects when the individual tests do not allow to conclude.