Communication à un séminaire :
Several classical time series models can be written as a regression model between the components of a strictly stationary bivariate process. Some of those models, such as the ARCH models, share the property of proportionality of the regression function and the scale function, which is an interesting feature in some econometric and financial models. In this article, we present a procedure to test for this feature in a non-parametric context. The test is based on the difference between two non-parametric estimators of the distribution of the regression error. Asymptotic results are proved and some simulations are shown in the paper in order to illustrate the finite sample properties of the procedure. We also study an extension of this paper to the case where the relation between the regression and the scale function has a given parametric form. This extension has important applications in the empirical finance literature.
(This is joint work with Holger Dette, Juan Carlos Escanciano and Juan Carlos Pardo-Fernandez.)
Econométrie et statistique