Since their introduction in 1937 by Neyman, smooth tests of order K proved to be a very effective tool to test the adequacy of a distribution to some data. In this work, we show how it is possible to adapt the strategy of Neyman to the particular context of dependent data by constructing a test of normality of the disturbances of an ARMA model with unknown mean (ARMA processes are a classical tool in the toolbox of every statistician and are widely used to model temporal phenomena). A Bayesian criterion is also applied to estimate the order K of the smooth test, and an approximation of order s of the test statistics's distribution is provided. In addition, simulations show that this test behaves very well in terms of power, against its direct competitors. This work is then extended to the multivariate context of VARMA models and a link with the popular test of Jarque and Bera is also established. Two examples end the talk, including one which comes from fMRI experiments on which methods of independent component analysis are also applied.
Note: Slides in English and talk in French