Title: Multiscale asymptotics and stationarity test for stable locally stationary processes
Authors: Alessandro Cardinali - University of Plymouth (United Kingdom) [presenting]
Abstract: Three main contributions to the study of multiscale locally stationary processes are provided. We first establish, assuming a (possibly nongaussian) stable marginal process distribution, the asymptotic independence and weak convergence for the multiscale periodogram and some related functionals. We then use this theoretical framework to propose a nonparametric approximation method for the unknown distribution function of unobservable LS innovations. We address this task by introducing a new method to produce pseudo innovations whose empirical CDF can be used to approximate the theoretical CDF of unobservable innovations. Finally, we use the above frameworks to derive a nonparametric bootstrap stationarity test for multiscale LS processes. The finite sample properties of this test are assessed through simulations showing that our method successfully controls rejection rates for processes having either Gaussian or nongaussian innovations. An empirical analysis based on exchange rates returns shows that, when used on a rolling window, our test can also help to successfully identify well known economic shocks.