Costationary Whitenoise Processes and Local Stationarity Testing

This paper provides three main contributions to the study of multiscale locally stationary processes. We introduce a new class of stochastic processes that we call Costationary Whitenoise (CWN) processes, and propose a theoretical framework to estimate their underlying parameters. We use this setup to devise a non-parametric approximation method for the unknown distribution function of unobservable innovations. We address this task by using CWN order statistics to approximate the quantiles of unobservable innovations. Finally, we use the above frameworks to derive a non-parametric bootstrap stationarity test for multiscale locally stationary processes. The finite sample performances of this test are assessed through simulations showing that our method successfully controls rejection rates for stationary and locally stationary processes with both Gaussian and Student-t distributed innovations. Finally, by applying our test to equity returns, we are able to associate the presence of non-stationarities to the occurrence of economic shocks.