Non-linear unit root testing with arctangent trend: Simulation and applications in finance

Abstract

We consider arctangent as the logistic function and compute the asymptotic critical values of the related non-linear unit root test via Monte Carlo simulation. While doing so, we got inspiration from some pioneering articles and use first-order Taylor approximation. We observe that this newly proposed test exhibits higher power than some well-known linear and non-linear tests. We apply our test to some stock indexes and find out that a non-linear arctangent trend can be at stage, rather than a linear unit root process.