Abstract
This chapter presents new linearity tests in smooth transition logistic time series models allowing for parameter instability. Building on work by Lundbergh and Teräsvirta (2003), Vogelsang (1998), and Harvey and Leybourne (2007), our linearity tests are constructed in such a way that they do not depend on the order of integration of the time series under consideration. As an important practical implication, this means that critical values from standard distributions can be used when testing for linearity, regardless of whether the process is linear I(0) or linear I(1). In fact, for many macroeconomic and financial time series, it is not evident whether a linear I(0) or linear I(1) process a priori should serve as the null hypothesis. Asymptotic properties of the tests are studied and consistency is shown. Monte Carlo simulations shed light on the tests’ empirical performance in finite samples. The tests, as well as its heteroskedasticity-robust wild bootstrap versions, are applied to 43 macroeconomic and financial US time series. Evidence of both nonlinearities and structural changes is found.