Unit Root Testing in Multiple Smooth Break Models with Nonlinear Dynamics

Abstract

This work builds a flexible model accommodating nonlinear dynamics around a trend function with multiple (up to m) gradual shifts. Such a model is suitable for capturing the behavior of many post World War II economic time‐series subject to the onset of external causes such as oil crises, financial crises, technology changes and regulatory changes. Deriving unit root tests in this nonlinear model is of particular interest. In fact, the options of a general trend specification and nonlinear dynamics are critical to remedy unit root tests not being biased toward a non‐rejection of a unit root hypothesis and prevents the first‐differences of a series from being used too often. An asymptotic theory for the unit root tests is also established. The unit root tests are applied to G7 industrial production series, and evidence in favor of nonlinear trend ‘stationary’ models is found in a majority of the cases. The merits of the new model are further demonstrated in an estimation exercise for the US industrial production series, and evidence of four gradual shifts in the trend, different growth patterns for different periods, and business cycle asymmetries is found.