A Stationarity Test in the Presence of an Unknown Number of Smooth Breaks

TLDR

Macroeconomic variables often exhibit structural breaks of unknown number, duration, and form, making proper modeling essential to avoid misspecification. The paper develops a stationarity test that approximates unknown structural breaks via a selected Fourier frequency component. The test uses a Fourier-based frequency component to approximate structural breaks and is applied to post‑Bretton Woods exchange rates. The test performs well on gradual breaks and demonstrates reasonable power, as shown in an application to post‑Bretton Woods exchange rates. Abstract.

Abstract

Abstract. Macroeconomic variables have been shown to display a wide variety of structural breaks of unknown number, duration and form. This poses a challenge since improperly modelled breaks can result in a seriously misspecified model. In this paper, we develop a new test for stationarity that approximates the unknown form of structural breaks using a selected frequency component from a Fourier approximation. Our proposed test performs quite well when breaks are gradual, and shows reasonable power. The appropriate use of the test is illustrated by examining real exchange rates in the post‐Bretton Woods period.