Testing for a Unit Root in the Logistic STAR Framework with a Fourier Function: an Application to the Unemployment Rates

Veli Yilanci
Statistika, 106(1): 92–103
https://doi.org/10.54694/stat.2025.25

Abstract
This paper introduces the Fourier-LSTAR (FLSTAR) test, which addresses the critical challenge of testing for unit roots in time series characterized by both unknown structural breaks and nonlinear dynamics. We propose and evaluate this novel unit root test, which integrates a logistic smooth transition autoregressive (LSTAR) model with a flexible Fourier function to capture such complexities. Critical values and simulation properties of the test are derived, demonstrating its robustness and stable performance across varying conditions. We apply the FLSTAR test to annual unemployment rates for CIVETS countries and find that unemployment hysteresis holds for most nations, except Colombia, where the plucking model is applicable. These results highlight the heterogeneous nature of unemployment dynamics in emerging economies and underscore the importance of employing robust testing procedures that accommodate data complexities to avoid misleading policy inferences. The FLSTAR test demonstrates superior power and size properties in Monte Carlo simulations, offering a valuable new tool for empirical researchers.

Keywords
Unemployment hysteresis, Unit Root Test, Fourier-LSTAR, structural breaks, nonlinear dynamics, CIVETS countries