A bootstrap test for threshold effects in a diffusion process

This paper proposes a bootstrap testing approach based on an approximate maximum likelihood method to discern whether a diffusion process is linear or whether there are threshold effects in the drift, the diffusion term or in both. It complements an alternative method based on the least-squares estimator which focuses on threshold effects in the drift. Monte Carlo simulations illustrate that the proposed testing approach is able to detect the source of the non-linearity. Two empirical applications show the importance of modeling threshold effects in the diffusion instead of the drift.