A doubly-threshold diffusion model: one threshold in drift, one in diffusion

Abstract This paper proposes a novel threshold diffusion model in which the drift and diffusion components undergo regime shifts at distinct thresholds. Specifically, the drift and diffusion terms are governed by separate threshold values. This doubly threshold specification offers greater flexibility for capturing asymmetric dynamics in both the conditional mean and volatility. To estimate the model, we develop an approximate maximum likelihood estimation (AMLE) procedure that remains computationally tractable despite the model’s structural complexity. Monte Carlo simulations demonstrate that the proposed estimator is both consistent and efficient, and that standard information criteria—the Akaike information criterion (AIC), Bayesian information criterion (BIC), and Hannan–Quinn information criterion (HQIC)—are useful for distinguishing between models with shared versus separate thresholds. Empirical applications to United States (U.S.) Treasury interest rate data—including the 3-Month Treasury Bill and the 10-Year/3-Month yield spread–further support the proposed framework. The results reveal structural asymmetries that are better captured by allowing distinct threshold mechanisms in the drift and diffusion terms.