A Multi-threshold Change Plane Autoregressive Model

This paper proposes a novel multi-threshold change plane autoregressive model with an unknown number of regimes, where the transition between regimes is governed by multiple threshold variables. We introduce an estimation approach that combines adaptive group fused Lasso with mixed-integer linear programming to simultaneously estimate the number of regimes and model parameters. Asymptotic properties of the estimators are established, which show that the proposed threshold estimators achieve a faster convergence rate than that of existing smoothed method. Simulation studies confirm the method’s effectiveness in finite samples. Additionally, an application to U.S. real GNP data reveals insightful findings and demonstrates a marked gain in forecast accuracy over existing alternatives.