A sequential test procedure for the choice of the number of regimes in multivariate nonlinear models

This article proposes a sequential test procedure for determining the number of regimes in nonlinear multivariate autoregressive models. The procedure relies on linearity and no additional nonlinearity tests for multivariate smooth transition and threshold autoregressive models. We conduct a simulation study to evaluate the finite-sample properties of the proposed test in small samples. Our findings indicate that the sequential procedure is capable of correctly identifying the number of regimes in the presence of both smooth and abrupt regime changes. The sequential procedure is also applied to real-world data. In the analysis of US monthly interest rates, the test identifies multiple regimes, confirming that the adjustment of interest rates toward their long-run equilibrium is state-dependent. Finally, when applied to Icelandic river flows, the procedure identifies a three-regime structure consistent with hydrological cycles.