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

This paper 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 both 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 test exhibits satisfactory size properties, with the rescaled version of the Lagrange Multiplier test statistics demonstrating the best performance in most simulation settings. The sequential procedure is also applied to two empirical cases, the US monthly interest rates and Icelandic river flows. In both cases, the detected number of regimes aligns well with the existing literature.