  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.
