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.

翻译：本文提出了一种用于确定非线性多元自回归模型中体制数量的序贯检验程序。该程序基于线性检验和无附加非线性检验，适用于多元平滑转换自回归模型和门限自回归模型。我们通过模拟研究评估了所提出检验在小样本下的有限样本性质。研究结果表明，该检验具有令人满意的尺度性质，其中拉格朗日乘数检验统计量的重标度版本在大多数模拟设定中表现出最佳性能。该序贯程序还应用于两个实证案例：美国月度利率和冰岛河流流量。在这两个案例中，检测到的体制数量与现有文献的结论高度吻合。