This paper aims to introduce a multiple output artificial neural network as a tool for testing nonlinearity in multivariate time series. Unlike previous studies, we use weights from trained networks to determine the support space for defining random weights of nonlinear regressors and obtain greater power. Moreover, this paper uses two hidden layer neural networks for univariate and multivariate nonlinearity tests. Simulation results show that the proposed method is more powerful than the Terasvirta, Lin, and Granger test in most functional forms and more powerful than the Tsay test in some cases. Taking into account univariate and multivariate time series, the neural network approach is much more powerful than both these tests.

中文翻译：

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神经网络用于单变量和多变量非线性测试

本文旨在介绍一种多输出人工神经网络作为测试多元时间序列非线性的工具。与以前的研究不同，我们使用来自训练网络的权重来确定定义非线性回归随机权重的支持空间，并获得更大的功效。此外，本文使用两个隐藏层神经网络进行单变量和多变量非线性测试。仿真结果表明，该方法在大多数功能形式上比Terasvirta，Lin和Granger测试更强大，并且在某些情况下比Tsay测试更强大。考虑到单变量和多元时间序列，神经网络方法比这两个测试都强大得多。