Abstract This paper is concerned with approximating nonlinear time series by an artificial neural network based on radial basis functions. A new data-driven modelling strategy is suggested for the adaptive framework by combining the statistical techniques of forward selection, cross validation and information criterion. The proposed method is fast and simple to implement while avoiding some typical difficulties such as estimation and computation of nonlinear econometric models. Two applications are provided to illustrate the benefits of using the neural network method in time series analysis. First, the proposed modelling method is applied to a neural network test for neglected nonlinearity in conditional mean of univariate time series. A simulation study is carried out to show how the size of the test is improved in finite samples. Further, the new test is compared with alternative popular tests to demonstrate its superior power performance using a variety of nonlinear time series models. Second, the proposed method is applied to obtain a nonlinear forecasting model for daily S&P 500 returns. Forecast accuracy is compared with that of a linear model and other neural network models used in the literature.

中文翻译：

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非线性时间序列分析的神经网络方法

摘要本文研究了一种基于径向基函数的人工神经网络逼近非线性时间序列的方法。通过结合前向选择，交叉验证和信息准则的统计技术，为自适应框架提出了一种新的数据驱动建模策略。该方法实现快速，简便，同时避免了一些典型的困难，例如非线性计量经济模型的估计和计算。提供了两个应用程序来说明在时间序列分析中使用神经网络方法的好处。首先，将所提出的建模方法应用于单变量时间序列条件均值中被忽略的非线性的神经网络测试。进行了仿真研究，以显示如何在有限样本中改善测试的大小。进一步，将该新测试与其他流行测试进行比较，以使用各种非线性时间序列模型证明其卓越的电源性能。其次，将所提出的方法应用于获得标准普尔500每日收益的非线性预测模型。将预测准确性与文献中使用的线性模型和其他神经网络模型进行了比较。