Testing and Modeling Threshold Autoregressive Processes
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门限自回归过程的检验与建模
- 研究问题
- 如何为门限自回归模型建立便于应用的建模流程，同时检验门限非线性、选择门限变量并确定潜在门限的位置？
- 方法与思路
- 作者基于预测残差构造回归检验统计量，并结合图形工具识别门限数量与位置，再据此建立门限自回归模型。
- 材料陈述的贡献
- 摘要称，本文推导检验统计量的性质，并通过模拟和实际资料评价有限样本表现；与一种既有检验相比表现良好。
- 阅读关注点
- 应核对预测残差的构造、检验分布与适用条件、门限搜索如何实施，以及模拟比较是否涵盖不同非线性和样本规模。
- 阅读边界
- 依据稿件版本未注明的索引摘要；检验条件、模拟设定及比较数值未说明，不能推断普遍优越性或后续刊本变化。
原文摘要
The threshold autoregressive model is one of the nonlinear time series models available in the literature. It was first proposed by Tong (1978) and discussed in detail by Tong and Lim (1980) and Tong (1983). The major features of this class of models are limit cycles, amplitude dependent frequencies, and jump phenomena. Much of the original motivation of the model is concerned with limit cycles of a cyclical time series, and indeed the model is capable of producing asymmetric limit cycles. The threshold autoregressive model, however, has not received much attention in application. This is due to (a) the lack of a suitable modeling procedure and (b) the inability to identify the threshold variable and estimate the threshold values. The primary goal of this article, therefore, is to suggest a simple yet widely applicable model-building procedure for threshold autoregressive models. Based on some predictive residuals, a simple statistic is proposed to test for threshold nonlinearity and specify the threshold variable. Some supplementary graphic devices are then used to identify the number and locations of the potential thresholds. Finally, these statistics are used to build a threshold model. The test statistic and its properties are derived by simple linear regression. Its performance in the finite-sample case is evaluated by simulation and real-world data analysis. The statistic performs well as compared with an alternative test available in the literature. Further applications of threshold autoregressive models are also suggested, including handling heterogeneous time series and modeling random processes with periodic variances whose periodicity is not fixed. The latter phenomenon is commonly encountered in practice, especially in econometrics and biological sciences.