发表机构
Paula and Gregory Chow Institute for Studies in Economics; Xiamen University; Department of Statistics and Data Science Tsinghua University; Department of Statistics, London School of Economics（Paula和Gregory Chow经济研究学院; 厦门大学; 清华大学统计与数据科学系; 伦敦政治经济学院统计系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为非技术性注记，回顾阈值原理在时间序列分析中的现代化作用，类比人工神经网络，追溯其在计量经济学中的采用与平滑扩展，警示误用，并探讨其在条件方差及非实值领域的应用，强调其持久方法论意义。
AI 中文摘要
这主要是一篇非技术性的注记，反映了作者对时间序列分析的哲学观点和个人见解，为简洁起见，参考文献仅限少数代表性作品。阈值原理由Tong（1990）正式提出，通过引入一系列子系统来建模复杂的非线性动态，使时间序列分析现代化。我们探讨了阈值原理的概念架构，并与机器学习中的人工神经网络进行了类比和对比。我们追溯了阈值自回归在计量经济学中的有影响力采用。我们考察了一个平滑扩展，即由Chan和Tong（1986）引入的平滑阈值自回归，该模型后来在计量经济学文献中得到推广。我们提出警示，以帮助计量经济学用户避免误用此模型。此外，我们研究了如何系统地将阈值原理应用于条件方差，以实现有意义的波动率分类。最后，我们提及了阈值原理在非实值领域的一些现代应用，强调了其作为阈值自回归所体现的持久半个世纪的方法论意义。
英文摘要
This is mostly a non-technical note, reflecting the author's philosophy and personal views on time series analysis, with references limited to only a few representatives for brevity. The Threshold Principle, formally announced in Tong (1990), modernised time series analysis by introducing a collection of sub-systems to model complex nonlinear dynamics. We explore the conceptual architecture of the Threshold Principle drawing parallels and contrasts with artificial neural network in machine learning. We trace the influential adoption of Threshold Autoregression in econometrics. We examine a smooth extension, namely the smooth threshold autoregression introduced by Chan and Tong (1986) that was later popularized in the Econometric literature. We sound cautions to help econometric users to avoid misuse of this model. Furthermore, we examine how we can systematically apply the Threshold Principle to conditional variance to enable meaningful volatility classification. Finally, we mention some of the modern applications of the Threshold Principle to non-real-valued domains, underscoring its enduring half-century methodological significance as embodied in the threshold autoregression.
