In this work, the concept of Braced Fourier Continuation and Regression (BFCR) is introduced. BFCR is a novel and computationally efficient means of finding nonlinear regressions or trend lines in arbitrary one-dimensional data sets. The Braced Fourier Continuation (BFC) and BFCR algorithms are first outlined, followed by a discussion of the properties of BFCR as well as demonstrations of how BFCR trend lines may be used effectively for anomaly detection both within and at the edges of arbitrary one-dimensional data sets. Finally, potential issues which may arise while using BFCR for anomaly detection as well as possible mitigation techniques are outlined and discussed. All source code and example data sets are either referenced or available via GitHub, and all associated code is written entirely in Python.

翻译：本文提出了支撑傅里叶延拓与回归（BFCR）的概念。BFCR是一种新颖且计算高效的方法，用于在任意一维数据集中寻找非线性回归线或趋势线。首先概述了支撑傅里叶延拓（BFC）和BFCR算法，随后讨论了BFCR的性质，并展示了如何将BFCR趋势线有效用于任意一维数据集内部及边缘位置的异常检测。最后，阐述并讨论了使用BFCR进行异常检测时可能出现的潜在问题及其缓解技术。所有源代码和示例数据集均通过GitHub提供或给出参考文献，且所有相关代码均完全使用Python编写。