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：本文引入了基于支撑的傅里叶延拓与回归（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或趋势线。首先概述了基于支撑的傅里叶延拓（BFC）和 BFCR 算法，随后讨论了 BFCR 的特性，并演示了如何有效地利用 BFCR 趋势线在任意一维数据集内部及边缘进行异常检测。最后，概述并讨论了使用 BFCR 进行异常检测时可能出现的潜在问题以及可能的缓解技术。所有源代码和示例数据集均已引用或可通过 GitHub 获取，且所有相关代码完全使用 Python 编写。