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.