This paper describes a method for estimating regime switches in non-monotonic relationships, using polynomial regressions. Data from the UK financial services industry are used to illustrate the technique. The methodology provides a means of statistically ascertaining the existence of turning points, as well as a means of locating them, should they exist. While the methodology is most suited to applications that involve cross-sectional data, it may also be useful in short-horizon time series turning point prediction.