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In this paper we study automatically recognized trends and investigate theirstatistics. To do that we introduce the notion of a wavelength for time seriesvia cross correlation and use this wavelength to calibrate the 1-2-3 trendindicator of Maier-Paape [Automatic One Two Three, Quantitative Finance, 2013]to automatically find trends. Extensive statistics are reported for EUR-USD,DAX-Future, Gold and Crude Oil regarding e.g. the dynamic, duration andextension of trends on different time scales.

Empirical Study of the 1-2-3 Trend Indicator