Fibonacci Retracements and Extensions
Fibonacci tools draw correction and extension levels from Fibonacci ratios (23.6%, 38.2%, 61.8%, 78.6%) and Dow theory's 50% level; they ship with charting software and appear in market commentary. Murphy covers them in chapter 13 of Technical Analysis of the Financial Markets. Tested on the Dow Jones from 1915 to 2003, these ratios (except 23.6%, which the test leaves out) occur no more often than chance (Batchelor and Ramyar, 2006).