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Does Technical Analysis Work?, YEUNG et al, 2002
Yeung et al. found that using Fibonacci Retracements failed to work.
When trading cost is factored in, only Bollinger Bands seem to have statistical significance.

Misconceptions about the Golden Ratio, Markowsky, 1992
The golden ratio has captured the popular imagination and is discussed in many books and articles. Generally, its mathematical properties are correctly stated, but much of what is presented about it in art, architecture, literature, and esthetics is false and seriously misleading. Unfortunately, these statements about the golden ratio have achieved the status of common knowledge and are widely repeated. This paper discusses some of the most commonly repeated misconceptions.
The cult of the golden ratio, Gardner, 1994
The efforts of phi cultists to find golden rectangles in architecture, painting, and sculpture reached absurd heights. My discussion here of what can be called pseudomathematics is based mainly on George Markowsky's sensible paper, "Misconceptions About the Golden Ratio".
Fibonacci Flim-Flam
The internet is cluttered with "educational" sites that have documents on "Fibonacci numbers in nature" and similar topics. A search of the internet, or your local library, will convince you that the Fibonacci series has attracted the lunatic fringe who look for mysticism in numbers. You will find fantastic claims. Of course all of this is patently nonsense.
Fibonacci and the Financial Revolution , GOETZMANN, 2003
"This paper examines the contribution of Leonardo of Pisa [Fibonacci] to the history of financial mathematics. Evidence in Leonardo's Liber Abaci (1202) suggests that he was the first to develop present value analysis for comparing the economic value of alternative contractual cash flows. He also developed a general method for expressing investment returns, and solved a wide range of complex interest rate problems. The paper argues that his advances in the mathematics of finance were stimulated by the commercial revolution in the Mediterranean during his lifetime, and in turn, his discoveries significantly influenced the evolution of capitalist enterprise and public finance in Europe in the centuries that followed. Fibonacci's discount rates were more culturally influential than his famous series".
Fibonacci - The Man and the Markets, Douglas, S&P's Economic Research Paper, 2001
"Everybody with exposure to the commentary of technical analysts has come across the name Fibonacci or its common abbreviation, Fibo. We hear of Fibonacci retracements, Fibonacci levels, Fibonacci targets and Fibonacci fans among others. These Fibonacci comments are often supplied with a number such as 0.382 or 0.618. We are told that Fibonacci can help to forecast support and/or resistance as well as to suggest potential target levels for existing trends. Some analysts even use Fibonacci in efforts to calculate the timing of future market turning points. While there is little empirical evidence to support the statistical reliability of the regular formation of many of the relationships mentioned above, observations over time have shown that these relationships do appear often enough to be considered a useful part of the technical analysts' toolbox".
Biased Judgments on What Moves Stock Prices: How Financial Analysts Perceive Macroeconomic, Political News and Technical Analysis Signals, ZIELONKA, 2000
"More than 60% of the respondents market the following technical signals as having the predictive value: MACD, RSI, Ultimate, ROC, Elliott waves and Fibonacci proportions".