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There are many resistance and support indicators. Fibonacci, pivots, channels, moving averages, trend lines, etc., can be counted in the category of resistance and support.

The question is: has anyone used mathematical methods to prove whether the statement of "resistance, support" is reliable?

While there isn't a definitive answer to whether resistance and support indicators are reliable, there have been numerous studies and analyses conducted to evaluate their effectiveness. Some studies have shown that support and resistance levels can have predictive power, while others have found mixed or inconclusive results.

Here are a few studies on this topic:

  1. Osler, C. L. (2000): "Support for Resistance: Technical Analysis and Intraday Exchange Rates," Economic Policy Review, Federal Reserve Bank of New York, 6(2), pp. 53-68. Link to paper

    Osler's study found that support and resistance levels derived from technical analysis techniques, such as head-and-shoulders patterns and double tops/bottoms, were statistically significant and had predictive power for intraday exchange rates.

  2. Lo, A. W., Mamaysky, H., and Wang, J. (2000): "Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation," The Journal of Finance, 55(4), pp. 1705-1765. Link to paper

    In this paper, the authors present a framework for evaluating the effectiveness of technical analysis techniques, including support and resistance levels. They found that certain technical trading rules had predictive power, but the results were not strong enough to overcome transaction costs.

  3. Menkhoff, L., & Taylor, M. P. (2007): "The Obstinate Passion of Foreign Exchange Professionals: Technical Analysis," Journal of Economic Literature, 45(4), pp. 936-972. Link to paper

    This comprehensive survey of the literature on technical analysis in foreign exchange markets found mixed evidence for the effectiveness of support and resistance levels. The authors concluded that further research was needed to understand the conditions under which these techniques may be useful.

It's worth noting that support and resistance levels are not foolproof, and their effectiveness can depend on factors such as market conditions, the specific asset being traded, and the time horizon of the analysis. Additionally, much of the success of technical analysis, including support and resistance levels, can be attributed to the self-fulfilling nature of these concepts. If a large number of traders believe in and act upon these levels, they can indeed influence price behavior.

In conclusion, while there is some evidence to suggest support and resistance levels can be effective in certain circumstances, their reliability is not universally proven. As with any trading strategy, it's essential for traders to manage risk and use a combination of tools and techniques to develop a comprehensive approach to the markets.

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