overwhelming statistical confidence for each of the patterns using the data set of all S&P 500 stocks daily for the five-year period 1992–1996. Among the most basic ideas of conventional technical analysis is that a trend, once established, tends to continue. However, testing for this trend has often led researchers to conclude that stocks are a random walk. One study, performed by Poterba and Summers, found a small trend effect that was too small to be of trading value. As Fisher Black noted, "noise" in trading price data makes it difficult to test hypotheses. One method for avoiding this noise was discovered in 1995 by Caginalp and Constantine who used a ratio of two essentially identical closed-end funds to eliminate any changes in valuation. A closed-end fund (unlike an open-end fund) trades independently of its net asset value and its shares cannot be redeemed, but only traded among investors as any other stock on the exchanges. In this study, the authors found that the best estimate of tomorrow's price is not yesterday's price (as the efficient-market hypothesis would indicate), nor is it the pure momentum price (namely, the same relative price change from yesterday to today continues from today to tomorrow). But rather it is almost exactly halfway between the two. Starting from the characterization of the past time evolution of market prices in terms of price velocity and price acceleration, an attempt towards a general framework for technical analysis has been developed, with the goal of establishing a principled classification of the possible patterns characterizing the deviation or defects from the random walk market state and its time translational invariant properties. The classification relies on two dimensionless parameters, the Froude number characterizing the relative strength of the acceleration with respect to the velocity and the time horizon forecast dimensionalized to the training period. Trend-following and contrarian patterns are found to coexist and depend on the dimensionless time horizon. Using a renormalisation group approach, the probabilistic based scenario approach exhibits statistically significant predictive power in essentially all tested market phases. A survey of modern studies by Park and Irwin showed that most found a positive result from technical analysis. In 2011, Caginalp and DeSantis have used large data sets of closed-end funds, where comparison with valuation is possible, in order to determine quantitatively whether key aspects of technical analysis such as trend and resistance have scientific validity. Using data sets