Normal diffusion laws can be used to predict the probability of finding a stock at a certain price, after N steps into the future, if price movement follows a random walk.
Random walk assumptions do NOT predict that support or resistance “lines” will have any effect. Parallax has been testing this assumption by isolating and testing price action following contact with these lines. We seek to find out how much reality deviates from random assumptions and then map these deviations.
Statistical tests done on horizontal support and resistance lines revealed a 65% probability of price being found above support (below resistance) when price starts out above and nearby. This figure shows the probability map with this boundary correction.
Parallax has extended our research to channel lines, which may be sloped at any angle. This figure shows what a probability map might look like with a reflecting support line that is also attracting price toward it.
The existence of non-random geometric structure in price charts is evident at all scales. The example shown below was taken on January 6th, 2023, of the hourly S&P 500 cash index. The circled areas show price repeatedly contacting the same trendline over and over again. This behavior is not random. The presence of geometrical structures such as this is an emergent property fully explained by Complexity Theory. The attraction and repulsion from key price levels is one of the simple “rules” followed by investment “agents”. Our channel search tool finds these non-random trend channel structures (p<0.001) in price charts at any scale and identifies actionable events related to them, such as reflections and breakouts.