Stochastic price processes can generate paths that appear to trend or cycle, so visual resemblance to a trading pattern alone does not establish exploitable predictability.

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for all the world, appear predictable and bankable. But a financial market is especially prone to such statistical mirages. My mathematical models can generate charts that—purely by the operation of random processes—appear to trend and cycle. They would fool any professional “chartist.” Likewise, bubbles and crashes are inherent to markets. They are the inevitable consequence of the human need to find patterns in the patternless. ### Rule V. Market time is relative. There is what one may call a relativity of time in financial markets. Early on, but mostly when developing the multifractal model, I came to think of markets as operating on their own “trading time”—quite distinct from the linear “clock time” in which we normally think. This trading time speeds up the clock in periods of high volatility, and slows it down in periods of stability. Mathematically, I can write an equation showing how one time frame relates to the other and use it to generate the same kind of jagged price series that we observe in real life. This is how the successful forgery shown among the previous charts was made. It is almost as if dealing rooms need, besides the standard row of wall-clocks showing the time in Tokyo, London, and New York, a fourth clock showing “Greenwich Market Time.”

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That volatility varies because the pricing mechanism varies. Wrong. A striking example. My analysis of cotton prices over the past century shows the same broad pattern of price variability at the turn of the last century, when prices were unregulated, as there was in the 1930s when prices were regulated as part of the New Deal. Rule 4. Markets Mislead Patterns are the fool's gold of financial markets. The power of chance suffices to create spurious patterns and pseudo-cycles that, for all the world, appear predictable and bankable but a financial market is especially prone to such statistical mirages my mathematical models can generate charts that, purely by the operation of random processes, appear to trend and cycle. They would fool any professional chartist. Likewise, bubbles and crashes are inherent to markets. They are the inevitable consequence of the human need to find patterns in the patternless. Rule 5. Market time is relative.