The Noah effect describes abrupt large changes, while the Joseph effect describes temporal dependence; they are distinct features that can coexist in a financial process rather than interchangeable names for volatility.

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Behind it is the influence of long-range dependence and an otherwise random process, or, put another way, a long-term memory, through which the past continues to influence the random fluctuations of the present. I call these two distinct forms of wild behavior the Noah effect and the Joseph effect. They are two aspects of one reality. One, the other, and usually both, can be read in many financial charts. They mix together like two primary colors. The red of one blends with the blue of the other to produce an infinite palette of purples and violets. Evidence so far suggests each market, wheat, cotton, dollar, yen, S&P or GM, may have a different hue, a different mix of the two forms of wildness. To measure these two effects, I developed new statistical tools. Some focus on alpha, the index mentioned earlier. A low alpha market would be risky, prone to wild price swings. A market with higher alpha differs less from the classic coin tossing market.

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The cards are all out of sequence now. Whatever Joseph effect was originally present is scrambled out of existence. Only the face value of the cards, the relative size of the events, or NOAH effect, remains visible before and after the shuffling. To complete the test, just compare the deck before and after shuffling. If there is a difference, it must be due to the long-term dependence in the original data. The precise sequence must have been important in the original data, and the degree of that importance can be measured. If there is no before and after difference, then whatever dependence was originally present must have been negligible. a measure for long-term dependence. Now as fate would have it, under some circumstances these two effects are so closely interrelated that h is simply equal to one over alpha. Take the coin tossing case. Its h is one half and its alpha is two. Mathematically, the relation between the two effects is quite profound.