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# What is a Hurst Exponent?

Article Details
• Written By: Danielle DeLee
• Edited By: Heather Bailey
2003-2018
Conjecture Corporation
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The Hurst exponent is a measurement of persistence in trends. It is used in data prediction to modify random series. According to some financial theorists, stock prices fluctuate randomly. If this is the case, then estimating the Hurst exponent is important in predicting future prices because it describes trends within the seemingly random movements.

The Hurst exponent can take any value between zero and one. If it is greater than 0.5, the trend is persistent, which means that an increase is likely to be followed by another increase, while decreases are likely to be followed by decreases. An exponent lower than 0.5 indicates anti-persistence, which means that a movement in one direction makes a movement in the other direction more likely. If the Hurst exponent is close to 0.5, then the pattern is random, and no movement predicts the next.

In finance, the concept of the Hurst exponent is relevant for predicting financial data like stock prices. Some investors believe in patterns in stock prices. They try to predict the motion of a stock by looking at graphs of its past performance. One example of a stock pattern is “head and shoulders:” a stock rises initially because of initial enthusiasm, and then when interest wanes investors move in to buy low. After the price reaches its peak and begins to fall, it rallies once more and then settles to a fairly stable level.

The random walk theory, proposed by Maurice Kendall in 1953, dismisses the importance of patterning in stock prices. The theory is based on an image of a drunken man standing at a lamp post. With every step, he has an equal probability of stepping in any direction, so after any amount of time the most reasonable place to look for him is at the place where he started.

The stock market, according to the theory, is like this man. It may fluctuate wildly in one direction, but it tends to revert to a central position. The stock market, however, tends to go up. The random walk theory includes a prediction of upward trending over time to accommodate historical stock price data.

If random walk is correct, then knowledge of the Hurst exponent is important in stock analysis. Investors could observe a stock’s recent behavior and make predictions about its future movements based on the strength of persistence in the market. The exponent must be estimated for any series, so stock analysis would remain an imprecise art.