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# Hurst exponent

Discussion in 'Trading' started by lojze, Jul 19, 2002.

1. ### lojze

In the 1930s, British hydrologist H.E. Hurst examined ancient records from the Nile River Delta and discovered that, while he could not predict the river's water level at any given time, he could predict trends in water level. The statistic he developed to predict these trends, known as the Hurst exponent, is now used to evaluate trends in stock prices.

The Hurst exponent (H) is a number between zero and one, derived from a formula that analyzes the variation in a particular value (like water level or stock price) over specified intervals of time. For example, an investment analyst might look at an interval of one month and use the Hurst exponent to determine the likelihood that a stock will behave the same way during the following month.

When H lies between 0 and 0.5, the stock price reverses direction from the previous interval. When H = 0.5, the stock price behaves randomly, fluctuating up and down from interval to interval. Analysts are most interested in H values between 0.5 and 1, which indicate that the stock price will continue in the same direction as the previous interval.

Anybody knows this? Uses this?

Lojze

2. ### JS11374

The H-Exponent does not work that way. It is simply an indication to see whether a time-series is random, that is, whether it exhibits the behaviors of Brownian random walk. It does it have any statistically significant value when it comes to predict reversals.

3. ### dotslashfuture

well, that still sounds like it might be a usefull screening tool. I do stock scans at home on daily data to try to get lists of interesting stocks. I could also scan to see how much pure randomness is in individual stocks. It might be an addition to looking just at volatility.

4. ### ArchAngel

As I recall, the Hurst was interpreted as:

1/2 = purely random Brownian motion of the series

>1/2 = the more above 1/2 the greater the tendency of the series to follow through in its current direction (i.e., trendiness)

<1/2 = the more below 1/2 the greater the tendency of the series to revert back toward its mean (i.e., anti-trendiness)

Technically not a statistical indicator that a reversal is about to (or not about to) happen, just a high level reading of the characteristic of the data series

5. ### dotslashfuture

so I would interpret a reading dead equal to 1/2 or very close as something totally random ? In that case I wouldn't touch it. Does that make sense according to the theory ?

6. ### JS11374

It's possible to use it as a method to screen for trend (which is rather incorrect.... one should really use the word "cycle" here). However, keep in mind that just screening for 0.5 is pointless. There must be a method to test statistical significance of that H-E measurement. That is, does 0.52 signify random walk, or does 0.6 signfiy cyclic behavior? Simply set a number (say 0.55) as a threshold is a meaningless experience. I suggest you try to find a book called "Fractal Market Analysis." Lots of math, but it does introduce a significance test to validate the H-E.

You might also check out "Chaos and Order in the Capital Markets" by Edgar Peters which has some explanation about H. ArchAngel is right both in terms of the meanings of different values of H and in terms of its use in trading. H runs from 0 to 1, with the two halves on either side of H=0.5 having the interpretation that he presented. Because H is not an indicator, it is not something that tells you about the right-edge of the chart. Instead, it is a property of the time series as a whole that MIGHT be useful at picking a trading system.

But like JS11374, said, you need to develop confidence intervals on the values, before using it to decide the type of trading system to suit the market that you are in. Although, I have never run the numbers, I would fear that H values would have unpleasantly large confidence intervals. The Hurst exponent calculation looks at the behavior of High-to-Low extrema over many timeframes. Because markets tend to have heavy-tailed distributions, the distribution of High-to-Low values is wide. And so Hurst exponent would tend to have a broad distribution.

H might be useful, might not, but its worth thinking about in times of changing markets.

8. ### JS11374

Another thing to keep in mind that Hurst, like just about everything, is a lagging indicator. Even if the series is at 0.99999+, does that mean you can safely run with the trend. yes and no. yes as in, it's clearly within your confidence interval. No, as in there is no guarantee whatsoever, if factor in the --NEXT-- set of periods that Hurst wouldn't drop down to 0.00000....01.

... trading is 90% psycholgy and 10% analysis.

10. ### JS11374

Not that I disagree with you completely, but should by your assertion there exists a mechanical system that can win 90% of all trades?

#10     Jul 19, 2002
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