Forecasting markets and a no-so-random walk along the Nile River

It would be a long walk from Wall Street to the Nile River but data about river flows has provided an interesting tool for analysing investments (and the economy).  This tool raises doubts about the theory of the random walk on Wall Street.  It may the basic tool used by a lot of “quants” who have had some success working the markets.

Harold Edwin Hurst was a hydraulic engineer working on the Nile River early in the twentieth century who was concerned with managing the river flows with the new dams.  With access to extensive historical data on the varying annual flows he decided to prove that they were random.  Through a number of years he worked out a way to determine if a time series is random or not.  If the Hurst Exponent is .5 then the series is random.  If it is greater than . 5 there is some probability a the series will continue its trend.  (The maximum is one.)  To Hurst’s surprise the exponent for the Nile River flows was about .8.

If the Hurst exponent for a time series is greater than .5 then it is not random and there should be some potential to predict what it will do.  There is software available to calculate the Hurst exponent using several different calculations.  One requires just 32 data points.  When one applies the Hurst exponent to market (and probably) economic data one finds it varies up to .8 and sometimes higher.

Not only are markets non-random, they are also fractal in nature.  This means they go up and down and within each up and down there other ups and downs.  This applies regardless of the time applied to the series.  If you have a time series at one minute intervals all the series at longer intervals will also be fractals and when a longer time series changes direction all the shorter ones will also change direction.  The key to analysing fractals then is to identify the turning points.

The key is a concept called fractal dimension.  This is a measure the extent of the ups and downs.  It appears that changes in fractal dimension indicates changes in the direction of the time series.  If several time series of the same data change fractal dimension at the same  then the time series is probably going to change direction.  If one is playing a market or trying to predict the economy this should  be useful information.

The formula for fractal dimension is simple: 2 – H, where H is the Hurst exponent.

If one wants to apply this to market data one probably needs a lot of programming skills and some very fast computers. These are available to the “quants” who also certainly know about the Hurst exponent and fractal dimension.   There is also a problem in that if this works and a lot of people are successful they will even out the swings in the prices.

Who is correct:  the academics who claim Wall Street is a random walk or those who believe it is not true?  My guess is that some times it is random and at other times there are patterns which may be identified.

Could this be used for forecasting economic ups and         downs?  Perhaps.  Economic data are difficult and expensive to obtain and not always accurate.  There may also be problems with the number of data points needed to get accurate results.

When Hurst walked along the Nile River I wonder if he thought about Wall Street and economic forecasting?  He probably realized the potential for his exponent beyond river flows as he published an article about his exponent.


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