Archive for June 16th, 2011:
Use of the Hurst Exponent in Technical Analysis
There are many reasonable questions, which may arise during forex trading, and one of them concerns the possibility to predict a given financial time series in advance; you should decide whether it is worth trying to forecast its development and model the data.
The Hurst Exponent allows to estimate the time series predictability and express it numerically. In other words, the Hurst Exponent allows you to understand whether a time series has a tendency to regress to a longer term mean value, or it has a tendency to “cluster” in a direction.
The algorithm of the Hurst Exponent is based on the hypothesis that the time series is a pure fractal, but it is not always right in most cases. Therefore, this is the reason of the Hurst Exponent being an estimate and not a definitive measure.
Anyway, everything abovesaid is not very important. The main advantage of the Hurst Exponent in technical analysis is the possibility to use the Hurst Exponent as a tool for classification of time series in terms of predictability.
Explanation of the Hurst Exponent
The Hurst Exponent values lie in range between 0 and 1.
•   If a Hurst Exponent value H is close to 0.5, it means that there is a fractional Brownian motion time series or a random walk. There is no correlation between current and future elements in a random walk, therefore, the probability of future return values moving in one of directions (up or down) makes approximately 50%. As you see, prediction of such type of time series is almost impossible.
•   If a Hurst Exponent value H lies between 0 and 0.5, it means that there is a so-called “anti-persistent” time series. In this case a decrease will occur after an increase, and vice versa. In other words, you may call such behavior “mean reversion”; in this case, future values will tend to return to a longer term mean value. The closer H is to 0, the stronger this “mean reversion” is.
•   If a Hurst Exponent value H lies between 0.5 and 1, it means that there is a so-called “persistent” or trending time series. It means that in case of decreases (or increase) in the time interval from [t-1] to [t] there is a high probability of decreases (or increase) in the time interval from [t] to [t+1]. It means that an increase will follow an increase, and a decrease will follow a decrease. The closer H is to 1, the stronger the trend is. Persistent time series are the best time series for prediction in comparison to the previous two categories.
It should be mentioned that there is a difference between volatility and the Hurst Exponent. For example, an index or a fund can have an H close to 0.5 and a relative low volatility at the same time. As a rule, mature markets are less predictable and more efficient than emerging markets, and that is why they very often have Hurst Exponents closer to 0.5.
So, you can use the Hurst Exponent for classification of time series, and it is a very useful ability, for example, for making a list of stocks with greater short term predictability. For instance, you could make a list of stocks with particular Hurst Exponent values, and then examine and study their profit generating characteristics. You could close all investment positions in a particular stock, if its Hurst Exponent dropped below a certain threshold value.
You also can use the Hurst Exponent in combination with neural networks or technical indicators. In this case the Hurst Exponent will help you to make priorities and decide which assets to ignore and which ones to forecast.
About the Hurst Exponent
The Hurst Exponent occurs in several areas of applied mathematics, including fractals and chaos theory, long memory processes and spectral analysis. Hurst Exponent estimation has been applied in areas ranging from biophysics to computer networking.
The direct connection of the Hurst Exponent to the fractal dimension of a process allows to measure the roughness of the process. For instance the roughness of coastlines has been measured by means of the fractal dimension. There are other areas of application of the fractal dimension: measurement of neuronal growth in medicine, the simulation of mountains in computer graphics, and mold colony’s boundaries measurement in biology
As a rule, the Hurst Exponent is not calculated, but estimated by means of several different techniques. From the other hand, assessment of the accuracy of the estimation is not a simple task. The Heisenberg Uncertainty Principle also limits fidelity and accuracy of H.
The estimation of the Hurst Exponent can be done by means of calculating the average rescaled range (R/S) over multiple overlapping regions of the data. As a rule, it is possible to use only regions with lengths larger than 31. The results of such approach are quite robust, standard deviations are small, but there is a negative side, too: the estimated value is a bit biased.
Manual forex trading strategy based on Hurst Exponent
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