Contents
What is the Hurst phenomenon?
The Hurst phenomenon is a well-known feature of long-range persistence first observed in hydrological and geophysical time series by E. Hurst in the 1950s. It has also been found in several cases in turbulence time series measured in the wind tunnel, the atmosphere, and in rivers.
How long do market cycles last?
Market Cycle Timing A cycle can last anywhere from a few weeks to a number of years, depending on the market in question and the time horizon at which you look. A day trader using five-minute bars may see four or more complete cycles per day while, for a real estate investor, a cycle may last 18 to 20 years.
How do you calculate fractal dimension?
Fractal Dimensions of Geometric Objects. In the last section, we learned how scaling and magnification relate to dimension, and we saw that the dimension, D, can be seen as the log of the number of pieces divided by the log of the magnification factor. Expressed as an equation, we have D = log(N) / log(r).
How to calculate the Hurst exponent for n?
To estimate the Hurst exponent, one must first estimate the dependence of the rescaled range on the time span n of observation. A time series of full length N is divided into a number of shorter time series of length n = N, N/2, N/4, The average rescaled range is then calculated for each value of n.
Why is the Hurst exponent too high in MATLAB?
Specifically, we found that if we set the maximum number of lags too high, the results became quite inaccurate. These values are the defaults used in some other implementations, such as the standard Hurst function in MATLAB.
Are there any unexpected results from using Hurst?
However, if you’ve ever used Hurst, you know that it can be a bit bewildering: not only does it often give unexpected results, but it also returns different results depending on the implementation used in its calculation.
How is the Hurst of a series determined?
We determine Hurst by firstly calculating the standard deviation of the difference between a series and its lagged counterpart. We then repeat this calculation for a number of lags and plot the result as a function of the number of lags.