# Questions tagged [fractal]

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### How to show dfferent Hurst Parameters on the same random process

I would like to show on a graph the effect of different Hurst Parameters on the same random process. I can show this using the package here: https://pypi.org/project/fbm/ By running the below (3 times ...
0answers
149 views

### Interpretation of box-counting method from R

I tried to calculate the fractal dimension of a dataset using the box-counting method with R programming. I used two packages: The first one is fractaldim, ...
0answers
20 views

### Fractional Brownian motion with additional terms

Fractional Brownian motion seems fairly a straight forward random process with a kind of auto-correlation function,  \mathbb{E}\left[ B^H_t B^H_s \right] = \frac{1}{2} \left( |t|^{2H} + |s|^{2H} - |...
0answers
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### Compare long range dependence among non-stationary multivariate time series'

I have 5 non-stationary multivariate time series' and I need to compare the "strength" of long range dependence among them. I have found many papers on long range dependence estimation (parametric, ...
0answers
279 views

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### Assumptions for Hurst exponent calculation

Are there any general assumptions for the calculation of the Hurst exponent? Does the signal need to be stationary, for example? Does it depend on the method? What about the length of the time ...
0answers
39 views

### Determining the roughness of a multidimensional optimization surface [duplicate]

Is there a way to determine the roughness of an n-dimensional optimization surface (n > 3)? Preferably a method that uses measures from fractal geometry/chaos theory...
2answers
3k views

### Hurst exponent calculation methodology

I am looking for the Hurst exponent calculation methodology. Please suggest online materials / methodology papers.
2answers
610 views

### Fractal alternative to correlation

I am looking for a fractal-based statistical measure which could be used as alternative to correlation between two variables (I know that hurst exponent can be used for auto-correlation). Is anyone ...
1answer
728 views

### Statistics based on fractal mathematics

I am looking for books / textbooks on statistics based on fractal mathematics. I know it is not a very well known area and it is rather difficult to find good literature. Any suggestions are welcome (...