Questions tagged [fractal]
The fractal tag has no usage guidance.
19
questions
0
votes
0answers
5 views
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 ...
3
votes
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, ...
1
vote
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} - |...
0
votes
0answers
68 views
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, ...
2
votes
0answers
279 views
How to simulate anomalous diffusion of a 1D point like particle?
I want to simulate 3 types of diffusion processes:
normal diffusion $[\langle x^2(t)\rangle \propto t ]$.
subdiffusion $[\langle x^2(t)\rangle \propto t^\alpha ; \alpha<1 ]$
superdiffusion $[\...
4
votes
0answers
88 views
Hausdorff (fractal) Dimension of a Stochastic Process
It is well known that Brownian motion (BM) has a Hausdorff dimension (ie fractal dimension) of 2, for topological dimension >= 2. In other words, BM always "behaves like" a plane surface, no matter ...
1
vote
0answers
544 views
Fractal dimension of time series
What does fractal dimension values of 1.02 and 1.6 indicate?
How is fractional differencing related to fractal dimension?
0
votes
1answer
306 views
Test for fractional Brownian motion in Matlab
Is there a test in Matlab if a time series satisfies properties of being a fractional Brownian motion?
1
vote
1answer
558 views
Generalized Hurst Exponent - What value to specify for $\tau_{\max}$?
Consider a time series $X: S \to \mathbb{R}$, where $S := \{\nu, 2\nu, 3\nu, \ldots T\}$, and $T$ is a multiple of $\nu > 0$. For each $\tau \in (0, \tau_{\max}] \cap S$ and $q \in \mathbb{N}$, ...
13
votes
2answers
1k views
What are the known, existing practical applications of chaos theory in data mining?
While casually reading some mass market works on chaos theory over the last few years I began to wonder how various aspects of it could be applied to data mining and related fields, like neural nets, ...
1
vote
0answers
34 views
Intensity of fractional Gaussian noise
I try to understand the 2nd formula stated in the picture. It yields the intensity/volatility of an fGN process. It depends solely on H ?? Why is that?
How is this volatility different from simply ...
0
votes
1answer
370 views
Quantification of the extent of periodicity in a time series using fractal analyses
I need metrics to quantify the extent of periodicity between of a time series (for comparison with other time series), considering the time series is almost periodic. By almost periodic I mean: if I ...
4
votes
0answers
369 views
Why is generating fractional Brownian motion (fBm) so complicated?
An fBm is characterized by a power spectrum $P(f) = Cf^{-(2H + 1)}$ with $0 < H < 1$ being the Hurst parameter. Why can't I just take the square root of the power spectrum $P(f) = Cf^{-\alpha}$,...
1
vote
0answers
91 views
Finding parameters in power spectral density function
I have a process where $z$ varies with $x$. $z$ is well described by a fractal function given by
$z(x)= K \Big( \frac{H}{K} \Big)^{D-1} \sum_{n=0}^{\infty} cos\Big(\frac{2 \pi \beta^n x}{K}\Big) \...
1
vote
0answers
286 views
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 ...
2
votes
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...
4
votes
2answers
3k views
Hurst exponent calculation methodology
I am looking for the Hurst exponent calculation methodology. Please suggest online materials / methodology papers.
7
votes
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 ...
12
votes
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 (...
