Fractals Etc

[dangermouseb 10]

Hi

 

Not sure which forum to post this. Can anyone resource me regarding, fractal and fractional brownian motion. I want to understand the components in estimating the hurst exponent, what long term memory means intuitively, how to generate series of fractal and fractional brownian random numbers to use in monte carlo simulations.

 

Web links, books, authors, papers, insights, etc all welcome...

 

Many thx

 

-- DM

[motorway 10]

imo unless You understand "Intrinsic Time" and how different reality is from the illusions created by clock time ...... FAR REMOVED

 

Any such research will not get very FAR

 

 

The viewpoint of fractal theory

 

The fractal approach to analyzing objects of different kinds, including time series, can be

formulated as follows:

Objects are analyzed on different scales, with different degrees of resolution, and

the results are compared and interrelated.

 

In the introduction to the concept of fractals in (Mandelbrot, 1983), an example is presented that

was first analyzed by Richardson. The length of the coastline of Great Britain is measuredwith

yardsticks of different sizes

 

. The length of the coastline is a function of the size of the yardstick:

the smaller this size, the longer the total lengthmeasured because smaller yardsticks can follow

more details of the coastline. The total length as a function of the size of the yardstick follows

a power law.

 

If this principle is adopted to time series analysis, itmeans using different “time yardsticks”,

 

The conventional time series analysis, focusing exclusively on a time series of regularly

spaced observations, is far removed from both the fractal viewpoint and the real nature of

the raw data: a regularly spaced economic time series is not original data but a preprocessed

artifact. R B Olsen

 

 

Fifth Video...>. Intrinsic Time

 

OlsenScale: Video Archive

 

In terms of Traditional Technical Approaches

 

An Intrinsic "Fractal" Methodology would be one of the oldest

 

POINT and FIGURE charting...

 

Which can use high frequency data

And log BOXES

 

That making it a type of ( and not necessarily inferior) LOG/LOG chart revealing POWER LAWS.

 

Motorway

[BlowFish 10]

I didn't answer when you first posted mainly because I didn't have much to offer that could not be found with google. There have been a couple of discussions here though they often tend to descend into the 'are markets fractal' debate.

[dangermouseb 10]

Thx... my hunch is twofold 1)that if a timeseries is fractal with hurst exponent > 0.5 then a random entry system should work, 2) that a market where a random entry system works (i.e. has trends) then the hurst exponent >0.5. I want to prove that to myself using some montecarlo generated price series.

 

Basically I wanted to proved to myself that a fractal market isn't necessarily random.

 

Also I want a hurst exponent estimator so I can see if there are trends in a set of data and see how effective that is at identifying good places to trade.

 

I've done some googling already but you know what a chase down rabbit holes that can be.

 

Has anyone done any analysis on random entry systems?

 

-- DM