The Misbehavior of Markets: A Fractal View of Financial Turbulence

Category: Mathematics
Author: Benoit Mandelbrot, Richard L. Hudson
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by v64   2019-07-21

The mathematician Benoit Mandelbrot (the fractal guy) in the Misbehavior of Markets makes a strong mathematical argument for why technical analysis is bunk along the same lines. A lot of his research on the market came during his time at IBM when he studied historical price data of wheat futures.

For one demonstration, he created a series of random charts much in the same way you did, and took them to professional technical analysts to get their opinions. Not only did they come to wildly different conclusions looking at the same charts, none of them raised the suspicion that the charts were fake. Some of them felt so strongly about the conclusions they drew that they asked Mandelbrot to tell them what stock they were looking at so that they could enter a position. Only then did he reveal that the charts were fake.

by Cabarius   2019-07-21

>you continually reject the use of statistical methods to quantitatively assess the statistical significance of a single observation of bi-modal behavior on what is presumed to be a normal distribution.

I don't reject statistical methods I stated my post was about experiences and hunches. I never intended to imply that I was doing anything formal or proving anything. I was describing some programmer's hunches.

> You don't measure or control dozens of possible independent variables that could result in bi-modal behaviors. Most of these seem very unlikely, but your theory of having a sticky behavior associated with your loadout seems just as unlikely.

There sure are lots of other variables. That's why I am here, but my runs were pretty consistent and when i ran groups I observed cases where I was running hot and another person was running cold then i had them apply my fix and we both continued to run hot. Over the course of the next 12 hours of the same runs we both ran hot. Maybe this is just a twist of luck... Again I did not do a formal study but it was not behaving like I would expect from a properly implemented RNG that I had implemented so hence my post of my non-rigorous analysis using some mathematical reasoning. Remember that we start with these ideas and then validate them with increasingly rigorous testing. First check equations and run some basic sanity tests. Then do some small samples and then do large samples and go more formal.

>You don't provide any raw data. Psychological/Emotional bias plays a huge roll in interpreting results. Do you actually believe craps players have "hot streaks" and "cold streaks"? Are dice bi-modal?


However when I get runs of hot that i can switch to cold by doing something and then later switch to hot by doing something and then others who have been running cold trigger a switch to hot after doing my fix then I start to suspect something is up in the code. Dice are not code (philosophy aside) in the way that the anthem loot system is implemented in code.

>There are people attempting more rigorous approaches to collecting data, with the same group of 4 people, with a fixed gear set, killing the same mob over and over again, measuring Legendary/MW drops per loot drop. That data is way more meaningful than your descriptive interpretation of your experiences.

Thank you for sharing these links. The graphs plot overall distribution of loot results in various things including freeplay. What I would like to see is a histogram the backpack distribution sampled over multiple runs. That may show this idea is full of shit or may confirm it. I would love to see either outcome as my goal is to find the truth or at least the best model of truth that we can deduce.

The other person just posted a graph that shows a summary of the breakdown of types of loot for one mob.

Neither of those things with just the charts say anything about my claim that the runs are bimodal. We would need the raw data to see (if I missed a link to the raw data in either of those posts please help me out and point me to it).

What we really need, IMHO, is to collect samples from a specific kill path and sets of mobs to fill a backpack while picking up all loot in order to test my hypothesis. Maybe the best thing would be to just pick a sequence of dungeons to visit (since afiak they always spawn the same kinds of mobs except for world events) and if a dungeon spawns a world event then exit freeplay and restart the run. From that data we can build a histogram of the number of blues, purples, mw, legos per backpack. I want to see the shape of the data before we compute mean, var, stddev and conclude that we have a normal distribution.

Side note: various things can appear like normal processes until something happens that puts things into a state that exposes their non normal aspects. If this subject interests anyone here is a really interesting read about how this shit fails in the pricing of options in a volatile market

but back to the current subject...


I have reached out to this person to see if I can get access to their raw data and maybe they have the info.

by akg_67   2017-08-20
The (mis)Behavior of Markets, A Fractal View on Risk, Ruin, and Reward by Benoit B. Mandelbrot and Richard L. Hudson.

You may enjoy this book if you are interested in Financial Markets, have some knowledge of Efficient Market Theory, and aware of existence of Fractal Geometry.

by buckie   2017-08-20
This is not at all surprising. Statistics isn't the right tool for financial analysis... it's just the best tool that we have. Incredibly unlikely statistical events happen all the time in finance.

A great read on an alternative view on the topic of using statistics for finance is The (Mis)Behavior of Markets by Benoit Mandlebrot [1]. It's very well written, basic enough for most to comprehend and first book on finance I read in college (before I went on to major in finance + math).

The aforementioned book has some very interesting notions with Trading Time being my favorite. Basically one can near-perfectly "forge" financial data with fractal objects called "financial cartoons" [2]. The objects are composed to two distinct fractals - one for price vs trading time and another for trading time vs clock time [3]. The latter rescales the volatility seen former, either compressing or expanding it. Rescaling volatility isn't a new idea, but it was a parallel "discovery".

There has been some work on figuring out how to use Fractal Geometry to analyze financial time series data but it's still in its infancy. The problem is figuring out how to transform the data into the fractals domain + figuring out what the results from a fractal based analysis would mean for forecasting future events. I've been working on these problems for many years (in earnest in college and as a hobby thereafter) but made little true progress.




by dpapathanasiou   2017-08-20
Market prices as fractal patterns? Where have I seen that before?

Ah, yes, here: