An Autonomous Agent

exploring the noosphere

Category: math (Page 3 of 10)

Simulated Stock Price Data – Ising Type Model

I am currently exploring stock price movements. I hope to publish a full post on my insights soon. Perhaps linking Elliott Waves with the fundamental tug-of-war between buy and sell price action. Here is a neat simulation of traders in an Ising type model. The resulting stock price simulation can be seen in the PDF. The model was created using 1,000,000 traders. If this is really the underlying nature of the movement of stock prices, then by observing a stock trajectory, an observer is really only getting a tiny fraction of the information about the state of the system. If there was a way to implement this model on a wide scale, the results would be really neat.

GIF animation of the model:
Red dots are traders short the stock. Yellow dots are traders long the stock. Orange dots are traders neither short nor long the stock.

Chaotic Maps and Feigenbaum Constants

Randomly came across this insightful image on the internet. It shows the importance of the Feigenbaum constants:

Going to wikipedia’s page: List of chaotic maps, one can find some really neat mathematical transformations. Arnold’s cat map seems like it would have some neat practical uses.

Gingerbread Man Map
Exponential Map
Chirikov–Taylor map

Circle map with Poincare recurrence
Arnold’s Cat Map

Structural Harmony of Systems – Eduard Soroko

Today, I read some interesting things on harmony mathematics. Here is a remarkable quote from a guy named Eduard Soroko (I can not find a Wikipedia entry on him):
“The Generalized Golden Proportions are invariants, which allow for natural systems in process of their self-organization to find harmonious structure, stationary regime of their existence, structural and functional stability.”

 

Here is a link to the paper which contains this quote: Structural Harmony of Systems. I want to find more papers and information on this “Belarusian philosopher.”

Mathematics of Harmony – Alexey Stakhov

Fascinating book: Mathematics of Harmony by Alexey Stakhov. I found this book while doing some research on Elliott Waves. Other topics of interest: Golden Ratio and Fibonacci p-codes. Chapter nine is fascinating and it’s incredible that George M. Bergman was only twelve years old when he published the paper, A number system with an irrational base.

Who is Alexey Stakhov? Do a Google search on him to learn more about this scientist with over 500 publications, 14 books, and 65 international patents. Note: Do a Google search for the book’s ISBN number: 981277582X to find a pdf on DepositFiles 🙂

The Elliott Wave Principle

 

In the financial industry many models are based on Geometric Brownian Motion. However, these models tend to be inadequate and breakdown when the assumptions are violated. Searching for better stochastic models to model the market, I recently ran across an interesting topic in the field of market prediction and structure — the ideas of Ralph Nelson Elliott. It is remarkable that his ideas of market waves and structure were formulated in the 1930’s.  His ideas were popularized by Robert Prechter who has numerous books and articles written on the subject. In this post I have introduced these ideas and will post all the articles and books I have and will read on this subject. I hope to develop these ideas further.

 

Books:

Harmonic Elliott Wave: The Case for Modification of R. N. Elliott’s Impulsive Wave Structure – Ian Copsey

Mastering Elliott Wave Principle: Elementary Concepts, Wave Patterns, and Practice Exercises – Constance Brown

Elliott Wave Principle: Key to Market Behavior

The Wave Principle of Human Social Behavior and the New Science of Socionomics

Articles:

An Introduction to the Elliott Wave Principle – Jordan Kotick

Multi-classifier based on Elliott wave’s recognition

Fuzzy time-series based on Fibonacci sequence for stock price forecasting

Elliott Wave Theory and neuro-fuzzy systems, in stock market prediction: The WASP system

Unconscious Herding Behavior as the Psychological Basis of Financial Market Trends and Patterns

Videos:

Mastering Elliott Wave – Jamie Saettele

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