Where Chaos is Born

Sergey Okun  This article was written by Sergey Okun – Senior Financial Analyst at I Know First, Ph.D. in Economics.

Highlights

  • We can detect chaos even in a system in which everything seems determined.
  • Lorenz attractor provides evidence that there is orderly behavior in a chaotic system.
  • If the stock market is chaotic, it does not mean that it is not predictable, and I Know First provides stock market forecasts based on chaos theory approaches.

The Demon of Determinism

(Source: pxhere.com)

The predestination of human destiny is one of the conceptual ideas in Ancient Greek Philosophy. In 1814 Pierre-Simon Laplace created the concept of the demon to show the need for a statistical description of the processes in the world around us. Laplace’s demon precisely knows the position and speed of every atom in the universe at every moment of time, he also knows all physical laws, and he can predict the future of each atom and describe its past. In the beginning, there were a lot of proofs of the demon’s existence from achievements in different science areas. For example, the periodicity of Halley’s Comet appearance was calculated. Later, Heisenberg’s uncertainty principle provided proof that the demon cannot control processes in the quantum mechanic systems, because there is fundamental uncertainty that cannot be predicted.

The demon was not forgotten and found a place in the deterministic systems where everything is predetermined. We can assume that if we know all rules which determine a system’s behavior, have access to all data, and have a powerful computer, then we can totally calculate and predict the behavior of this system. However, our calculation could have small mistakes because variables stored in the computer memory can have limited precision, or statistical data could be rounded at a tenth digit after a point. So is it ok for us to get an approximate forecast which goes to absolute precision forecast but never reaches it? In other words, is it ok to get a stock prediction that is wrong by only one cent?

Introducing the Butterfly

나 파도 결과 에 미치는 - Pixabay의 무료 이미지
(Source: pixabay.com)

Edward Lorenz created a computer model to forecast the weather in 1960th. His computer program based on weather input data provided a weather forecast in a short period. Outputs from previous calculations became inputs for the next days and etc. It means that everything in this model was totally determined. At one moment, E. Lorenz decided to analyze his model and used output data as initial data. The idea was that the computer model had to totally repeat further forecasts. However, the result was absolutely different and the difference increased for future periods. Therefore, the computer model, where randomness did not exist at all, provided different outputs with the same initial conditions (data). The problem was that E. Lorenz took data with three digits after a point to repeat the model calculations while the original data had six digits after a point. So, small changes in initial conditions created system behavior which was totally different from the original one. Actually, this went against the principles of Newtonian mechanics, which says that small inaccuracy at the input should lead to small changes at the output.

This discovery was the first step in the studies of chaos nonlinear deterministic systems, where the strong sensibility to initial conditions creates unpredictable systematical behavior. Now we know this dependency from initial conditions as the “Butterfly Effect“, which describes the narrative of a butterfly fluttering its wings in one region of the earth, which then caused a storm to happen in another one.

Welcome to Chaos

File:Intermittent Lorenz Attractor - Chaoscope.jpg - Wikimedia Commons
(Source: commons.wikimedia.org)

E. Lorenz continued to research behavior deterministic systems and found an attractor from the family of strange attractors which has got the name of Lorenz attractor. E. Lorenz offered a system of ordinary differential equations which has a set of chaotic solutions for certain parameter values and initial conditions. Instead of solutions being chaotic, their graph image represents a certain behavior. Especially, the graph image has the shape of “two wings of a butterfly”. E. Lorenz showed that we can detect chaos even in a system in which everything seems determined. Therefore, Laplace’s demon does not have any power even in the face of a not complex deterministic system. Also, Lorenz attractor shows that there is orderly behavior in a chaotic system.

Predictive Chaos with I Know First

If the stock market is chaotic, it does not mean that it is not predictable, and I Know First provides stock market forecasts based on chaos theory approaches. Previously, we discussed the Conceptual Framework of Applying ML and AI Models to Analyze and Forecast Financial Assets and we examined the presence of long-term memory in the stock market. The I Know First predictive algorithm is a successful attempt to discover the rules of the market that enable us to make accurate stock market forecasts. Taking advantage of artificial intelligence and machine learning and using insights of chaos theory and self-similarity (the fractals), the algorithmic system is able to predict the behavior of over 10,500 markets. The key principle of the algorithm lays in the fact that a stock’s price is a function of many factors interacting non-linearly. Therefore, it is advantageous to use elements of artificial neural networks and genetic algorithms. How does it work? At first, an analysis of inputs is performed, ranking them according to their significance in predicting the target stock price. Then multiple models are created and tested utilizing 15 years of historical data. Only the best-performing models are kept while the rest are rejected. Models are refined every day, as new data becomes available. As the algorithm is purely empirical and self-learning, there is no human bias in the models and the market forecast system adapts to the new reality every day while still following general historical rules.

Basic Principle of the "I Know First" Predictive Algorithm

I Know First has used algorithmic outputs to provide an investment strategy for institutional investors. Below you can see the investment result of our World Indices package which was recommended to our clients for the period from November 24th, 2020 to July 19th, 2022 (you can access our forecast packages here).

The Investment Result for the period from November 24th, 2020 to July 19th, 2022

The investment strategy that was recommended by I Know First accumulated a return of 286.02%, which exceeded the S&P 500 return by 278.94%.

Conclusion

We can detect chaos even in a system in which everything seems determined. E. Lorenz’s “Butterfly Effect” says that small changes in initial conditions lead to unpredictable changes in a system’s behavior. At the same time, Lorenz attractor provides evidence that there is orderly behavior in a chaotic system. If the stock market is chaotic, it does not mean that it is not predictable, and I Know First provides stock market forecasts based on chaos theory approaches.

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