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

The concept of human destiny being predetermined is an idea that originated in Ancient Greek Philosophy. In 1814, Pierre-Simon Laplace introduced the notion of a demon to emphasize the necessity of a statistical explanation for the processes occurring in our world. This hypothetical demon possesses complete knowledge of the position and velocity of every atom in the universe at any given moment, as well as a comprehensive understanding of all physical laws. With this information, the demon can accurately predict the future trajectory of each atom and describe its past. Initially, numerous scientific achievements seemed to support the existence of such a demon. For instance, the periodicity of Halley’s Comet’s appearance was successfully calculated. However, the Heisenberg uncertainty principle, later discovered, provided evidence that the demon cannot exert control over quantum mechanical systems. This principle establishes an inherent uncertainty that prevents precise prediction.

The demon has not been forgotten and has found a place within deterministic systems, where everything is predetermined. It is posited that if we possess complete knowledge of the governing rules that dictate a system’s behavior, have access to all relevant data, and possess a powerful computer, we can accurately calculate and predict the behavior of said system. Nevertheless, our calculations may contain minor errors due to limitations in computer memory precision or the rounding of statistical data. Thus, is it acceptable to obtain an approximate forecast that approaches absolute precision but never quite attains it? Stated differently, is it satisfactory to have a stock prediction that deviates from the actual value by a mere one cent?

Introducing the Butterfly

In the 1960s, Edward Lorenz developed a computer model to predict the weather. His program relied on input data regarding weather conditions to generate short-term forecasts. Each subsequent calculation utilized the output from the previous one as its input, establishing a fully determined model. However, at a certain point, Lorenz decided to examine the model by using the output data as the initial input. His expectation was that the computer model would replicate the subsequent forecasts exactly. Surprisingly, the result turned out to be significantly different, with the divergence increasing over time. Thus, even in a computer model devoid of randomness, the outputs differed despite identical initial conditions (data).

The issue arose because Lorenz truncated the data to three decimal places when repeating the model calculations, whereas the original data contained six decimal places. As a result, minor changes in the initial conditions led to entirely different system behavior compared to the original. This discovery challenged the principles of Newtonian mechanics, which dictate that small inaccuracies at the input should yield minor changes at the output.

This revelation marked the initial exploration of chaos theory in nonlinear deterministic systems, characterized by their strong sensitivity to initial conditions, resulting in unpredictable and systematic behavior. We now refer to this dependency on initial conditions as the “Butterfly Effect” illustrating the idea that a butterfly flapping its wings in one region of the Earth could potentially trigger a storm in another region.

Welcome to Chaos

E. Lorenz continued to research behavior deterministic systems and found an attractor from the family of strange attractors which has got the name Lorenz attractor. E. Lorenz offered a system of ordinary differential equations that 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’s 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.

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 24^th, 2020 to July 19^th, 2022 (you can access our forecast packages here).

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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Please note-for trading decisions use the most recent forecast.