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

Highlights

• The Chaos theory is an alternative to the Theory of Probability which does not consider tossing a coin for making investment decisions.
• One of the approaches to analyzing multidimensional nonlinear data series is to imitate the behavior of participants in the stock market.
• I Know First provides stock market forecasts based on chaos theory approaches.

Chaos vs Stochastic

The different aspects of awareness of the financial market functions create a system of axioms and paradigms. From a classical point of view, the Efficient Market Hypothesis is the framework for the analysis of financial assets based on the assumption of the randomness of financial asset returns that allows using methods based on the Theory of Probability. The Chaos theory is an alternative to the Theory of Probability which does not consider tossing a coin for making investment decisions. In the context of the Chaos theory, uncertainty has a different nature than in the stochastic processes, where a final result depends a lot on initial conditions. At the same time, the structure of making decisions does not change which allows us to assume a functional connection between a cause and effect, which is difficult to formulize by standard mathematical methods, which creates interest in Machine Learning models and especially in Neural Network.  

The econometric models enable us to identify quantitative connections between variables. These models assume the probability approach and are based on a randomness component (the mean plus a confident interval). There is a component of irremovable uncertainty in econometric models which depends on two factors: forecast based on probability, and dependency on initial conditions.

There are dynamic models based on the Chaos paradigm. Chaos can be defined as the extreme unpredictability of a nonlinear and irregular complex behavior in a dynamic system. However, Chaos is not random in spite of its unpredictability. It is dynamically determined. According to the Chaos theory, a stock price movement is an orderly movement. If the stock market dynamic is chaotic, it is not random but it is unpredictable. Chaos unpredictability explains its dependency on initial conditions. This dependency means that even small mistakes in measurable variables can create absolutely incorrect predictions. These mistakes appear when we do not know completely all initial factors.

Features of the Stock Market

The stock market is a nonlinear system that has the following characteristics:

1. Long-term correlations and trends as a result of feedback mechanics.
2. Price Fluctuations between fair value and critical points.
3. Fractal structure in stock returns time series (i.e., a fragment of a price trajectory will be similar to a price trajectory as a whole).
4. Strong dependency on initial conditions, and decreasing influence of the long-term memory (Prediction confidence decreases as a horizon forecast increases).

The stock market can be efficient and inefficient in the same cases. The order in market chaos is due to nonlinearity. To determine the fair value, investors use information about returns and the current economic environment, and they also take into account the willingness of other investors to pay for financial assets. If they see that a trend goes in line with their expectations, they start to buy stocks as other investors do. This behavior can change when a price reaches an upper bound of its fair value. The appearance of new information can also change the current market situation. The Chaos theory enables us to measure the dynamics of uncertainty and find an order in the irregularity of uncertainty. The Chaos theory says that the financial market is not efficient and its behavior can be predicted. All market cycles are identical in global meaning and different in details (all of them have individual attractors). For instance, any bull or bear market has periods of price increases or decreases during a business cycle. However, the reasons for these price movements are individual for each business cycle. For investors, this means that there is always a way to make money but there is not a single system that can guarantee it.   

One of the approaches to analyzing multidimensional nonlinear data series is to imitate the behavior of participants in the stock market. Neural Network is ideally adapted to finding nonlinear dependences in absence of a priori knowledge about the initial model. The feature of Neural Network models is the ability to generalize, which allows teaching a model on a small fraction of all possible cases with which the model will make a deal in the future. Advances of Neural Networks model compared with statistical models:

• There is no need for complex calculations.
• A forecast is visual and minimally dependent on subject factors.
• Calculation time is within acceptable limits.
• It is possible to add new data to the Neural Network model to complete its training without the need to restart all training processes from the beginning.
• The quality of the forecast only depends on completeness and type of input data.

What Does I Know First Put on the Table?

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 August 29^th, 2022 (you can access our forecast packages here).

The investment strategy that was recommended by I Know First accumulated a return of 426.85%, which exceeded the S&P 500 return by 414.19%.

Conclusion

The different aspects of awareness of the financial market functions create a system of axioms and paradigms. The Chaos theory enables us to measure the dynamics of uncertainty and find an order in the irregularity of uncertainty. The Chaos theory says that the financial market is not efficient and its behavior can be predicted. One of the approaches to analyzing multidimensional nonlinear data series is to imitate the behavior of participants in the stock market. 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.