Unpacking the Ins and Outs of a Chaotic System – How Can We Predict it



  • What is Chaos Theory?
  • Earthquakes – An example of a Natural Chaotic System
  • Randomness vs Chaos 
  • What makes a Chaotic System a Chaotic System
  • Modeling a Chaotic System
  • Can We Really Predict the Stock Market? Psychology of Trading and Feedback Loops

What is Chaos Theory?

Source: Medium

In a chaotic system like weather, a tiny change can make a huge impact. Weather is predicted a few days in advance because small changes in input can produce dramatically different results. 

The most commonly used example to explain chaos theory is the butterfly effect. It says that a butterfly flapping its wings on one end of the world can give rise to a hurricane in another part of the world. It sounds bizarre but it illustrates the huge impact small changes in the factors can have on the outcome. 

Without going into too much mathematical details, I would like to briefly explain how chaos theory falls into play when predicting stock markets. But first, let us take a look at some examples and basic principles that will help us reach that understanding.

Earthquakes – An Example of a Natural Chaotic System

Source: FEMA

Earthquakes is one example of a natural chaotic system. Even though earthquakes are seemingly random and only happen once in a blue moon, scientists have been able to predict with a high accuracy when the earthquake will strike. With the collection of data of the different factors over many years, predicting earthquakes have become possible.

Chaotic systems sound foreign to us, but actually it is very commonly found in our everyday lives. Other such examples is the weather, tides, ocean temperatures, population growth, DNA codes and even fashion trends.

Such systems are complicated and seem unpredictable to the untrained eye. However, with the advancement of data science, algorithmic models are able to spot trends that humans cannot.  

Randomness vs Chaos 

Firstly, one should be vaguely familiar with the terms randomness and chaos. 

Source: Medium

Randomness means the past has no effect on the future. Like rolling a dice, or flipping a coin. The previous coin flips do not predict future ones. Also, randomness is a stationary process. This means that its statistical values do not change over time. Such as flipping a fair coin, there will always be a 50 percent chance of landing on either heads or tails. 

Another important property of a random process is that it has to be ergodic. Ergodicity is when a collection of many random samples represents the overall statistics. Imagine rolling a fair dice thousands of times, you will notice that each number appears almost the same number of times. This is because the probability of landing on a number is ⅙ on a fair dice. Conversely, a process that is not ergodic changes erratically at an inconsistent rate.

Whereas, chaos is simply the opposite. Chaotic systems are neither stationary nor ergodic.

Once, we have established that chaos and randomness are two polar opposite things, we can then start to unpack the key properties of a chaotic system. 

What Makes a Chaotic System a Chaotic System

Source: Forbes

Statistics of chaotic systems are constantly changing over time. It is also not ergodic, which means that past data is not representative of what is to come. 

However, three competing paradigms control the chaotic systems. They are stability, memory, and sudden and drastic change.

Stability means there are persistent trends over time. The memory property indicates that past data has an impact on future trends. Lastly, sudden and drastic change reverses a trend with little or no warning. Together, these properties make it possible to predict chaotic systems using probability.

Modeling a Chaotic System

“ All models are wrong, some models are useful ”  

– George E.P. Box

Modeling a chaotic system is a long and complicated process. As mentioned in the beginning, a change in the parameter can have a huge effect. 

The stock market can be modeled using 1/f noise model. The f stands for frequency of an event. In other words, if an event happens frequently, it will have a small impact on the model.

For more technical details about Dr Lipa Roitman’s algorithmic strategy, please read his slides.

Can We Really Predict the Stock Market?

The stock market is a chaotic system, it is not random. A random system is impossible to predict. On the contrary, chaotic systems can be predicted accurately to some extent. Past events affect future events. Hence, through analysis of past data, we can start to predict future events using machine learning and artificial intelligence. The more historical data one has, the more accurate the future prediction. 

The psychology of trading and feedback loops are two key concepts of how the stock market is a chaotic but predictable system.

Psychology of Trading

In the stock market, it is subjected to the psychology of how people feel towards gains and losses. People react based on the news that they hear. However, basic economic assumptions are formed. Most people will steer towards reaching the highest returns with the least risk involved. Over time, the algorithm learns trading patterns, allowing it to predict future stock prices. 

Stock Price Showing Patterns in 5 Years Horizon
Stock price showing patterns over a 5 years horizon

Feedback Loops in Trading

Systems become chaotic when there is feedback. The two basic types of feedback loops in a stock market explain its chaotic nature. As the value of a stock rises or falls, people are inclined to buy or sell that stock. This in turn further affects the price of the stock, causing chaotic stock price movements.

Example of Positive and Negative Feedback Loops
Positive and negative feedback loop in stock trading

When the positive and negative feedback loops interact, it gives rise to a dynamic equilibrium. This means that the stock price oscillates around a certain price level. There will also be market bubbles from the feedback loops.  

A characteristic of chaotic systems, feedback loops are seemingly unpredictable. However, the algorithm can recognise the patterns of such feedback loops, allowing it to predict future behavior. 

I Know First Algorithm


This means the algorithm is able to create, modify, and delete relationships between different financial assets. Based on the relationships and the latest market data, the algorithm calculates its forecasts. Since the algorithm learns from its previous forecasts and is continuously adapting the relationships, it adapts quickly to changing market situations.



The model is 100% empirical, meaning it is based on historical data and not on any human derived assumptions. The human factor is only involved in building the mathematical framework and initially presenting to the system the “starting set” of inputs and outputs.

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