We employ the theoretical framework from Complexity theory, Chaos theory measurement tools, and machine learning modeling methods to construct new forecasting applications to help solve the market dynamics problem. This problem breaks down classically into fundamental-related and crowd-related dynamics as shown here:

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Feedback

In the financial markets, price movement, news, or influential people produce investment bias “output” that is fed into the heads of the investment community, who then produce new outputs in the form of buy and sell decisions. In other words, the market is always producing feedback for itself, which must be taken into account.

Scale Invariance

Scale invariance (also known as self-similarity) is defined as a feature of objects or laws that do not change if length scales are multiplied by a common factor. Its presence means that the financial series has been produced by feedback and is governed by the rules and the predicted behavior of Chaos theory.

Chaos theory is the science of feedback systems. As financial scientists, we seek to understand which market characteristics are predicted by Chaos theory and then build a set of predictive tools that capture what is theoretically possible.

Complexity Theory

Complexity is the theory of multi-agent systems. It is our contention that price chart anomalies that today are the domain of technical analysis, are really the direct result of this theory. To be subject to Complexity Theory, the system must have a large compliment of “agents”, that are connected, collectively experience positive and negative feedback, and follow a simple set of rules. Our millions of investment agents are connected by price, pursue price, are attracted and repulsed from key price levels, and collectively participate in both positive (chasing price) and negative feedback (supply and demand contention) effects. Emergence of geometric patterns, not unlike those due to birds flocking, are due to Complexity and explain the many non-random geometric chart patterns. Chaos theory, which is a subset of Complexity, explains the quasi-periodicity of price cycles that seem to randomly invert.

Spatial Probability Mapping

Normal diffusion laws can be mapped and used to predict the probability of finding a stock at a certain price.

Neural Networks

A neural network is a mathematical modeling tool that has the capacity to learn by example. This is an extraordinarily useful ability, especially in financial modeling, where the predictive inputs are usually known and there are countless example forecasts. 

Predictor Validation

Parallax has been producing neural network-based financial predictors since 1990, so it is an integral part of our business to validate these predictors using reliable statistical methods.