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:

Click the headings below to learn more!

## 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 & Chaos Theory

**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.

## 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.