## Model

We find that commodity, equity and currency markets display periods of rising and falling prices that recur at fixed intervals. As traditional fundamentals of supply and demand, seasonal variations and other external factors cannot account for the presence of these patterns we developed a model that suggests that the patterns are the product of a market's internal structure. Here are some key features of what we found:

## Common Structure

We believe markets share a common internal structure. We see the variations found in the price action of different markets as the result of markets expressing this common structure in different ways. This may be similar to the way elements of the Periodic Table all share the same structure of a nucleus with orbiting electrons. Variations in the configuration of the nucleus and electrons give each element its unique characteristics. Or by way of another analogy, flowers offer a great diversity of shapes and configurations yet each is designed to the mathematics of the golden ratio (1.618).

The structure we model is that of a torus or vortex. As this structure is common to much of the natural world we believe that price action of a market unfolds in accordance with naturally occurring principles.

The structure we model is that of a torus or vortex. As this structure is common to much of the natural world we believe that price action of a market unfolds in accordance with naturally occurring principles.

## Base Frequency

Each market has what we call a base frequency. This is the primary frequency at which the recurring periods of rising and falling prices can be found. For example:

**Brent Crude**A simple strategy of trading the base frequency of Brent Crude would have delivered over 100 times the market return since 1990.**Natural Gas**has one of the shortest base frequencies we have encountered. Trading recurring fixed periods of rising prices followed by falling prices has produced an average annual return of 29% since 1992 from this completely natural market feature.- The base frequency of the
**AUDUSD**currency pair has since 1982 and average price movement during a period of 6%. The natural pattern has a 72% success rate.

## Balance of Rising and Falling Prices

A key feature of the recurring price patterns is that the periods of rising prices are balanced by equal periods of falling prices. This symmetry to the market’s structure is always present. In upward trending markets such as equities the win rate of the periods of falling prices may be less but the underlying pattern is nevertheless visible.

## Secondary Frequencies

As well as the base frequency, most markets also display secondary frequencies where fixed recurring periods of price rise and fall can be found. These frequencies are never random. Instead they are always harmonics of the base frequency (i.e. half or double the base frequency) or are in golden mean (1.618) proportion to the base frequency.

The result is that a market may have numerable periods of rising and falling prices that can be relied on. We model these secondary frequencies in the same way as the base frequency, as a torus or vortex. If the secondary frequency is shorter than the base frequency this torus sits inside the torus of the base frequency.

The result is that a market may have numerable periods of rising and falling prices that can be relied on. We model these secondary frequencies in the same way as the base frequency, as a torus or vortex. If the secondary frequency is shorter than the base frequency this torus sits inside the torus of the base frequency.

## Filters

We find that the consistency of certain recurring price patterns can be improved through the use of filters. Three filters are proven to be effective:

- The standard deviation of returns
- The electrical output from the Sun (Solar Wind)
- Changes to the Earth’s own electromagnetic output.