## What Is a Sine Wave?

A sine wave is a geometric waveform that oscillates (moves up, down or side-to-side) periodically, and is defined by the function *y = sin x*. In other words, it is an s-shaped, smooth wave that oscillates above and below zero.

Sine waves are used in technical analysis and trading to help identify patterns and cross-overs related to oscillators.

### Key Takeaways

- A sine wave is an S-shaped waveform defined by the mathematical function y = sin x.
- In finance, market participants may identify cyclical patterns or oscillator signals from sine-wave based functions.
- The sine wave as a technical chart analysis tool is based on advanced mathematics and is designed to indicate whether a market is trending or in a cycle mode.

## Understanding Sine Waves

The sine wave indicator is based on the assumption that markets move in cyclical patterns. After quantifying a cycle, a trader may try to use the pattern to develop a leading indicator. This works extremely well when the market is indeed moving in a cycle. When the market is trending, however, this system fails (and one should adjust for that).

Markets alternate between periods of cycling and trending. Cyclical periods are characterized by price bouncing off support or resistance levels and failed breakouts or overshoots. Trending periods are characterized by new highs or new lows and pull backs that then continue in the direction of the trend, until exhausted.

In technical analysis, oscillators are often used that may have sine-shaped characteristics. An oscillator exists between two extreme values and then builds a trend indicator with the results. The analysts then use the trend indicator to discover short-term overbought or oversold conditions. When the value of the oscillator approaches the upper extreme value, analysts interpret that information to mean that the asset is overbought, and as it approaches the lower extreme, analysts consider the asset to be oversold.

## Sine Waves as Analytical Tools

The sine wave as a technical chart analysis tool is based on advanced mathematics and is designed to indicate whether a market is trending or in a cycle mode. It helps traders identify the start and finish of a trending move as well as possible shifts in the trend.

This leading indicator is also called the MESA indicator and was developed by John Ehlers based on an algorithm that was originally applied to digital signal processing. It consists of two lines, called the Sine Wave and the Lead Wave. When the price is trending, the lines do not cross and usually run parallel and distant from each other.

Line crossovers could indicate turning points and generate buy or sell signals under the right conditions. The indicator can also signal an overbought or oversold market (i.e., unjustifiably high or unjustifiably low), which can have implications on the prevailing trend. Whether used alone or in combination with other techniques or non-correlated indicators (such as moving average-based indicators), the sine waves are very useful for a trader.

The Composite Index of Lagging Indicators resembles a sine wave since the measures that make up the index (i.e. ratios and interest rates) tend to oscillate between a range of values.

For example, inflation is always kept between specified rates and if/once inflation meets or exceeds a specified limit, interest rates will be adjusted to either increase or decrease inflation so it is brought within a target range. Thus, as the rate of inflation increases, decreases or stays the same, interest rates will oscillate up and down to control an undesired rate of inflation.