Sine Wave: Definition, What It's Used for, and Causes

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 by stock traders and analysts to help them identify short-term buying or selling opportunities in stocks based on the usual limits of their oscillations up or down.

Sine waves can be useful as an indicator when a market is moving in a cyclical pattern but not when the market is trending.

Understanding Sine Waves

The sine wave indicator to stock investors and analysts is based on the assumption that markets move in cyclical patterns. After quantifying a cycle, a trader will 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, the system fails. No reliable pattern can be discerned.

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 pullbacks that then continue in the direction of the trend until exhausted.

An oscillator exists between two extreme values and then builds a trend indicator with the results. The analyst then uses the trend indicator to discover short-term overbought or oversold conditions.

When the value of the oscillator approaches the upper extreme value, analysts interpret it as an indication that the asset is overbought. As it approaches the lower extreme, analysts consider the asset to be oversold.

Sine Wave As an Analytical Tool

The sine wave as a technical chart analysis tool is based on advanced mathematics. It is designed to indicate whether a market is trending or in a cyclical 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, a prominent figure in technical analysis, 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 useful for a trader.

For example, the Federal Reserve works to keep the inflation rate within an acceptable range. When inflation exceeds acceptable maximum or minimum limits, interest rates will be adjusted to bring them 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.

Who Uses Sine Waves in the Markets?

Technical traders who employ Fourier analysis use sine waves to guide their trading decisions.

Fourier analysis is a technique that breaks down complex time series data into a series of simpler components that are based on the sine or other trigonometric functions. This allows a trader to separate the signal from the noise in the data.

For instance, a trader who spots "noise" in the price history of a consumer cyclical stock may try to identify a sine wave that fits the inflation pattern and remove the noise.

While Fourier analysis is widely used, financial researchers remain unconvinced that it is a viable or effective strategy.

The Bottom Line

Stock traders and analysts who rely on technical analysis use sine waves to plot the upper and lower limits of a stock's movement up and down over time. This helps them spot fleeting opportunities to buy or sell the stock, based on its movements outside its usual range.

The sine wave can be a useful tool when stocks are generally moving cyclically. It fails, however, when the markets overall are trending, meaning they are moving in a way that is less predictable.