A Game of Musical Markets

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So what has music got to do with financial markets? “Nothing” is probably what you would be inclined to think. However, in this post, I hope to show you how they are connected and it is all to do with waves.

Quiz

Before we get into it let’s do a quiz.

Click to reveal the quiz question below. Once you think you know click to reveal the answer.

Quiz: Which price chart is the ‘imposter’? (Click to reveal question)

The following graphs show some market prices but one is something else. Which one is the imposter? (Note that price levels and dates have been stripped off so we’re just looking at the shape of the graphs.)

Answer: and the imposter is … (Click to reveal answer)

So the first one is not a real market. Did you guess right?

Oddly the first chart looks more like a price series and the others do not. Often we are accustomed to looking at stock market charts which tend to slope upwards. This is not true all of the time of course and futures commodity markets such as the one above can be volatile or even stay sideways for a long time such as Cocoa.

So what is the imposter? If it’s not a real market then what is it? Reveal what it is below:

What is the imposter? (Click to reveal)
Humpback whale

It is the sound of a humpback whale’s song converted into a price series!

Below is the sound of the humpback whale that I used to create the price series. Press play to hear it.

How is it even possible to convert sound into a price series?

Sound Waves and Prices

This is where we start to get a connection with waves and prices. So what is a sound wave?

A sound wave is the pattern of disturbance caused by the movement of energy traveling through a medium (such as air, water, or any other liquid or solid matter) as it propagates away from the source of the sound.

The source is some object that causes a vibration, such as a ringing telephone, or a person’s vocal cords. The vibration disturbs the particles in the surrounding medium; those particles disturb those next to them, and so on. The pattern of the disturbance creates outward movement in a wave pattern, like waves of seawater on the ocean. The wave carries the sound energy through the medium, usually in all directions and less intensely as it moves farther from the source.

We can look at a sound wave by loading the sound into an application such as Audacity (which you can download for free at audacityteam.org) which is used by sound engineers to edit and modify the audio. This is what it looks like when you open the whale sound into Audacity:

Audio waveform of the sound of a humpback whale

Now, this doesn’t look much like a price series. Before we can understand the connection we must do a deeper dive into prices.

Price Series as a Wave Form

A price series is constructed by using a price value for a given day (or another time period). Price series are made up of price behaviour that represents movement over different time scales. This can be represented as waves (or frequencies). See my post on DSP Explained to learn more about this.

It is also possible to represent prices at returns which is the change from the previous period such as a daily change. If we convert a price series to returns it removes the effect of accumulation over time. For example, if we look at the returns of Corn we get the following:

Corn waveform

Now the price series is starting to look more like an audio waveform.

Price Series as Sound

Now that we have our market in the form of a waveform it’s now possible to convert it into sound.

Conversion is not straightforward because not all sound frequencies are audible. So I had to convert the waves to be relative to an audible sound, in this case, a continuous Convert A pitch note. I then adjusted the amplitude and set the audio samples that made it long enough to listen to. This was some custom code I wrote in Java. The price series was 20 years of data but from an audio perspective is hardly any data at all which is why I had to set the sampling to get 5 seconds of audio.

So what does the Corn Futures market sound like?

Press play to hear:

What did that sound like to you?

What it will sound like is white noise. White noise refers to a noise that contains all frequencies across the spectrum of audible sound in equal measure. Because white noise spans multiple bands of sound, it is sometimes referred to as broadband noise. Anecdotally, people often liken white noise to the static that comes from an untuned radio or television.

Are Prices Random White Noise?

So if prices converted to audio just sound like random white noise does that mean that markets are just random? What can we learn from this:

  • Markets are made up of many frequencies which represent oscillations with multiple frequencies and multiple amplitudes. In fact, there are so many frequencies its almost impossible for the human ear to distinguish between them
  • There are no dominant frequencies. If there were then we would be able to hear a discernable note or tone. Since there is none then perhaps there is no one dominant frequency for this market. Considering Corn is a cyclical crop it’s a surprise that there isn’t a dominant frequency.

Audio Filters

The synergy between audio and markets is that they are composed of multiple frequencies and can be analysed using Digital Signal Processing (DSP). We use DSP to analyse market frequencies and also to design filters for extracting information from market waveforms. DSP is widely used in audio. In the Audacity app mentioned above, you can use DSP filters to adjust the sound.

We can apply one of our filters to the Corn sound to enhance one of the frequencies we are interested in:

Rather than white noise we can now hear a tone. This is because filters are able to suppress the noise and emphasis the frequency we are interested in. In this example, we can still hear some white noise but it is quieter than before and the dominant sound is the frequency we are extracting. Also, if you listen carefully to the tone you can hear it undulating slightly. The waveform after the filter has been applied looks like this:

Filtered Corn waveform

As you listen to the audio you can hear slight changes in volume, particularly towards the end which correspond to the humps in the chart above.

Summary

Prices and sound are made from waves. I have a more detailed post in DSP Explained which describes some of the background theory and how multiple waves are extracted from prices.

DSP technology is widely applied in areas of audio and communications and many other areas of science and engineering where signals need to be analysed and interpreted.

What is little known is that this technology can also be applied to filtering interesting information from prices. The conversion from sound to prices and prices to sound demonstrates the applicability of the techniques. We use DSP as a theoretical framework for designing signal filters for detecting directional behaviour in markets.


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