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#137: A Furrier Transforms a Fourier

#137: A Furrier Transforms a Fourier

micksonmatch
September 03, 2024

S2N Spotlight

When growing up that there was a time when getting a fur jacket was all the rage. I remember my mum going to the furrier for a fitting and getting her dream “mink” as a gift from my dad. This was before the time when activists were getting their knickers in a not. I only mention this story as I needed a reason to mention a furrier in my subject line. I love to play on words, even if I am the only one who laughs.

Today I am going to spotlight a concept that is very close to the name I chose for this business, Signal2Noise (S2N). Hat tip to Jason Strimpel for the code foundation. We are going to explore how to transform fast Fourier signals. Clint Eastwood would say, “Are you feeling lucky, punk?” I would say, “How smart do you think you are?” Probably not so smart if you look up the definition of Fourier Transform.

Let me explain this in a non-scientific way, you are going to be blown away by the chart output below. I am probably a little too excited. Never in a million years did I expect the result I got.

First an analogy to get a grasp of the power of this concept.

I pour myself a drink, dim the lights, and lie on the couch to listen to music. A song comes on with Mariah Carey signing a duet with Brian Johnson the lead singer of heavy metal band AC/DC, each one belting out the song in their respective signature voices. I have a headache so I want to get rid of Brian Johnson, I write a program that easily deletes his voice from the song. It is very easy to identify their different voice frequencies from the pitch in their voices. Brian Johnson is noise to me, at least on this night. I am left with Mariah Carey’s smooth tone and pitch frequency. Mike is now happy and chilled.

When you apply fast fourier transform techniques to a time series of data such as the S&P 500 from May 2000 until now you transform the time series into a frequency period. Don’t mistake a period for the day in a time series. A period measures the cycle identified within the time series. If I am confusing you ignore this detail lets focus on the big picture. I have counted 6000 periods in this time series and I have chosen the top 500 dominant periods of this series and reconstructed a price series from these “signals” and I get what I have marked the “recovered” line in orange.

Based on all the mathematical transformations of identified cycles within the time series we get an incredibly bearish forecast from the Fast Fourier Transform. When I started writing this I had no idea this would play out like it did as the example I looked at was more than a year ago and the parameters chosen painted a very different picture. It will be very interesting to see if the orange line forecast proves accurate.