Studying Periodicity Using Discrete Fourier Transforms (DFT) and Potential Applications to Financial Markets

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One of the most fascinating demonstrations of nature’s laws is how protein structure is fundamentally directed by the underlying amino acid sequence and the interplay in the residues’ chemical interactions.  Understanding this phenomenon is so critical because the biological activity of a protein only manifests itself after the protein folds into its three-dimensional structure.

Back at Columbia, I worked on a project where I explored the question of whether spectral techniques could guide the analysis of Trans-membrane (TM) proteins, a uniquely interesting class of proteins for their structural and functional properties.  Functionally, TM proteins are able to mediate nearly all functional aspects of the lipid bilayer, including signaling, transport, and adhesion.

Discrete Fourier Transform (DFT) techniques seemed an elegant way to observe non-local interactions which are not easily captured by other window-based computational techniques.

While the results were not conclusive, as is often the case when theory meets practice, there were some promising observations.  For example, the characteristic frequency of Alpha-strands (a protein sub-structure) at 0.29 correlated well with the known structural periodicity of 3.6 residues per turn observed in nature.

To illustrate, here’s a picture of a 1c17 Alpha TM protein and the composite DFT spectrum for Alpha strands showing a sharp peak at frequency 0.29.

Contrast the above with the composite DFT spectrum of Beta TM proteins shown below.  On the left is a picture of a 2a9h Beta TM protein. and on right is the composite DFT spectrum with a distinct peak at frequency 0.46. 

While there is some promise in using DFT to study protein structure, what about its application to financial markets? It would seem that short-term volatility may be a good candidate for DFT analysis. The 6-month volatility chart for the S&P500 (courtesy Google Finance) shown below appears to have some periodicity.

I don’t know the answer and I haven’t explored this topic in depth.  That said,  if anyone has done more work in this area or has a strong view I would love to hear from them.

On a somewhat related note, if you’re even remotely interested in Information Theory, including The Kelly Formula, and its application to the financial markets, I highly recommend Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street by William Poundstone.

 

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