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About this paper
Alex Iosevich, Vishal Gupta
A mathematical framework explains why large values in real-life time series often show structured patterns, using the Fourier ratio as a complexity measure and a generalized Chang's Lemma. This approach demonstrates that a small Fourier ratio corresponds to a small additive generating set for a time series's large values, which successfully spanned extreme points in US inflation and Delhi climate data.
Key insights
- The Fourier ratio serves as a quantifiable diagnostic for the presence and strength of additive structure in the tails of time series.
- When a time series has a small Fourier ratio, its largest values can be additively generated by a significantly smaller set of indices using simple combinations.
- Additive combinatorics provides a rigorous mathematical explanation for the empirically observed 'structured tails' phenomenon in diverse real-world time series.
Summary by alphaXiv.
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