Ramsey Theory and Curve-Fitting

Named after Frank P. Ramsey, Ramsey Theory, which proves the idea that within some sufficiently large systems, however disordered, there must exist some types of patterns. In other words, true randomness does not exist given any large sets of data derived off nature, or the financial markets.



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Key theorems of Ramsey theory are:

• Van der Waerden's theorem: For any given c and n, there is a number V, such that if V consecutive numbers are colored with c different colors, then it must contain an arithmetic progression of length n whose elements are all the same color.

• Hales-Jewett theorem: For any given n and c, there is a number H such that if the cells of a H-dimensional n×n×n×...×n cube are colored with c colors, there must be one row, column, etc. of length n all of whose cells are the same color. That is, if you play on a board with sufficiently many dimensions, then multi-player n-in-a-row tic-tac-toe cannot end in a draw, no matter how large n is, and no matter how many people are playing. Hales-Jewett theorem implies Van der Waerden's theorem.

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Relevance to algorithmic trading

Outside of fundamentally sound arbitrage, quantitatively found patterns, or so-called "edges", off empirical data have very little merit, or certainty of persistence into the future. This partly explains large failure rates for purely quant based trading entities. Truth is, it takes more than math and stats to make money in this game.