This project builds a market-regime complexity indicator inspired by polynomial slow entropy in dynamical systems.
The implementation is a finite-sample symbolic proxy rather than a direct estimate of measure-theoretic slow entropy. Daily returns are converted into symbolic states that encode direction and volatility quartile. Inside each rolling window, the indicator counts distinct symbolic words of different block lengths and estimates how quickly this word inventory grows.
p_W(n) = number of distinct symbolic return words of length n in window W
alpha_W ~= slope of log p_W(n) versus log n
I applied the indicator to SPY daily prices from 2016-05-09 to 2026-05-08 using a one-year rolling window. The highest-complexity windows cluster around the 2020 COVID shock and recovery, when the market moved through abrupt drawdown, policy response, liquidity shifts, and rapid rebound.
The reading is not simply high volatility. The indicator asks whether the symbolic return-pattern inventory keeps expanding as the observation block gets longer. In the 2020 windows, SPY paths were harder to compress into short recurring motifs, which is consistent with regime instability and weaker short-horizon signal reliability.
Repository: github.com/minhua-cheng/slow-entropy-market-complexity