[QUANT LECTURE] Local predictability via divergence
Market Inefficiencies - Information Theoretic Approach
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Local predictability via divergence
This chapter treats an inefficiency claim as a statement about distributional separation. Fix an outcome variable R and a horizon at which R is measured. The future becomes the probability law of R at decision time. The object of interest is the gap between the baseline future and the state-conditioned future, where X is a declared state variable. A divergence measures this gap by quantifying how much the predictive law of R changes when we move from “no state” to “state x,” and it keeps the research claim separate from the execution layer that turns structure into PnL.
What’s inside:
What divergence is for in trading research. Divergence serves as a dependence detector that lives in conditional laws, so the claim stays tied to how the future distribution changes across states.
Scope and limits of divergence. The chapter draws a boundary between divergence evidence and realized profit, and it frames the inefficiency claim inside a declared horizon, state region, and environment class.
Local divergence maps. The workflow treats R and X as design objects, then compares P(R|X≈x) to P(R) across state domains to build a field of separations over the state space.
Local inefficiency domains. A local inefficiency corresponds to a state domain that supports a stable statement across repeated visits, with an activation domain and a transition zone where the conditional law returns toward the baseline mixture.
Tail divergences. The chapter introduces tail-focused separation to target structure that lives inside extremes, where distributional shape changes matter most for constraint-relevant outcomes.
Divergence stability under perturbation. Evidence is checked under perturbations of the measurement lens (domain rules, estimation choices) and recomputed on held-out path segments to verify persistence.
Predictability has geometry. The chapter treats predictability as a geometric object with locality, boundaries, and transitions, so the research claim becomes measurable along the market’s movement through state regions.
