Empirical Predictability Limits of Financial Markets via Correlated–Decorrelated Structure Function Decomposition: A Departure from Atmospheric Turbulence Theory

Theoretical predictability limits of the atmosphere have been derived, in prior work by the author

and others, from a multifractal cascade formalism in which the correlated and decorrelated

components of a turbulent field’s polyspectrum are tracked as a function of lead time, with the

predictability limit defined as the time at which correlated energy falls to a fixed fraction of total

energy (Ramanathan et al., 2019; Ramanathan & Satyanarayana, 2019, 2021). This paper investig‐

ates whether the same formalism transfers to financial markets. We show that it does not transfer

directly: financial return/price-increment fields are empirically conservative (Hurst-type non-

conservation exponent H ≈ 0), which collapses the moment-scaling relationship (ξ(q) = qH −

K(qη) + qK(η)) that the atmospheric derivation depends on, and removes the spatial dimension

(and with it, the entire generalized-scale-invariance anisotropy apparatus — sphero-scale, aspect

ratio, vertical stratification exponent) that the atmospheric formula’s lead-time dependence is

built on. We therefore abandon the parametric route and construct the correlated and decorrel‐

ated structure functions directly and empirically, defining the predictability limit operationally as

the lag at which they are equal, and — going further — treating the full gap between them as a

function of lag as the object of interest rather than a single crossing time. Applied to a raw

(untransformed) multi-asset universe spanning equities, commodities, crypto, rates, FX, and

volatility, this reveals that the correlated fraction of the moment budget is bounded within an

instrument-specific range across the entire 300-trading-day lag window tested — never reaching

full correlation or full decorrelation, unlike the atmospheric picture’s terminal state. But the

shape of that boundedness is not uniform, and is not uniformly unlike the atmosphere either:

classifying instruments by how many times their correlated and decorrelated components swap

dominance reveals three distinct regimes. A minority of instruments (Treasury bonds and a few

sector ETFs) remain correlation-dominant for the entire year tested, never crossing into decorrel‐

ation at all. One instrument (VIX) shows, at typical (q=2) moment order, a single clean transition

that closely resembles the atmospheric formalism’s own monotonic picture, just plateauing at a

bound rather than reaching zero — though this resemblance disappears at higher moment order

(q=4), where VIX’s extreme fluctuations show the same repeated-crossing behavior as everything

else. The majority of equities and Bitcoin show that repeated-crossing behavior throughout: pre‐

dictability that comes and goes in discrete, recurring “pockets” at specific lags rather than

decaying once and staying gone. A pocket at approximately 21–24 trading days recurs across most

equities tested; a second pocket near 252 trading days (one calendar year) is prominent for SPY

specifically, and coincides with the strongest validated-signal concentration independently found

for SPY by the authors’ unrelated Conditional Probability of Exceedance (CPE) framework — a

nonparametric methodology sharing no assumptions with the structure-function approach used

here. We argue this cross-method convergence, together with the observed asset-class and

moment-order-dependent heterogeneity in crossing behavior, supports treating the pocket struc‐

ture as a genuine, economically meaningful feature of market structure for the instruments that

show it, rather than an artifact of either method or a universal law applying uniformly across all

instruments.