Scale-Ordered Contagion: A Spectral Theory of Heterogeneous Information Adaptation in Financial Networks

In this paper, an attempt is made to examine how the speed at which financial markets absorb information governs the way shocks travel between them. It may be noted that a market which digests news slowly will register an incoming shock more gradually, and hence over longer horizons, than a market which reacts quickly. Building on the Heterogeneous Agents Contagion versus Interdependence (HACI) framework, in which advanced economies adapt quickly and emerging economies slowly, we develop a spectral theory of contagion in which both the originating and the receiving market filter the shock. The central result is an intuitive one: the slower of the two markets determines the time horizon over which contagion is felt most strongly. From this we obtain three testable predictions, jointly the Scale-Ordered Contagion Hypothesis, namely that contagion involving slower markets peaks at longer horizons; that the horizon pattern is the same in both directions for any pair of markets; and that only the strength of contagion, and not its timing, differs by direction. We then turn the theory into an estimator that recovers each market's speed of adaptation from the data, and bring the predictions to G20 equity markets over the period 2006 to 2026. The results are supportive, though we report them honestly: the horizon-ordering prediction holds (p=0.042); the symmetry prediction, which is the sharpest of the three, holds for all twenty-eight market pairs (p>0.05); the strength-asymmetry prediction lies in the predicted direction but is not statistically significant; and the method identifies India and China cleanly as the slowest adapters, though the fastest markets cannot be told apart from daily data. The framework thus offers a simple and testable account of why short-horizon and long-horizon contagion differ systematically with the speeds of the markets involved.