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This paper examines whether standard price-discovery measures can reliably identify directional predictive precedence in a highly correlated commodity-equity system. Using 21 years of daily data for Petrobras and the Ibovespa (2005–2026), the study separates a measurement problem in forecast error variance decomposition from the reduced-form question of directional predictability in the conditional mean. The empirical strategy combines Monte Carlo simulation, generalized and Cholesky forecast error variance decompositions, full-sample and rolling-window Granger causality tests, a continuous Granger Leadership Index, Gaussian mixture regime classification, robustness checks, and out-of-sample forecasting validation. The results show that Cholesky-based FEVDs can be systematically misleading in high-correlation settings: at the observed contemporaneous correlation, generalized FEVD symmetry is mechanically induced by row normalization, while Cholesky attribution changes sharply under alternative orderings. By contrast, first-moment predictability reveals a directional asymmetry from Petrobras to the Ibovespa, interpreted as conditional-mean predictive precedence rather than structural informed trading or definitive price discovery. This asymmetry survives alternative lag structures, weekly aggregation, univariate GARCH filtering, within-dataset proxy controls, and a stylized equal-weight ex-Petrobras benchmark. Rolling evidence further identifies five persistent predictive regimes that alternate between firm-led, neutral, and macro-dominant states, indicating that firm-index predictive relations are regime dependent rather than static. Out-of-sample forecasting shows that the identified predictive precedence does not generate exploitable one-step-ahead gains (RMSE ratio = 1.002, OOS-R2 = −0.003, DM p = 0.451), thereby delimiting the economic scope of the findings. Overall, the results support a reduced-form interpretation of Petrobras–Ibovespa predictive dynamics and highlight the need to distinguish variance connectedness from conditional-mean predictive content when contemporaneous correlation is high.
Domínguez et al. (Thu,) studied this question.