Regularized Error Correction Framework with Multivariate Simulation for Multi Product Crack Spread Forecasting

This paper proposes a probabilistic forecasting framework for the crack spread of petroleum derivatives, defined as the log-price ratio between each derivative and Brent crude oil. Motivated by a risk analysis context, the framework is designed to enable joint multivariate simulation of multiple derivatives. Inspired by the Error Correction Model (ECM) structure, the methodology captures both short- and long-term dynamics while avoiding the complexity of modeling each spot price individually. Two variants are explored: a multivariate regularized regression and a simpler univariate formulation. Both approaches are evaluated under an expanding-window scheme, using scenario-based simulations via multivariate bootstrap. A case study involving ten petroleum derivatives and two benchmark models—random walk and mean reversion—assesses forecast accuracy for horizons of up to 24 months. Results suggest that the univariate model delivers competitive or superior performance in several settings, especially for short-term forecasts.