A MULTIVARIATE AUTOREGRESSIVE FRAMEWORK FOR ESTIMATING S & P 500 FUTURES

Abstract

This study aims to model and estimate the behavior of S&P 500 index futures through an econometric framework that moves from multiple linear regression (OLS) to a first-order autoregressive specification AR (1). Using daily historical series for the period between May and June 2026—a period without precedent globally due to the United States–Iran conflict—the influence of West Texas Intermediate (WTI) crude oil and gold futures was analyzed as explanatory variables. The results of the baseline model indicate a moderate explanatory power (R² = 0.632), but with evidence of positive serial autocorrelation (DW = 1.409) that compromises the efficiency of the estimators. The transition to the AR (1) model proved essential, achieving a better fit (R² = 0.666) and, more importantly, correcting residual dependence by reaching a Durbin–Watson statistic of 2.164. The findings suggest that, based on the autoregressive model obtained to estimate the behavior of S&P 500 index futures, although the independent variables are statistically significant, the temporal persistence of the index itself is the determining factor for obtaining stochastically neutral residuals.