Nonlinear dynamics in arbitrage of the S&P 500 index and futures: A threshold error-correction model

Using a three-regime threshold error-correction model, we investigate the nonlinear dynamics of the S&P 500 index and futures. First, using the SupLM statistic, we report estimates of two thresholds for the three-regime model to explain the nonlinear dynamics in arbitrage of the S&P 500 index and futures. This provides empirical evidence of the no-arbitrage band predicted by the cost-of-carry model. Second, using quasi-maximum likelihood estimation, we demonstrate that those indexes that are located outside the no-arbitrage band are a nonlinear stationary process of mean-reversion to the no-arbitrage band. However, index and futures that are located within the no-arbitrage band are non-stationary. Third, we confirm an earlier finding that futures price leads the nonlinear mean-reverting behavior of the index but not vice versa. Impulse response function analysis and forecasting performance of three-regime error-correction model reinforce our findings and our estimation results are robust with different specifications of pricing error terms and endogenous variables.