Abstract
We employ dynamic time warping (DTW), a non-parametric pattern recognition technique based on a dynamic programming algorithm, to analyze whether futures markets for crude oil and natural gas have facilitated price discovery over the last decade. Should futures prices absorb and reflect information before spot prices, they will move first and lead spot prices, suggesting that they dominate spot prices and play an important role in price discovery. The results show that natural gas futures prices led spot prices more frequently between 2019 and 2023 than during the five years preceding this turbulent period. In the case of crude oil, however, futures prices lagged spot prices more often than leading them. The evidence suggests that futures prices have not consistently fulfilled their price discovery role in the two energy markets. The results also indicate that short-term futures contracts play a more dominant role in price discovery than long-term contracts. Additionally, we demonstrate the advantages of DTW: it lends itself well to analyzing small samples with different orders of integration; it can discover linear and nonlinear relationships between time series; notably, it can detect period-to-period changes in the duration and direction of lead-lag associations between two series and present the results intelligibly.