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.

中文翻译：

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价格发现回归 — 使用动态规划方法分析能源现货和期货价格


我们采用动态时间扭曲 （DTW），这是一种基于动态规划算法的非参数模式识别技术，来分析原油和天然气期货市场在过去十年中是否促进了价格发现。如果期货价格先于现货价格吸收和反映信息，它们将首先移动并引领现货价格，这表明它们主导现货价格并在价格发现中发挥重要作用。结果显示，与这一动荡时期之前的五年相比，2019 年至 2023 年期间，天然气期货价格更频繁地引领现货价格。然而，就原油而言，期货价格落后于现货价格的频率高于领先于现货价格。证据表明，期货价格在这两个能源市场中并未始终如一地发挥其价格发现作用。结果还表明，短期期货合约在价格发现中比长期合约起着更主导的作用。此外，我们还展示了 DTW 的优势：它非常适合分析具有不同积分顺序的小样品;它可以发现时间序列之间的线性和非线性关系;值得注意的是，它可以检测两个序列之间超前滞后关联的持续时间和方向的期间变化，并清晰地呈现结果。