We study causality between bivariate curve time series using the Granger causality generalized measures of correlation. With this measure, we can investigate which curve time series Granger-causes the other; in turn, it helps determine the predictability of any two curve time series. Illustrated by a climatology example, we find that the sea surface temperature Granger-causes the sea-level atmospheric pressure. Motivated by a portfolio management application in finance, we single out those stocks that lead or lag behind Dow-Jones industrial averages. Given a close relationship between S&P 500 index and crude oil price, we determine the leading and lagging variables.

中文翻译：

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二元平稳曲线时间序列的格兰杰因果关系

我们使用 Granger 因果关系广义相关性度量来研究双变量曲线时间序列之间的因果关系。通过这个度量，我们可以调查哪个曲线时间序列格兰杰导致另一个；反过来，它有助于确定任意两条曲线时间序列的可预测性。以气候学为例，我们发现海面温度格兰杰导致海平面大气压。受金融投资组合管理应用程序的启发，我们挑选出那些领先或落后于道琼斯工业平均指数的股票。鉴于标准普尔 500 指数与原油价格之间的密切关系，我们确定了领先和滞后变量。