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.

翻译：我们用“Granger”的因果关系通用度量来研究双轨曲线时间序列之间的因果关系。 通过这一计量,我们可以调查哪个曲线时间序列是另一个“Granger”的原因;反过来,它有助于确定任何两个曲线时间序列的可预测性。以气候学为例,我们发现海面温度指数是海平面大气压力的原因。受金融投资组合管理应用的驱动,我们专门挑出那些导致或落后于Dow-Jones工业平均值的种群。鉴于S & P 500指数和原油价格之间的密切关系,我们决定了领先和滞后变量。