  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.
