  What is the dominating mechanism of the price dynamics in financial systems
is of great interest to scientists. The problem whether and how volatilities
affect the price movement draws much attention. Although many efforts have been
made, it remains challenging. Physicists usually apply the concepts and methods
in statistical physics, such as temporal correlation functions, to study
financial dynamics. However, the usual volatility-return correlation function,
which is local in time, typically fluctuates around zero. Here we construct
dynamic observables nonlocal in time to explore the volatility-return
correlation, based on the empirical data of hundreds of individual stocks and
25 stock market indices in different countries. Strikingly, the correlation is
discovered to be non-zero, with an amplitude of a few percent and a duration of
over two weeks. This result provides compelling evidence that past volatilities
nonlocal in time affect future returns. Further, we introduce an agent-based
model with a novel mechanism, that is, the asymmetric trading preference in
volatile and stable markets, to understand the microscopic origin of the
volatility-return correlation nonlocal in time.
