  Describing a time series parsimoniously is the first step to study the
underlying dynamics. For a time-discrete system, a generating partition
provides a compact description such that a time series and a symbolic sequence
are one-to-one. But, for a time-continuous system, such a compact description
does not have a solid basis. Here, we propose to describe a time-continuous
time series using a local cross section and the times when the orbit crosses
the local cross section. We show that if such a series of crossing times and
some past observations are given, we can predict the system's dynamics with
fine accuracy. This reconstructability neither depends strongly on the size nor
the placement of the local cross section if we have a sufficiently long
database. We demonstrate the proposed method using the Lorenz model as well as
the actual measurement of wind speed.
