  The curve time series framework provides a convenient vehicle to accommodate
some nonstationary features into a stationary setup. We propose a new method to
identify the dimensionality of curve time series based on the dynamical
dependence across different curves. The practical implementation of our method
boils down to an eigenanalysis of a finite-dimensional matrix. Furthermore, the
determination of the dimensionality is equivalent to the identification of the
nonzero eigenvalues of the matrix, which we carry out in terms of some
bootstrap tests. Asymptotic properties of the proposed method are investigated.
In particular, our estimators for zero-eigenvalues enjoy the fast convergence
rate n while the estimators for nonzero eigenvalues converge at the standard
$\sqrt{n}$-rate. The proposed methodology is illustrated with both simulated
and real data sets.
