  Recurrent event time data arise in many studies, including biomedicine,
public health, marketing, and social media analysis. High-dimensional recurrent
event data involving large numbers of event types and observations become
prevalent with the advances in information technology. This paper proposes a
semiparametric dynamic factor model for the dimension reduction and prediction
of high-dimensional recurrent event data. The proposed model imposes a
low-dimensional structure on the mean intensity functions of the event types
while allowing for dependencies. A nearly rate-optimal smoothing-based
estimator is proposed. An information criterion that consistently selects the
number of factors is also developed. Simulation studies demonstrate the
effectiveness of these inference tools. The proposed method is applied to
grocery shopping data, for which an interpretable factor structure is obtained.
