  Recommender systems have been extensively used by the entertainment industry,
business marketing and the biomedical industry. In addition to its capacity of
providing preference-based recommendations as an unsupervised learning
methodology, it has been also proven useful in sales forecasting, product
introduction and other production related businesses. Since some consumers and
companies need a recommendation or prediction for future budget, labor and
supply chain coordination, dynamic recommender systems for precise forecasting
have become extremely necessary. In this article, we propose a new
recommendation method, namely the dynamic tensor recommender system (DTRS),
which aims particularly at forecasting future recommendation. The proposed
method utilizes a tensor-valued function of time to integrate time and
contextual information, and creates a time-varying coefficient model for
temporal tensor factorization through a polynomial spline approximation. Major
advantages of the proposed method include competitive future recommendation
predictions and effective prediction interval estimations. In theory, we
establish the convergence rate of the proposed tensor factorization and
asymptotic normality of the spline coefficient estimator. The proposed method
is applied to simulations and IRI marketing data. Numerical studies demonstrate
that the proposed method outperforms existing methods in terms of future time
forecasting.
