Distinguished from traditional knowledge graphs (KGs), temporal knowledge graphs (TKGs) must explore and reason over temporally evolving facts adequately. However, existing TKG approaches still face two main challenges, i.e., the limited capability to model arbitrary timestamps continuously and the lack of rich inference patterns under temporal constraints. In this paper, we propose an innovative TKGE method (PTBox) via polynomial decomposition-based temporal representation and box embedding-based entity representation to tackle the above-mentioned problems. Specifically, we decompose time information by polynomials and then enhance the model’s capability to represent arbitrary timestamps flexibly by incorporating the learnable temporal basis tensor. In addition, we model every entity as a hyperrectangle box and define each relation as a transformation on the head and tail entity boxes. The entity boxes can capture complex geometric structures and learn robust representations, improving the model’s inductive capability for rich inference patterns. Theoretically, our PTBox can encode arbitrary time information or even unseen timestamps while capturing rich inference patterns and higher-arity relations of the knowledge base. Extensive experiments on real-world datasets demonstrate the effectiveness of our method.