Traffic signal control systems often operate with a fixed time strategy when practical conditions prohibit adaptive traffic control built upon real-time traffic data. One of the most important challenges to have good performance for a fixed time strategy is to optimally identify the breakpoints that divide one day into different partitions, which is a time-of-day (TOD) breakpoints optimisation problem. Various solutions to this problem have been proposed based on classic clustering methods. However, these methods require empirical adjustment since they are not capable of incorporating the temporal information among traffic data. In this study, the TOD breakpoints optimisation problem is formulated as a time series data partitioning problem. A recursive algorithm is proposed to partition one day into several time periods based on the dynamic programming reformulation of the original problem. The appropriate number of partitions is determined through the elbow method. Then the authors present a case study based on the real data from Qingdao City in China that evaluates the proposed method against the existing ones. From simulation experiments, they illustrate that the proposed method is more effective in terms of operational performance measures such as maximum queue length and delay time than the existing ones.