  In this paper, we explore an optimal timing strategy for the trading of price
spreads exhibiting mean-reverting characteristics. A sequential optimal
stopping framework is formulated to analyze the optimal timings for both
entering and subsequently liquidating positions, all while considering the
impact of transaction costs. Then we leverages a refined signature optimal
stopping method to resolve this sequential optimal stopping problem, thereby
unveiling the precise entry and exit timings that maximize gains. Our framework
operates without any predefined assumptions regarding the dynamics of the
underlying mean-reverting spreads, offering adaptability to diverse scenarios.
Numerical results are provided to demonstrate its superior performance when
comparing with conventional mean reversion trading rules.
