The present study focuses on the rigorous analysis of the order and structural configuration of memory in big data models regulated by polynomial memory functions. Polynomial memory-based frameworks are examined herein, as they offer a more accurate representation for capturing nonlinear dependencies within large-scale datasets while exhibiting a greater potential for convergence as the data volume increases. A comprehensive theoretical framework is developed to estimate the memory order of a general polynomial time series model, wherein it is demonstrated that the memory order uniformly escalates to three under the revised formulation, irrespective of the polynomial indices or any embedded parameters. To substantiate the theoretical findings, extensive simulations are conducted, providing empirical validation and illustrating the robustness of the proposed model, which is further supported by its successful application to real-world financial time series data.