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Multimedia stream monitoring refers to removing unwanted and malicious records from multimedia streams. In this application, a large number of filtering queries are registered on time-critical multimedia streams. Each filtering query contains multiple meta filters and a meta filter is shared among multiple filtering queries. The filtering queries and meta filters form a bipartite graph, and the objective is to minimize the overall evaluation time of the queries in the bipartite graph. In order to achieve this goal, some heuristic algorithms were proposed to order the shared meta filters in the graph to reduce the overall evaluation cost. While these methods can achieve near-optimal solutions in ideal stream environments that have stationary probability distributions, in this paper we propose an Adaptive Shared-filter Ordering Model (ASOM) for efficient filtering in dynamic data stream environments. To capture new trends and patterns along dynamic data streams, ASOM uses a time-based exponential smoothing forecasting method to adaptively order the shared meta filters for fast estimation. Experiments demonstrate that ASOM outperforms existing heuristic ordering methods in dynamic stream environments.