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Inspired by the philosophy of ancient Chinese Taoism, Xu's Bayesian ying-yang (BYY) learning technique performs clustering by harmonizing the training data (yang) with the solution (ying). In our previous work, the BYY learning technique was applied to a fuzzy cerebellar model articulation controller (FCMAC) to find the optimal fuzzy sets; however, this is not suitable for time series data analysis. To address this problem, we propose an incremental BYY learning technique in this paper, with the idea of sliding window and rule structure dynamic algorithms. Three contributions are made as a result of this research. First, an online expectation-maximization algorithm incorporated with the sliding window is proposed for the fuzzification phase. Second, the memory requirement is greatly reduced since the entire data set no longer needs to be obtained during the prediction process. Third, the rule structure dynamic algorithm with dynamically initializing, recruiting, and pruning rules relieves the ??curse of dimensionality?? problem that is inherent in the FCMAC. Because of these features, the experimental results of the benchmark data sets of currency exchange rates and Mackey-Glass show that the proposed model is more suitable for real-time streaming data analysis.