Kernel recursive least squares (KRLS) is a kind of kernel methods, which has attracted wide attention in the research of time series online prediction. It has low computational complexity and updates in a recursive form. However, as data size increases, computational complexity of calculating kernel inverse matrix will raise. And it has some difficulties in accommodating time-varying environments. Therefore, we have presented an improved KRLS algorithm for multivariate chaotic time series online prediction. Approximate linear dependency, dynamic adjustment, and coherence criterion are combined with quantization to form our improved KRLS algorithm. In the process of online prediction, it can bring computational efficiency up and adjust weights adaptively in time-varying environments. Moreover, Lorenz chaotic time series, El Nino-Southern Oscillation indexes chaotic time series, yearly sunspots and runoff of the Yellow River chaotic time series online prediction are presented to prove the effectiveness of our proposed algorithm.

中文翻译：

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基于改进核递归最小二乘算法的多元混沌时间序列在线预测


核递归最小二乘法（KRLS）是一种核方法，在时间序列在线预测研究中受到广泛关注。它的计算复杂度较低，并且以递归形式更新。然而，随着数据量的增加，计算核逆矩阵的计算复杂度将会增加。而且它在适应时变环境方面存在一些困难。因此，我们提出了一种改进的KRLS算法用于多元混沌时间序列在线预测。近似线性相关性、动态调整和相干性准则与量化相结合，形成了我们改进的 KRLS 算法。在在线预测过程中，它可以提高计算效率并在时变环境中自适应调整权重。此外，还给出了洛伦兹混沌时间序列、厄尔尼诺-南方涛动指数混沌时间序列、年度太阳黑子和黄河径流混沌时间序列在线预测，证明了算法的有效性。