We present an improved kernel recursive least squares (KRLS) algorithm for the online prediction of nonstationary time series. In order to adaptively sparsify a selected kernel dictionary for the KRLS algorithm, the approximate linear dependency (ALD) criterion based KRLS algorithm is combined with the quantized kernel recursive least squares algorithm to provide an initial framework. In order to sufficiently track the strongly changeable dynamic characteristics due to nonstationarity, a forgetting factor is further inserted into the proposed combined algorithm. It is shown that our proposed algorithm, referred to as the FFIKRLS algorithm, provides a clearly compatible algorithm structure and can be improved by the existing modeling techniques from both mapping and weights updating perspectives. Numerical simulations using benchmark Lorenz time series in comparison with existing methods have demonstrated that the proposed algorithm has superior performance in terms of both predictive accuracy and kernel dictionary size.

中文翻译：

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基于改进核递归最小二乘算法的非平稳时间序列在线预测


我们提出了一种改进的核递归最小二乘（KRLS）算法，用于非平稳时间序列的在线预测。为了自适应地稀疏KRLS算法所选择的核字典，将基于近似线性相关性(ALD)准则的KRLS算法与量化核递归最小二乘算法相结合以提供初始框架。为了充分跟踪由于非平稳性而产生的强烈变化的动态特性，在所提出的组合算法中进一步插入了遗忘因子。结果表明，我们提出的算法（称为 FFIKRLS 算法）提供了明显兼容的算法结构，并且可以从映射和权重更新的角度通过现有建模技术进行改进。使用基准洛伦兹时间序列与现有方法进行的数值模拟表明，所提出的算法在预测精度和核字典大小方面都具有优越的性能。