<p>To address the issue of degraded chaotic time series prediction performance due to second-order statistical characteristic noise and outliers, this paper proposes a novel robust kernel generalized soft root sign (KGSRS) adaptive filtering algorithm. The algorithm effectively suppresses the steady-state error and significantly improves the prediction accuracy by designing a negligible weight updating mechanism for outliers. The study explores the theoretical properties of the KGSRS algorithm in depth, not only establishing the energy conservation relationship and deducing sufficient conditions for the algorithm's convergence but also analyzing its computational complexity in detail. The validation experiments of Lorenz chaotic time series and sunspot chaotic time series in Bernoulli–Gaussian noise and α-stable distribution noise environments show that the KGSRS algorithm significantly improves the prediction accuracy in Lorenz series prediction and demonstrates excellent anti-noise performance when dealing with sunspot data. The experimental results fully demonstrate that compared with the existing algorithms, the KGSRS algorithm shows significant advantages in impulse noise suppression, steady-state performance optimization, and convergence speed improvement. The high consistency between predicted and expected values further validates the effectiveness and reliability of the algorithm in chaotic time series prediction.</p>