Online prediction of noisy time series: Dynamic adaptive sparse kernel recursive least squares from sparse and adaptive tracking perspective

Abstract

With the deepening of the research on kernel recursive least squares (KRLS), significant researches have been applied to time series online prediction. However, it usually ignores the extraneous and redundant factors in the raw data, which can cause bias in the prediction. In addition, it usually contains both noise and non-stationary characteristics, resulting in deteriorated prediction accuracy and reduced model efficiency. To ease the above two drawbacks of conventional KRLS, this brief presents a dynamic adaptive sparse kernel recursive least squares (DASKRLS) filtering algorithm. It first uses the online vector projection standard and the approximate linear dependence criterion to effectively constrain kernel matrix dimension, and reduce the computational complexity of the model. After that, the regularized maximum correlation entropy criterion to significant process noise-containing data from the perspective of improving generalization ability. Moreover, the adaptive update mechanism can dynamically track the real-time weight of non-stationary signals. The dynamic sparse process is essentially equivalent to a feature selection process that maintains low-dimensional manifold information. Lorenz benchmarking experiments and real data experiments show that DASKRLS achieves better prediction performance in complex systems with noise and nonstationary.