Chen, Aoxiang; Li, Qingna Multivariate series noise reduction via sequential majorization method and its extensions. (English) Zbl 1498.62166 Pac. J. Optim. 18, No. 3, 545-564 (2022). Summary: Based on the Hankel structured low-rank approximation and the technique of majorization, the sequential majorization method (SSM-Cadzow) proposed by H.-D. Qi et al. [Stat. Interface 11, No. 4, 615–630 (2018; Zbl 06944671)] has been proven to be an effective and fast method for the signal extraction from noisy time series. This method elevates the approximation of low-rank matrix by designing a new object function. In this paper, we use the idea of multivariate analysis to reconstruct the SMM-Cadzow method and therefore form the multivariate version of SSM-Cadzow (MSMM-Cadzow). We thoroughly describe the problems of selecting two important parameters (window length and the rank of the low-rank matrix). The result of signal extraction largely depends on the two parameters. The condition which perfectly fits the MSMM-Cadzow model is also introduced in the paper. Focusing on denoising the weak signal, we propose two new schemes (recycling MSMM algorithm and variate accumulation MSMM algorithm) using the MSMM-Cadzow. The numerical results demonstrated that MSMM-Cadzow has a significant importance on signal extraction and the denoising of weak signal has been improved by the proposed algorithms (recycling MSMM algorithm and variate accumulation MSMM algorithm). MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M15 Inference from stochastic processes and spectral analysis 62-08 Computational methods for problems pertaining to statistics 65F55 Numerical methods for low-rank matrix approximation; matrix compression 65K10 Numerical optimization and variational techniques Keywords:signal extraction; multivariate analysis; weak signal recovery; Hankel matrix Citations:Zbl 06944671 PDFBibTeX XMLCite \textit{A. Chen} and \textit{Q. Li}, Pac. J. Optim. 18, No. 3, 545--564 (2022; Zbl 1498.62166) Full Text: Link