Statistics and Its Interface
Volume 10 (2017)
Iterative algorithms for weighted and unweighted finite-rank time-series approximations
Pages: 5 – 18
The problem of time series approximation by series of finite rank is considered from the viewpoint of signal extraction. For signal estimation, a weighted least-squares method is applied to the trajectory matrix of the considered time series. Matrix weights are chosen to obtain equal or approximately equal weights in the equivalent problem of timeseries least-squares approximation. Several new methods are suggested and examined together with the Cadzow’s iterative method. The questions of convergence, computational complexity, and accuracy are considered for the proposed methods. The methods are compared on numeric examples.
time series, time series of finite rank, weighted low-rank approximation, signal estimation, singular spectrum analysis, Cadzow’s iterative method
2010 Mathematics Subject Classification
Primary 62G05, 94A12. Secondary 37M10, 60G35.