Statistics and Its Interface

Volume 10 (2017)

Number 1

Iterative algorithms for weighted and unweighted finite-rank time-series approximations

Pages: 5 – 18

DOI: http://dx.doi.org/10.4310/SII.2017.v10.n1.a1

Authors

Nikita Zvonarev (Department of Statistical Modelling, Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia)

Nina Golyandina (Department of Statistical Modelling, Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia)

Abstract

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.

Keywords

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.

Full Text (PDF format)