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

TL;DR

This paper introduces new iterative algorithms for finite-rank approximations of time series, focusing on signal extraction, with analysis of convergence, complexity, and accuracy, and compares them to existing methods through numerical experiments.

Contribution

It proposes novel weighted least-squares iterative algorithms for finite-rank time series approximation, enhancing signal extraction techniques.

Findings

New algorithms demonstrate improved convergence properties

Methods achieve comparable or better accuracy than existing approaches

Numerical examples validate effectiveness and computational efficiency

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 time-series 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.