Statistics and Its Interface

Volume 8 (2015)

Number 3

Application of structured low-rank approximation methods for imputing missing values in time series

Pages: 321 – 330

DOI: http://dx.doi.org/10.4310/SII.2015.v8.n3.a6

Authors

Jonathan Gillard (School of Mathematics, Cardiff University, Cardiff, Wales, United Kingdom)

Anatoly Zhigljavsky (School of Mathematics, Cardiff University, Cardiff, Wales, United Kingdom)

Abstract

In this paper we consider an important statistical problem of imputing missing values into a time series data. We formulate this problem as a problem of structured low-rank approximation (SLRA), which is a problem of matrix analysis. One of the main difficulties in this SLRA problem is related to the fact that the norm which defines the quality of low-rank approximations is different from the Frobenius norm.We argue that the arising SLRA problem is a very difficult optimization problem and then consider and compare a number of algorithms for its solution.

Keywords

time series, missing data, Hankel structured low-rank approximation

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