Corrigendum: Error bounds and asymptotic expansions for Toeplitz product functionals of unbounded spectra

Abstract

We investigate error orders for integral limit approximations to traces of products of Toeplitz matrices generated by integrable functions on having some singularities at the origin. Even though a sharp error order of the above approximation is derived in Theorem 2 of Lieberman and Phillips (2004, Journal of Time Series Analysis, 25(5) 733–753), its proof contains an inaccuracy. In the present article, we reinvestigate error orders of the above trace approximation problem and rigorously validate the sharp error order derived in Lieberman and Phillips (2004, Journal of Time Series Analysis, 25(5) 733–753).