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Discussion Paper

Error Bounds and Asymptotic Expansions for Toeplitz Product Functionals of Unbounded Spectra

This paper establishes error orders for integral limit approximations to traces of powers to the pth order) of products of Toeplitz matrices. Such products arise frequently in the analysis of stationary time series and in the development of asymptotic expansions. The elements of the matrices are Fourier transforms of functions which we allow to be bounded, unbounded, or even to vanish on [-π,π], thereby including important cases such as the spectral functions of fractional processes.