A Wiener–Kolmogorov Filter for Seasonal Adjustment and the Cholesky Decomposition of a Toeplitz Matrix

D. Stephen G. Pollock () and Emi Mise ()
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D. Stephen G. Pollock: University of Leicester
Emi Mise: University of Leicester

Computational Economics, 2022, vol. 59, issue 3, No 1, 913-933

Abstract: Abstract A flexible method for removing the seasonal fluctuations from economic data is described. It can be used to remove not only the elements at the seasonal frequencies but also the adjacent elements, which may contribute significantly to the seasonal fluctuations but which are liable to be only mildly attenuated by the usual filters. The method has been implemented in a computer program, SEADOS, which, together with its accompanying manual, is available at the address http://www.sigmapi.org.uk/seados.zip/ . The program employs a specialised version of a Cholesky decomposition, which is adapted to the case of a narrow-band Toeplitz matrix, in which each band contains a unique repeated element and where the number of bands is considerably less than the order of the matrix, which is assumed to be large. The Pascal code of this algorithm is presented here together with that of some accompanying procedures.

Keywords: Seasonal adjustment; Wiener–Kolmogorov filters; Narrow-Band Toeplitz matrices; Cholesky decomposition (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10614-020-10087-1

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