The Cholesky Decomposition of a Toeplitz Matrix and a Wiener-Kolmogorov Filter for Seasonal Adjustment

D.S.G. Pollock () and Emi Mise ()

No 20/01, Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester

Abstract: This note describes the use of the Cholesky decomposition in solving the equation Ab = y when A = A0 is a symmetric matrix of full rank. A specialised version of the algorithm is provided for the case where A is a banded 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. This circumstance demands that steps should be taken to minimise the use of the computer's memory. An example is provided of the use of the algorithm in implementing a finite-sample Wiener-Kolmogorov filter aimed at removing the seasonal fluctuations from economic data.

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