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Efficient computation of the discrete autocorrelation wavelet inner product matrix.

Research output: Contribution to journalJournal article

Published

Journal publication date19/04/2005
JournalStatistics and Computing
Journal number2
Volume15
Number of pages10
Pages83-92
Original languageEnglish

Abstract

Discrete autocorrelation (a.c.) wavelets have recently been applied in the statistical analysis of locally stationary time series for local spectral modelling and estimation. This article proposes a fast recursive construction of the inner product matrix of discrete a.c. wavelets which is required by the statistical analysis. The recursion connects neighbouring elements on diagonals of the inner product matrix using a two-scale property of the a.c. wavelets. The recursive method is an (log (N)3) operation which compares favourably with the (N log N) operations required by the brute force approach. We conclude by describing an efficient construction of the inner product matrix in the (separable) two-dimensional case.

Bibliographic note

RAE_import_type : Journal article RAE_uoa_type : Statistics and Operational Research