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Efficient computation of the discrete autocorrelation wavelet inner product matrix.

Eckley, Idris A. and Nason, Guy P. (2005) Efficient computation of the discrete autocorrelation wavelet inner product matrix. Statistics and Computing, 15 (2). pp. 83-92. ISSN 0960-3174

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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.

Item Type: Article
Journal or Publication Title: Statistics and Computing
Additional Information: RAE_import_type : Journal article RAE_uoa_type : Statistics and Operational Research
Uncontrolled Keywords: recursive wavelet relation - locally stationary time series - autocorrelation wavelets
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 2462
Deposited By: ep_importer
Deposited On: 29 Mar 2008 15:24
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 15:41
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/2462

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