Efficient computation of the discrete autocorrelation wavelet inner product matrix

IA Eckley, GP Nason

Research output: Contribution to journalArticle (Academic Journal)peer-review

17 Citations (Scopus)

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 O(log(N)(3)) operation which compares favourably with the O(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.
Translated title of the contributionEfficient computation of the discrete autocorrelation wavelet inner product matrix
Original languageEnglish
Pages (from-to)83 - 92
Number of pages9
JournalStatistics and Computing
Volume15
Publication statusPublished - Apr 2005

Bibliographical note

Publisher: Springer
Other identifier: IDS Number: 917WG

Fingerprint

Dive into the research topics of 'Efficient computation of the discrete autocorrelation wavelet inner product matrix'. Together they form a unique fingerprint.

Cite this