TitleDecorrelation Property of Discrete Wavelet Transform Under Fixed-Domain Asymptotics
Publication TypeJournal Articles
Year of Publication2013
AuthorsChang, X, Stein, ML
JournalIEEE Transactions on Information Theory
Date Published2013
KeywordsBusiness Analytics

Theoretical aspects of the decorrelation property of the discrete wavelet transform when applied to stochastic processes have been studied exclusively from the increasing-domain perspective, in which the distance between neighboring observations stays roughly constant as the number of observations increases. To understand the underlying data-generating process and to obtain good interpolations, fixed-domain asymptotics, in which the number of observations increases in a fixed region, is often more appropriate than increasing-domain asymptotics. In the fixed-domain setting, we prove that, for a general class of inhomogeneous covariance functions, with suitable choice of wavelet filters, the wavelet transform of a nonstationary process has mostly asymptotically uncorrelated components.