DocumentCode :
31783
Title :
Asymptotic Decorrelation of Wavelet Packet Transform for Certain Long-Memory Processes
Author :
Xiaojiang Yu
Author_Institution :
Dept. of Math., Tianjin Polytech. Univ., Tianjin, China
Volume :
59
Issue :
8
fYear :
2013
fDate :
Aug. 2013
Firstpage :
5051
Lastpage :
5062
Abstract :
The asymptotic decorrelation of the discrete wavelet transform for long-memory processes (such as the fractionally differenced (FD) process, the autoregressive fractionally integrated moving average (ARFIMA) process, and the Gegenbauer autoregressive moving average (GARMA) process) as well as the statistical inference techniques based on this property, have received much attention nowadays. In this paper, we investigate the asymptotic decorrelation property of the discrete wavelet packet transform (DWPT) for two classes of discrete-time long-memory processes containing the ARFIMA and the GARMA processes. Especially, we prove theoretically that the covariance across between-packet DWPT coefficients decays hyperbolically or exponentially fast as the width of the underlying Daubechies scaling and wavelet filters to generate the DWPT gets large. Meanwhile, we show that the covariance between within-packet DWPT coefficients converges hyperbolically fast to its corresponding counterpart when the underlying scaling and wavelet filters to generate the DWPT are the Shannon´s ideal low- and high-pass filters.
Keywords :
autoregressive moving average processes; discrete wavelet transforms; high-pass filters; low-pass filters; ARFIMA process; Daubechies scaling; GARMA process; Gegenbauer autoregressive moving average process; Shannon ideal low pass filters; asymptotic decorrelation property; autoregressive fractionally integrated moving average process; between packet DWPT coefficients; discrete time long memory processes; discrete wavelet packet transform; high pass filters; statistical inference; wavelet filters; Correlation; Decorrelation; Discrete wavelet transforms; Wavelet packets; White noise; Autoregressive fractionally integrated moving average (ARFIMA) process; Gegenbauer autoregressive moving average (GARMA) process; asymptotic decorrelation; long-memory process; wavelet packet transform;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2013.2255331
Filename :
6557028
Link To Document :
بازگشت