MODELLING FOR THE WAVELET COEFFICIENTS OF ARFIMA PROCESSES

We consider a model for the discrete nonboundary wavelet coefficients of autoregressive fractionally integrated moving average (ARFIMA) processes in each scale. Because the utility of the wavelet transform for the long‐range dependent processes, which many authors have explained in semi‐parametrical...

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Bibliographic Details
Published in:Journal of time series analysis Vol. 35; no. 4; pp. 341 - 356
Main Author: Nanamiya, Kei
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.07.2014
Subjects:
Asymmetry
Coefficients
discrete wavelet transform
long memory process
Modelling
Regression analysis
spectral density function JEL. C22
Studies
Time series
Utility theory
Vector-autoregressive models
Wavelet transforms
United States > US
ISSN:0143-9782, 1467-9892
Online Access:Get full text
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Summary:We consider a model for the discrete nonboundary wavelet coefficients of autoregressive fractionally integrated moving average (ARFIMA) processes in each scale. Because the utility of the wavelet transform for the long‐range dependent processes, which many authors have explained in semi‐parametrical literature, is approximating the transformed processes to white noise processes in each scale, there have been few studies in a parametric setting. In this article, we propose the model from the forms of the (generalized) spectral density functions (SDFs) of these coefficients. Since the discrete wavelet transform has the property of downsampling, we cannot directly represent these (generalized) SDFs. To overcome this problem, we define the discrete non‐decimated nonboundary wavelet coefficients and compute their (generalized) SDFs. Using these functions and restricting the wavelet filters to the Daubechies wavelets and least asymmetric filters, we make the (generalized) SDFs of the discrete nonboundary wavelet coefficients of ARFIMA processes in each scale clear. Additionally, we propose a model for the discrete nonboundary scaling coefficients in each scale.
Bibliography:istex:903E233986BC1F1F3EF422FCD3F1424130B1F64C
ark:/67375/WNG-2160GS3C-9
ArticleID:JTSA12068
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ObjectType-Article-2
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ISSN:0143-9782
1467-9892
DOI:10.1111/jtsa.12068