JSM 2005 - Toronto

Abstract #303605

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 395
Type: Contributed
Date/Time: Wednesday, August 10, 2005 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #303605
Title: Wavelet-based Bootstrap for Long Memory Time Series
Author(s): Priya Kulkarni*+ and David Hinkley
Companies: and University of California, Santa Barbara
Address: 3203 Avenel Blvd, North Wales, PA, 19454, United States
Keywords: long memory ; time series ; wavelets ; bootstrap
Abstract:

The application of bootstrap to long memory processes, in particular the fractional difference (FD) process is one of the difficult problems in statistics. The standard time domain bootstrap methods do not work well here due to the very slow decay of autocorrelation function (ACF). After the pioneering work by Flandrin (1992) showing the discrete wavelet transform (DWT) approximately decorrelates the long memory processes, many wavelet-based inference procedures based on this "approximate decorrelation" property were developed. The original discrete wavelet transform (ODWT) bootstrap algorithm fails to work for FD processes because the random sampling of correlated scaling coefficients is not justified. We propose an improvement: a MixedDWT algorithm where we treat the scaling coefficients as a time series and apply standard bootstrapping schemes while resampling. We demonstrate empirically that the MixedDWT algorithm outperforms other methods and works as well as the block bootstrap for short-memory processes such as AR.

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