Wavelet-based Inferences for Long Memory Processes

• Activity Number: 462
• Type: Invited
• Date/Time: Thursday, August 11, 2005 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Peter F. Craigmile*+
• Companies: The Ohio State University
• Keywords: wavelets ; long memory processes ; decorrelation ; time-varying

Abstract

In recent years, there has been increased interest in using wavelet transforms to analyze and model long memory time series (processes that exhibit a slowly decaying autocorrelation sequence). Wavelet transforms are ideal for examining the self-similar structure present in such time series models. We can use certain wavelet filters to decorrelate long memory processes across wavelet scales. In combination with approximating the within scale correlation structure of wavelet coefficients, we can model long processes. In this way, wavelet-based estimation methods are tractable and competitive with frequency-based estimation approaches. In this talk, we will review the use of wavelet transforms for estimating statistical features of interest in long memory processes. We will then demonstrate how this work can be extended to analyze time-varying long memory processes using nondecimated wavelet transforms. An example from climatology will be used to motivate this research.