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Activity Number: 538
Type: Contributed
Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #309882
Title: Wavelet-Based Estimation for Stationary Gaussian Time Series
Author(s): Wenjun Zheng*+
Companies: The Ohio State University
Keywords: Discrete wavelet transform ; Matern processes ; maximum likelihood estimator ; between and within-scale decorrelation
Abstract:

Modern time series analyses often require the modeling of long series, with complicated non-Markov time series dependencies. Traditional likelihood methods are computationally demanding for longer time series, leading us to consider approximate likelihood methods that are computationally efficient, while not overly compromising on the efficiency of the parameter estimates.

In this talk, various wavelet-based Whittle approximations are proposed to model stationary Gaussian time series. Wavelet transform can help decorrelate processes across and within wavelet scales, allowing for the simplified modeling of time series processes. In addition to being computationally efficient, the proposed wavelet-Whittle maximum likelihood estimators of a stationary Gaussian process are shown to be consistent and asymptotically normal. These asymptotic properties of the estimators are verified in simulation studies, demonstrating that the typical independence everywhere assumption assumed for wavelet-based estimation is not optimal. These methods are applied to the analysis of an environmental time series.


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