Bayesian wavelet approaches for parameter estimation and change point detection in long memory processes /

Bibliographic Details
Main Author:	Ko, Kyungduk, 1968-
Other Authors:	Vannucci, Marina (Thesis advisor)
Format:	Thesis eBook
Language:	English
Published:	[College Station, Tex.] : [Texas A&M University], [2005]
Subjects:	Major statistics. Bayesian Inference Long Memory Process Discrete Wavelet Transform Reversible Jump MCMC ARFIMA Models
Online Access:	Link to OAK Trust copy

Description
Abstract:	The main goal of this research is to estimate the model parameters and to detect multiple change points in the long memory parameter of Gaussian ARFIMA(p, d, q) processes. Our approach is Bayesian and inference is done on wavelet domain. Long memory processes have been widely used in many scientific fields such as economics, finance and computer science. Wavelets have a strong connection with these processes. The ability of wavelets to simultaneously localize a process in time and scale domain results in representing many dense variance-covariance matrices of the process in a sparse form. A wavelet-based Bayesian estimation procedure for the parameters of Gaussian ARFIMA(p, d, q) process is proposed. This entails calculating the exact variance-covariance matrix of given ARFIMA(p, d, q) process and transforming them into wavelet domains using two dimensional discrete wavelet transform (DWT2). Metropolis algorithm is used for sampling the model parameters from the posterior distributions. Simulations with different values of the parameters and of the sample size are performed. A real data application to the U.S. GNP data is also reported. Detection and estimation of multiple change points in the long memory parameter is also investigated. The reversible jump MCMC is used for posterior inference. Performances are evaluated on simulated data and on the Nile River dataset.
Item Description:	"Major Subject: Statistics" Title from author supplied metadata (automated record created on Nov. , 09:45:50.) Vita. Abstract. Electronic resource.
Format:	Mode of access: World Wide Web. System requirements: World Wide Web access and Adobe Acrobat Reader.
Bibliography:	Includes bibliographical references.