Abstract #300124

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JSM 2003 Abstract #300124
Activity Number: 85
Type: Contributed
Date/Time: Monday, August 4, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Stat. Sciences
Abstract - #300124
Title: Bayesian Wavelet Approach to ARFIMA(p,d,q) Models with Structural Changes
Author(s): Kyungduk Ko*+ and Marina Vannucci
Companies: Texas A&M University and Texas A&M University
Address: Dept. of Statistics, College Station, TX, 77843-3143,
Keywords: long-range dependence ; ARFIMA ; discrete wavelet transformation ; Markov chain Monte Carlo ; reversible jump
Abstract:

In this paper, we propose estimation procedures of parameters of Fractionally Integrated ARMA models, ARFIMA(p,d,q) models with unknown AR and MA parameters. These are well-known time series models that describe the phenomenon of long-range dependence between data points. These models have typically very complicated covariance structure due to non-negligible dependence between distant observations, so it is not easy to compute the likelihood function. Here we adopt discrete wavelet transformations in order to simplify the covariance structure. Indeed, wavelet transformations enable us to get nearly uncorrelated covariance structure when applied to data having long-range dependence. We use Markov chain Monte Carlo methods as procedures of parameter estimation given the wavelet coefficients. Furthermore, we focus on the changes over time in long-memory parameter. We use reversible jump MCMC for this purpose. We present results from simulations and applications to real data.

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