Browsing by Author "Bibhuti B. Bhattacharyya, Committee Member"

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Dirichlet Process Mixture Models For Markov Processes
(2003-12-03) Tang, Yongqiang; Subhashis Ghosal, Committee Chair; Anastasios Tsiatis, Committee Member; Peter Bloomfield, Committee Member; Bibhuti B. Bhattacharyya, Committee Member
Prediction of the future observations is an important practical issue for statisticians. When the data can be viewed as exchangeable, de Finneti's theorem concludes that, conditionally, the data can be modeled as independent and identically distributed (i.i.d.). The predictive distribution of the future observations given the present data is then given by the posterior expectation of the underlying density function given the observations. The Dirichlet process mixture of normal densities has been successfully used as a prior in the Bayesian density estimation problem. However, when the data arise over time, exchangeability, and therefore the conditional i.i.d. structure in the data is questionable. A conditional Markov model may be thought of as a more general, yet having sufficiently rich structure suitable for handling such data. The predictive density of the future observation is then given by the posterior expectation of the transition density given the observations. We propose a Dirichlet process mixture prior for the problem of Bayesian estimation of transition density. Appropriate Markov chain Monte Carlo (MCMC) algorithm for the computation of posterior expectation will be discussed. Because of an inherent non-conjugacy in the model, usual Gibbs sampling procedure used for the density estimation problem is hard to implement. We propose using the recently proposed "no-gaps algorithm" to overcome the difficulty. When the Markov model holds good, we show the consistency of the Bayes procedures in appropriate topologies by constructing appropriate uniformly exponentially consistent tests and extending the idea of Schwartz (1965) to Markov processes. Numerical examples show excellent agreement between asymptotic theory and the finite sample behavior of the posterior distribution.
Dynamic Time Series Analysis Using Logistic Function
(2004-08-08) Hwang, SangPil; David A.Dickey, Committee Chair; Sastry G. Pantula, Committee Member; Bibhuti B. Bhattacharyya, Committee Member; Matt Holt, Committee Member
This paper investigates a set of autoregressive time series models whose coefficients have the form of a logistic function. The transfer function type models give additional flexibility over the fixed coefficients models and include them as a special case. NLAR models with the AR(1) coefficient being a hyperbolic tangent function work well for modeling series which have asymmetric stochastic volatility or changing amplitude around 0 with a persistent autocorrelation and locally nonstationary behavior.
A New Approach to Unit Root Tests in Univariate Time Series Robust to Structural Changes
(2007-01-09) Kim, Seong-Tae; Sastry G. Pantula, Committee Member; Alastair R. Hall, Committee Member; Bibhuti B. Bhattacharyya, Committee Member; David A. Dickey, Committee Chair
Using methodology in panel unit root tests we propose a new approach to univariate unit root tests. Our method leads to an asymptotically normal distribution of the least squares estimator and is robust to contaminated data having structural changes or outliers while the power of the test does not drastically worsen. The main idea is that under the assumption that the process has a unit root we transform an AR(1) process [y t: 1 <= t <= T] to a double-index process [y [ij]: 1<= i <= m, 1 <= j <= n, mn=T] in such a way that the segments are independent for $i=1,2, ..., m. For this transformed data, we apply the same sequential limit as in Levin and Lin (1992, 2002). First, as n goes to infinity we obtain asymptotic results for each i. These have the same form as in conventional univariate unit root tests. Second, as m goes to infinity, we obtain an asymptotically normal distribution for the OLS estimator by the Lindeberg-Feller CLT. An advantage of this technique is that an undetected break has a relatively minor effect which, in fact, disappears as m increases. We also show that for a general ARMA (p,q) model we still obtain the asymptotic normality of the unit root statistics under the sequential limit assumption.