Browsing by Author "Sastry G. Pantula, Committee Member"

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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.
Inference Regarding Multiple Structural Changes in Linear Models Estimated via Two Stage Least Squares.
(2005-12-28) Han, Sanggohn; Alastair R. Hall, Committee Chair; David A. Dickey, Committee Co-Chair; Sastry G. Pantula, Committee Member; Atsushi Inoue, Committee Member
Bai and Perron(1998) develop methods that are designed to test for structural stability with an unknown number of break points in the sample. Their analysis is in the context of linear regression models estimated via Ordinary Least Squares(OLS). We extend Bai and Perron's framework for multiple break testing to linear models via Two Stage Least Squares(2SLS). Within our framework, the break points are estimated simultaneously with the regression parameters via minimization of the residual sum of squares on the second step of the 2SLS estimation. We establish the consistency of the resulting estimated break point fractions and obtain the standard convergence rate of break fraction estimators. Based on that convergence rate we derive the limiting distribution of the break point estimators. We prove that the break point estimator have the same limiting distribution of the arg max of two sided Brownian motion process, which is the same distribution considered by Bai and Perron(1998). We also show that various F-statistics for structural instability based on the 2SLS estimator have the same limiting distribution as the analogous statistics for OLS considered by Bai and Perron(1998). This allows us to extend Bai and Perron's(1998) sequential procedure for selecting the number of break points to the 2SLS setting. Simulation experiment and application to financial market has been implemented.
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.
Symmetry and Separability in Spatial-Temporal Processes
(2005-12-15) Park, Man Sik; Montserrat Fuentes, Committee Chair; Peter Bloomfield, Committee Member; David A. Dickey, Committee Member; Sastry G. Pantula, Committee Member; Jerry M. Davis, Committee Member
Symmetry is one of most standard assumptions that are needed for a covariance function in spatial statistics. However, many studies in spatial research fields show that environmental data have complex spatial-temporal dependency structures that are difficult to model and estimate, due to the lack of symmetry and other standard assumptions of a covariance function. So, not much literature exists in statistics about asymmetric covariance functions and formal tests for lack of symmetry in spatial-temporal processes. In this study, we introduce certain types of symmetry in spatial-temporal processes and propose new classes of asymmetric spatial-temporal covariance models by using spectral representations. We also clarify the relationship between symmetry and separability and introduce nonseparable covariance models. Based on the proposed concept of symmetry in spatial-temporal processes, new formal tests for lack of symmetry are proposed in this study by employing spectral representations of the spatial-temporal covariance function. The advantage of the tests is that simple analysis of variance (ANOVA) approaches are employed for detecting lack of symmetry inherent in spatial-temporal processes. Our new classes of covariance models are applied to the methods for the fine particulate matters with a mass median diameter less than 2.5 $mu m$ ($mbox[PM]_[2.5]$) observed from U.S. Environmental Protection Agency (EPA). We evaluate the performance of the tests by a simulation study and, finally, apply to the $mbox[PM]_[2.5]$ daily concentration calculated by the Models-3/Community Multiscale Air Quality (CMAQ) modeling system with the spatial resolution of $36km imes 36 km$.