Department of Statistics Seminar
North Carolina State University
presents
Kapil Sen, Chris Bodily & Li Chen
North Carolina State University
A Sampler of Graduate students
ABSTRACT
Title: SIMEX (Simulation -Extrapolation) based Unit Root Test in SVM(Stochastic Volatility Models)
Abstract: The Stochastic Volatility Model (SVM) has emerged as a popular alternative to ARCH / GARCH models to analyze economic time series. In SVM, the observed series r_{t} is modeled as the product of an unobserved variance component and an independent error component. The unobserved volatility process is in turn modeled as an autoregressive process. We can test for a unit root in the volatility process by testing for a unit root in the log-squared of the observed process, log(r_{t}). Standard unit root tests performed on log(r_{t}) suffer from severe size distortions due to the presence of large negative moving average root in its autoregressive moving average representation. Cook and Stefanski(1994) developed the Simulation-Extrapolation(SIMEX) procedure as a simulation-based method of estimating and reducing bias due to measurement error in nonstandard generalized linear measurement error models. We propose to apply the SIMEX method to standard unit root tests based on ordinary least squares, weighted symmetric estimators and instrumental variables to correct the size distortion and still obtain sufficient power.
Title: Numerical Differentiation Using Statistical Design
Abstract: Derivatives are frequently required by numerical procedures across many disciplines. Numerical differentiation can be useful for approximating derivatives. This dissertation will introduce computational differentiation (the process by which derivatives are obtained with a computer), focusing on statistical response surface (RSM) designs for approximating derivatives. The RSM designs are compared with two competing numerical methods: a rival saturated statistical design approach, and a method employing finite differencing. A covariance model incorporating function curvature and computer round-off error is proposed for estimating the derivative approximation variances. These variances and the computational workload each method requires become the basis for comparing the derivative approximations. A diagnostic test for variable scaling errors is also described.
Title: Bayesian Statistical Modeling of Wind Fields over the Chesapeake Bay
Abstract: Wind fields along a coastline are composed of many features that are spatially and temporally complex in nature. Our main objective is to develop a statistical model which is capable of providing reliable forecasts of wind fields. The model is designed in such a way that it has the capability of combining observed wind data and output from mesoscale meteorological models to improve the forecasts. We model the data in terms of an underlying but unobservable true wind process, which is a non-stationary spatial-temporal model, and we estimate the model in a Bayesian way. This provides improved spatial prediction of wind fields via the posterior distribution of the ground truth, and allows us to validate the meteorological model via the posterior predictive distribution of the observations. It also enables us to remove the bias in the meteorological model output by estimating additive and multiplicative bias parameters in the model. We applied our methods to wind data on the Chesapeake Bay.
Friday, August, 30, 2002
3:35 - 4:35 pm
206 Cox Hall
Refreshments will be served on the second floor of Dabney Hall (left of Room 222) at 3:00 pm.