David S. Stoffer

Time Series Analysis and Its Applications

Characteristics of Time Series * Time Series Regression and ARIMA Models * Dynamic Linear Models and Kalman Filtering * Spectral Analysis and Its Applications.

A monte carlo approach to nonnormal and nonlinear state–space modeling

Abstract A solution to multivariate state-space modeling, forecasting, and smoothing is discussed. We allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation, the observational equation, or both. An adaptive Monte Carlo integration technique known as the Gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework. The methodology is a general strategy for obtaining marginal posterior densities of coefficients in the model or of any of the unknown elements of the state space. Missing data problems (including the k-step ahead prediction problem) also are easily incorporated into this framework. We illustrate the broad applicability of our approach with two examples: a problem involving nonnormal error distributions in a linear model setting and a one-step ahead prediction problem in a situation where both the state and observational equations are nonlinear and involve unknown parameters.

The effects of prenatal alcohol and marijuana exposure: disturbances in neonatal sleep cycling and arousal.

ABSTRACT: Neonatal EEG and sleep findings are presented from a longitudinal study of the effects of maternal alcohol and marijuana use during pregnancy. Infant outcome has been examined relative to the trimester(s) of pregnancy during which use occurred. Disturbances in sleep cycling, motility, and arousals were noted that were both substance and trimester specific. Alcohol consumed during the first trimester of pregnancy was associated with disruptions in sleep and arousal, whereas marijuana use affected sleep and motility regardless of the trimester in which it was used. Although these findings are preliminary and based on a small sample of women exhibiting only moderate substance use during pregnancy, they do suggest that specific neurophysiological systems may be differentially affected by prenatal alcohol or marijuana exposure even in the absence of morphological abnormalities.

Dynamic Linear Models with Switching

Abstract The problem of modeling change in a vector time series is studied using a dynamic linear model with measurement matrices that switch according to a time-varying independent random process. We derive filtered estimators for the usual state vectors and also for the state occupancy probabilities of the underlying nonstationary measurement process. A maximum likelihood estimation procedure is given that uses a pseudo-expectation-maximization algorithm in the initial stages and nonlinear optimization. We relate the models to those considered previously in the literature and give an application involving the tracking of multiple targets.

Effect of prenatal marijuana exposure on the cognitive development of offspring at age three.

Marijuana is the most commonly used illicit substance among pregnant women. Although there has been substantial concern about the effects of substance use during pregnancy, few studies have assessed the effects of prenatal exposure to marijuana and even fewer have provided longitudinal data on the developmental outcome of offspring. This is a report from a longitudinal study of substance use during pregnancy. The women in the cohort were of lower socioeconomic status, most were single, half were white and half were African-American. Women were interviewed at the fourth and seventh prenatal months, and women and children were assessed at delivery, 8, 18, and 36 months. Pediatric assessment included physical and cognitive development. At each study phase, mothers were interviewed about life style, living situation, current substance use, sociodemographic, and psychological status. Findings are reported on 655 women and children who were assessed at the third year. There were significant negative effects of prenatal marijuana exposure on the performance of 3-year-old children on the Stanford-Binet Intelligence Scale. The effects were associated with exposure during the first and second trimesters of pregnancy. Among the offspring of white women, these effects were moderated by the childs attendance at preschool/day-care at age three.

Prenatal marijuana use and neonatal outcome.

In a longitudinal study of marijuana and other substance use during pregnancy, women were interviewed at each trimester of pregnancy. Growth parameters, morphological abnormalities and gestational age were assessed for the 519 liveborn singletons. There were few significant effects of marijuana use during pregnancy on birth weight, head or chest circumference, gestational age, or growth retardation after adjustment for covariates using a regression model for analysis. There was a small but significant negative effect of marijuana use during the first two months of pregnancy on birth length and a positive effect of marijuana use during the third trimester on birth weight.

Discrimination and Classification of Nonstationary Time Series Using the SLEX Model

Statistical discrimination for nonstationary random processes is important in many applications. Our goal was to develop a discriminant scheme that can extract local features of the time series, is consistent, and is computationally efficient. Here, we propose a discriminant scheme based on the SLEX (smooth localized complex exponential) library. The SLEX library forms a collection of Fourier-type bases that are simultaneously orthogonal and localized in both time and frequency domains. Thus, the SLEX library has the ability to extract local spectral features of the time series. The first step in our procedure, which is the feature extraction step based on work by Saito, is to find a basis from the SLEX library that can best illuminate the difference between two or more classes of time series. In the next step, we construct a discriminant criterion that is related to the Kullback–Leibler divergence between the SLEX spectra of the different classes. The discrimination criterion is based on estimates of the SLEX spectra that are computed using the SLEX basis selected in the feature extraction step. We show that the discrimination method is consistent and demonstrate via finite sample simulation studies that our proposed method performs well. Finally, we apply our method to a seismic waves dataset with the primary purpose of classifying the origin of an unknown seismic recording as either an earthquake or an explosion.

Estimation and Identification of Space-Time ARMAX Models in the Presence of Missing Data

Abstract A method for modeling and fitting multivariate spatial time series data based on current spatial methodology coupled with the parameterization of the ARMAX model is presented. Because of the physical constraints imposed on multivariate data collection in both space and time, the estimation and identification procedures tolerate general patterns of missing or incomplete data.

Walsh-Fourier Analysis and its Statistical Applications

Abstract The aim of this article is to acquaint statisticians and practitioners, whose research activities require statistical methodology, with the statistical theory and applications of Walsh-Fourier analysis. It has been suggested that Walsh spectral analysis is suited to (albeit not restricted to) the analysis of discrete-valued and categorical-valued time series, and of time series that contain sharp discontinuities. I explain the need for Walsh-Fourier analysis, review the history and properties of Walsh functions, and outline the existing Walsh-Fourier theory for real-time stationary time series. I discuss various statistical applications based on the Walsh-Fourier transform and provide an annotated bibliography.

A Walsh—Fourier Analysis of the Effects of Moderate Maternal Alcohol Consumption on Neonatal Sleep-State Cycling

Abstract Recent discussions of the functional significance of ultradian rhythms emphasize their importance to human physiology. Over the past 25 years, electroencephalographic (EEG) sleep patterns have been used in assessing the cerebral and central nervous system maturation of neonates. Through an interdisciplinary effort, spectral (Fourier) methods have been developed to discriminate between the various stages of sleep based on EEG recordings. Nevertheless, there has been little effort to develop methods for the statistical analysis of sleep-state cycling. In particular, attention has primarily been focused on the ultradian rhythm of sleep as it cycles between two states, active or rapid eye movement (REM) and quiet or non-REM sleep. There are, however, several components of REM and non-REM sleep, as well as a transitional state (indeterminate sleep) and abrupt alterations of state (arousal). Moreover, few studies have investigated the effects of prenatal alcohol exposure on the neurophysiological devel...