Timothy Johnson, Martin E. Kaliski. / Interim report. / Bibliography: leaf 3. / "June 8, 1981." / AFOSR Contract F49620-80-C-0002

by Paul Moroney, Alan S. Willsky, Paul K. Houpt. / Bibliography: leaves 32-34. / "October, 1979." / NASA Ames Grant NGL-22-009-124

by T. Pappas, A.J. Laub, N.R. Sandell, Jr. / Bibliography: leaf 38. / "May 1979." / Contract ERDA-E(49-18)-2087 Contract No. DAAG29-79-C-0031

D.G. Wimpey, T.L. Johnson, M.E. Kaliski. / Bibliography: p. 6. / "April, 1981." / U.S. Air Force Office of Scientific Research contract F49620-80-C-0002

Timothy L. Johnson. / Bibliography: p. 7. / "April, 1981"--report documentation page. "20th CDC." / U.S. Air Force Office of Scientific Research contract F49620-80-C-0002

Timothy L. Johnson. / Bibliography: p. 7. / "April, 1981"--report documentation page. "20th CDC." / U.S. Air Force Office of Scientific Research contract F49620-80-C-0002

Some problems of' statistical inference for discrete-valued time series are investigated in this study. New statistical theories and methods are developed which may aid us in gaining more insight into the understanding of discrete-valued time series data. The first part is concerned with the measurement of the serial dependence of binary time series. In early studies the classical autocorrelation function was used, which, however, may not be an effective and informative means of revealing the dependence feature of a binary time series. Recently, the autopersistence function has been proposed as an alternative to the autocorrelation function for binary time series. The theoretical autopersistence functions and their sample analogues, the autopersistence graphs, are studied within a binary autoregressive model. Some properties of the autopcrsistencc functions and the asymptotic properties of the autopersistence graphs are discussed, justifying that the antopersistence graphs can be used to assess the dependence feature. Besides binary time series, intcger-vall1ed time series arc perhaps the most commonly seen discrete-valued time series. A generalization of the Poisson autoregression model for non-negative integer-valued time series is proposed by imposing an additional threshold structure on the latent mean process of the Poisson autoregression. The geometric ergodicity of the threshold Poisson autoregression with perburbations in the latent mean process and the stochastic stability of the threshold Poisson autoregression are obtained. The maximum likelihood estimator for the parameters is discussed and the conditions for its consistency and asymptotic normally are given as well. Furthermore, there is an increasing need for models of integer-valued time series which can accommodate series with negative observations and dependence structure more complicated than that of an autoregression or a moving average. In this regard, an integer-valued autoregressive moving average process induced by the so-called signed thinning operator is proposed. The first-order model is studied in detail. The conditions for the existence of stationary solution and the existence of finite moments are discussed under general assumptions. Under some further assumptions about the signed thinning operators and the distribution of the innovation, a moment-based estimator for the parameters is proposed, whose consistency and asymptotic normality are also proved. The problem of conducting one-step-ahead forecast is also considered based on hidden Markov chain theory. Simulation studies arc conducted to demonstrate the validity of the theories and methods established above. Real data analysis such as the annual counts of major earthquakes data are also presented to show their potential usefulness in applications. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

Environmental flows (e.g. river and atmospheric flows) governed by the shallow water equations (SWE) are usually dominated by the advective mechanism over multiple time-scales. The combination of time dependency and nonlinear advection creates difficulties in the numerical solution of the SWE. A fully-implicit scheme is desirable because a relatively large time step may be used in a simulation. However, nonlinearity in a fully implicit method results in a system of nonlinear equations to be solved at each time step. To address this difficulty, a new method for implicit solution of unsteady nonlinear advection equations is developed in this research. This Time-Centered Split (TCS) method uses a nested application of the midpoint rule to computationally decouple advection terms in a temporally second-order accurate time-marching discretization. The method requires solution of only two sets of linear equations without an outer iteration, and is theoretically applicable to quadratically-nonlinear coupled equations for any number of variables. To explore its characteristics, the TCS algorithm is first applied to onedimensional problems and compared to the conventional nonlinear solution methods. The temporal accuracy and practical stability of the method is confirmed using these 1D examples. It is shown that TCS can computationally linearize unsteady nonlinear advection problems without either 1) outer iteration or 2) calculation of the Jacobian. A family of the TCS method is created in one general form by introducing weighting factors to different terms. We prove both analytically and by examples that the value of the weighting factors does not affect the order of accuracy of the scheme. In addition, the TCS method can not only computationally linearize but also decouple an equation system of coupled variables using special combinations of weighting factors. Hence, the TCS method provides flexibilities and efficiency in applications. / text

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