Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 218-221). Also available via the Internet

Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaves 126-131).

This dissertation deals with variance reduction techniques (VRTs) for improving the reliability of the estimators of interest through a controlled laboratory-like simulation experiment. This research concentrates on correlation methods of VRTs which include common random numbers, antithetic variates and control variates. The basic idea of these methods is to utilize the linear correlation either between the responses or between the response and control variates in order to reduce the variance of estimators of certain system parameters. Combining these methods, we develop procedures for estimating a system parameter of interest. First, we develop three combined methods utilizing antithetic variates and control variates for improving the estimation of the mean response in a single population model. We explore how these methods may reduce the variance of the estimator of interest. A combined method (Combined Method 1) using antithetic variates for the non-control variate stochastic components and independent streams for the control variates yields better results than by applying methods of either antithetic variates or control variates individually for several selected models. Second, we develop variance reduction techniques for improving the estimation of the model parameters in a multipopulation simulation model. We extend Combined Method 1 showing good performance in estimating the mean response of a single population model to the multipopulation context with independent simulation runs across design points. We also develop another extension of Combined Method 1 that incorporates the Schruben-Margolin method to estimate the parameters of a multipopulation model. Under certain conditions, this method is superior to the Schruben-Margolin method. Finally, we propose a new approach (Extended Schruben-Margolin Method) utilizing the control variates under the Schruben-Margolin strategy for improving the estimation in a first-order linear model. Extended Schruben-Margolin Method yields better results than the Schruben-Margolin method in estimating the model parameters of interest. / Ph. D.

This research is based on a detailed description of model building for multivariate time series models. Under the assumption of stationarity, identification, estimation of the parameters and diagnostic checking for the Vector Auto regressive (p) (VAR(p)), Vector Moving Average (q) (VMA(q)) and Vector Auto regressive Moving Average (VARMA(p, q) ) models are described in detail. With reference to the non-stationary case, the concept of cointegration is explained. Procedures for testing for cointegration, determining the cointegrating rank and estimation of the cointegrated model in the VAR(p) and VARMA(p, q) cases are discussed. The utility of multivariate time series models in the field of economics is discussed and its use is demonstrated by analysing quarterly South African inflation and wage data from April 1996 to December 2008. A review of the literature shows that multivariate time series analysis allows the researcher to: (i) understand phenomenon which occur regularly over a period of time (ii) determine interdependencies between series (iii) establish causal relationships between series and (iv) forecast future variables in a time series based on current and past values of that variable. South African wage and inflation data was analysed using SAS version 9.2. Stationary VAR and VARMA models were run. The model with the best fit was the VAR model as the forecasts were reliable, and the small values of the Portmanteau statistic indicated that the model had a good fit. The VARMA models by contrast, had large values of the Portmanteau statistic as well as unreliable forecasts and thus were found not to fit the data well. There is therefore good evidence to suggest that wage increases occur independently of inflation, and while inflation can be predicted from its past values, it is dependent on wages. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2012.