Modeling Linearly and non-Linearly Dependent Simulation Input Data

Abstract

Input modeling software tries to fit standard probability distributions to data assuming that the data are independent. However, the input environment can generate correlated data. Ignoring the correlations might lead to serious inaccuracies in the performance measures. In the past few years, several dependence modeling packages with different properties have been developed. In our dissertation, we explain how to fit non-Gaussian autoregressive models to correlated data and compare our approach with similar dependence modeling approaches that already exist. Moreover, we extend the Yule-Walker method so as to fit non-linear models to data samples using this method. <br /> We use in our dissertation also copulas for the purpose of fitting models to data samples. Copulas are used in finance and insurance for modeling stochastic dependency. Copulas comprehend the entire dependence structure, not only the linear correlations. In our dissertation, copulas serve the purpose to analyze measured samples of random vectors and time series, to estimate a multivariate distribution for them, and to generate random vectors with this distribution.