Model selection-regression and time series applications - Clark, Allan Ernest (Department of Statistical Sciences, 2016)
In any statistical analysis the researcher is often faced with the challenging task of gleaning relevant information from a sample data set in order to answer questions about the area under investigation. Often the exact data generating process that governs any data set is unknown, indicating that we have to estimate the data generating process by using statistical methods. Regression analysis and time series analysis are two statistical techniques that can be used to undertake such an analysis. In practice researcher will propose one model or a group of competing models that attempts to explain the data being investigated. This process is known as model selection. Model selection techniques have been developed to aid researchers in finding a suitable approximation to the true data generating process. Methods have also been developed that attempt to distinguish between different competing models. Many of these techniques entail using an information criterion that estimates the "closeness" of a fitted model to the unknown data generating process. This study investigates the properties of Bozdogan's Information complexity measure (ICOMP) when undertaking time series and regression analysis. Model selection techniques have been developed for both time series and regression analysis. The regression analysis techniques however often provide unsatisfactory results due to poor experimental designs. Poor experimental design could induce collinearities causing parameter estimates to become unstable with large standard errors. Time series analysis utilizes lagged autocorrelation- and lagged partial autocorrelation coefficients in order to specify the lag structure of the model. In certain data sets this process is not informative in determining the order of an ARIMA model. ICOMP guards against collinearity by considering the interaction between the parameters being estimated in a model. This study investigates the properties of ICOMP when undertaking regression and time series analysis by means of a simulation study. Bibliography: pages 250-263.