Testing for Constancy of Correlation in Autoregressive Conditional Heteroscedasticity (Arch) Models

96 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997.This thesis presents a test statistic for the constancy of correlation in the multivariate normal model. Following Chesher (1984) and Cox (1983), we focus on deriving a score test of the hypothesis that the variance of the parameter of interest is zero. Here the score test checks the local behavior of the log-likelihood function close to the null hypothesis of no parameter variation; i.e., it does not "require" the explicit specification of alternative hypothesis. Therefore it has good power with no regard to how the parameter are distributed under the alternative. We apply Pierce (1982)'s formula which is convenient for calculating the asymptotic variance when the nuisance parameters are substituted by their consistent estimators. Our test has an important implication for econometric model building and is also a valuable tool for understanding economic and financial issues. As an example of its use in model specification, our test can be directly applied to the constant correlation multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models (Bollerslev (1990)). Bollerslev (1990) states "... the validity of the model remains an empirical question". We show that the test statistic derived in the unconditional normal case can be applied to GARCH model without much change and present the application on the stock market indices of major developed countries.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD