Residual-Based Diagnostics for Conditional Heteroscedasticity Models

• Main Author: TSE, Yiu Kuen
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2002
• Subjects: Conditional heteroscedasticity; Lagrange multiplier test; Monte Carlo experiment; Portmanteau statistic; Residual-based diagnostic; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/498; https://ink.library.smu.edu.sg/context/soe_research/article/1497/viewcontent/Tse_Residualbaseddiagnosticsconditional_2002_pv.pdf
• Institution: Singapore Management University

We examine the residual–based diagnostics for univariate and multivariate conditional heteroscedasticity models. The tests are based on the parameter estimates of an autoregression with the squared standardized residuals or the cross products of the standardized residuals as dependent variables. As the regression involves estimated regressors the standard distribution theories of the ordinary least squares estimates do not apply. We provide the asymptotic variance of the regression estimates. Diagnostic statistics, which are asymptotically distributed as ?[sup 2], are constructed. A Monte Carlo experiment is conducted to investigate the finite–sample properties of the residual–based tests for both univariate and multivariate models. The results show that the residual–based diagnostics provide useful checks for model adequacy in both univariate and multivariate cases.