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This article mainly presents the fundamental theory, model and application of conditional heteroscedasticity residual sequence. And it also gives detailed, scientific and exact analysis and research on a financial security example. Then summarizing a conclusion: Financial Securities follows specific rules and tracks through above study. The research indicates that ARCH model only applies to a short-term, auto-correlative heteroscedastic function ,whereas the amended GARCH model has the opposite result, that is, GARCH fits a long-term, auto-correlative heteroscedastic function. Meanwhile, SAS program presents more intuitive, exact tables and figures. All analysis and results show that AR (m)-GARCH fits well. </p

The Application and Modeling for Conditional Heteroscedasticity Time Series