Statistical Inference for Nonlinear Time Series and Parallel Statistical Computing

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**The proposed research topics are aspects of my continuing research in areas of statistical inference and model diagnostic analysis for linear and nonlinear time series as well as parallel statistical computing and its**applications. The first part of the proposed research is to continue to work on residual processes based on nonlinear time series models such as GARCH and related models. The second part is to study multivariate GARCH models, develop corresponding asymptotic theory of consistency and normality of QMLE, and provide adaptive LASSO procedure. The third part is to continue developing Rmpi package for parallel statistical computing and build new packages for multivariate GARCH simulation, spatial statistical simulation and long-term mortality prediction. The objectives of this research are fourfold.**1. Construct and study residual processes based on nonlinear time series models. A modified empirical process is proposed. New results for other nonlinear time series such as GARCH-in-mean and co-integrated regressions models will be attempted. Applications of the proposed empirical processes will be change-point problems, goodness-of-fit tests and symmetric tests.**2. Develop asymptotic theory for a GARCH-in-mean model, one of the often used models in financial mathematics.**3. Develop asymptotic theory for multivariate GARCH models as well as provide adaptive LASSO procedure**to eliminate un-needed parameters. An application is the portfolio optimization and risk assessment, a very important area of financial mathematics.**4. Continue developing Rmpi package. Rmpi is considered to be one of two core packages for High-Performance and Parallel Computing in R community. It is used widely in areas of financial mathematics, bioinformatics, and Monte Carlo simulation. ******************