Mathematical Sciences: Inference for Nonstationary and Nonlinear Time Series

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The principal investigator will work on two projects. The first project is concerned with inference for nonstationary time series. The main objective is to study the consistency and efficiency of the model selection procedures that are either based on information criteria or on the predictive least squares principle. The second project is concerned with the inference for nonlinear time series. The main objective is to establish a unified estimation theory for the nonlinear autoregressive model and a general computation method for its functionals. Nonlinearity tests and conditions for stationarity are also considered. Since in applications the problems in general are nonstationary and nonlinear, these projects will contribute not only to the field of statistics, but also to other branches of science.