New Statistical Procedures For Time Series Data And Robust Modelling

People get used to record the data at successive time instants spaced at uniform time intervals. For example, Daily temprature, monthly CPI and annual GDP. In statistics, it is usually called time series data. Since time series data have a natural temporal ordering, it has a wide range of application. Time series analysis comprises methods for analyzing time sereis data in order to extract statistical regular patterns and characteristics. Time series forecasting is the use of a model to predict future values.Past theoretical facts and practice have proved that widely used Least Squares Method has bad performances under some conditons. Therefore, searching some robust methods is an important task for statistians. The M-estimate methed proposed by Huber (1964,1973) provides a good solution for these problems.In this research, the author elaborates about time series data and robust statcistical methods in three chapters. By Rigorous proofs, detailed simuaitons and comprehensive examples, author illustrated the modern development and ap-plication of these two classical statistical research area. There are five chapters in the thesis:Chapter1:Introduce the research background and relationship between main three chapters;Chapter2:Introduce weighted quantile regression for AR models with infinte variance errors. Propose an induced smoothing method to deal with compu-tational challenges in estimation of parameters and asymptotic convariance matrix. Illustrate the proposed methodology by Monte Carlo simulations and an empirical analysis;Chapter3:Introduce a new method for varying coefficient models for data with auto-correlated error process. Propose a profile least squares estimation pro-cedure to its regression coefficients. Apply variable selection technique to select the order of error process. Monte Carlo simulations and real data examples demonstrate the efficiency of proposed methodology;Chapter4:Intorduce M-estimate in ultra-high dimension. Propose nonconvex penalized M-estimate method. Under the framework of Difference Convex Programming, investigate the Oracle property in a more flexible way;Chapter5:Propose conclusion and prospect.