时间序列模型中稳健且有效估计及稳健变量选择问题的研究

时间序列分析在诸多领域有着广泛的应用，但目前的研究大多是在误差项服从高斯分布的假设下进行的，然而，大量的经验数据表明，经济、金融、通信、气象学以及水文学等领域的时间序列数据具有重尾分布。本项目试图构造一个新的损失函数，首先研究误差服从自回归的线性模型中回归系数与自相关阶数的稳健且有效估计；进而研究其稳健性质,即：有限样本崩溃点是多少？其影响函数是否有界？并且获得其大样本性质；在此基础上，研究其稳健变量选择方法以及对应的算法，并研究其Oracle性质与稳健性质以及对应算法的收敛性与收敛速度；尝试将方法推广至自回归模型、滑动平均模型以及自回归-滑动平均模型等重要的时间序列模型并给出其性质，为时间序列模型在经济、金融等领域的应用提供重要的理论依据和实践指导。

Time series analysis has a wide range of applications in many fields,but the study about time series analysis at present is mostly supposed that the error term is Gauss distribution. However, many empirical evidences show that the heavy-tailed distributions exist generally in many fields,such as economy,finances,traffic, meteorology and hydrology and so on. This project seeks to construct a new loss function, we first study the robust and efficient estimation for unknow regression coefficient and autoregressive orders in the linear regression models with autoregressive errors, and then investigate its robustness, e.g.,What is the finite sample breakdown point? Is its influence function bounded? Finally, we will show that the proposed estimation is consistent and asymptotically normal. We will consider the robust variable selection method on this base and corresponding algorithm, and then study the Oracle properties and robustness and the convergence of the corresponding algorithm and its convergence rate; We try to extend the proposed method to the other important time series models, such as autoregrssive model, moving average model, and autoregressive-moving average model and so on, and give their properties. This will provide an important theoretical evidence and practical guidance for the application of time series models in economy and finances.