摘要
自回归过程相比其它随机过程具有更好的建模灵活性,并能通过模型的参数设定来模拟其它一些随机过程。本文首先详细地介绍了自回归过程的基本定义其平稳性条件,接着对具有残差的自回归过程的参数估计进行简要探讨以便于具有残差且对称稳定的自回归过程的M-胡伯评估的研究。然后,证明具有残差的自回归过程是α-稳定随机变量,也是平稳过程,在此基础上利用马尔可夫不等式及相关理论来探讨具有残差且对称稳定的自回归过程的M-胡伯评估,最后进一步证明了这种估计的一致性和渐近正态性。
Autoregressive process is better than other stochastic processes, which models flexibility, and simulates some other stochastic processes by setting the parameters of model. This paper firstly describes in detail the basic definition of autoregressive process and its stationary conditions, and then studies estimation autoregressive process parameters with re-siduals briefly in order to research Hubor’s М-estimation for autoregressive process with symmetric stable residuals. Se-condly, prove autoregressive processes with residuals, which areα-stable random variables, are also stationary processes, and use Markov's inequality and related theories to discuss Hubor’sМ-estimation for autoregressive process with symmetric stable residuals. Finally, prove the consistency and asymptotic normality of this estimate further.
出处
《软件》
2014年第10期54-59,共6页
Software
基金
黑龙江省自然科学基金(A201301)
高等学校博士学科点专项科研基金资助课题(20122303120005)
第51批中国博士后科学基金面上资助(2012M510926)
黑龙江省政府博士后资助经费(LBH-Z12069)
关键词
自回归过程
参数估计
差分方程
平稳条件
Autoregressive process
Parameters estimations
Difference equation
Stationary process