非平稳AR(p)时间序列的统计推断
Inference for Non-Stationary AR(p) Time Series
设Yt=β1Yt-1+…+βpYt-p+εt 为一非平稳p阶自回归滑动平均过程且至少有一特征根落在单位球上, {εt}为一落在指数为α< 2 的稳定律吸引场的独立同分布随机变量列。通过借助Kurtz and Protter (1991)的随机积分的结果,本文证明了自回归参数β=(β1, …, βp)T的最小二乘估计的极限分布收敛于积分稳定过程的函数表达式。给了估计量及其极限分布的一些模拟结果。
Let Yt=β1Yt-1+…+βpYt-p+εt be an AR(extitp) process with at least one of its characteristic roots lies on theunit circle and {εt} be an i.i.d random variables and in thedomain of attraction of a stable law with index α< 2. In this paper, the limit distribution of the least squares estimator (LSE) ofβ=(β1, …, βp)T for such a nonstationary time series {Yt} is established. In particular, byvirtue of the result of Kurtz and Protter (1991) of stochasticintegrals, it is shown that the limit distribution of the LSE is afunctional of integrated stable process. Simulationsfor the estimator of βand its limit distribution are also given.
张荣茂
数学
自回归过程α 稳定噪声最小二乘估计积分稳定过程单位根
utoregressive processα-stable noiseleast squaresestimateintegrated stable processesunit-root problem
张荣茂.非平稳AR(p)时间序列的统计推断[EB/OL].(2012-03-09)[2025-08-23].http://www.paper.edu.cn/releasepaper/content/201203-350.点此复制
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