带有干扰噪声的自回归过程的参数估计及渐近性质

THE ESTIMATION OF THE PARAMETERS OF AUTOREGRESSIVE PROCESS WITH DISTURBING NOISE AND ITS ASYMTOTIC PROPERTIES

摘要: 本文讨论了带有干扰噪声的自回归过程Y（t）=X（t）+Z（t）,其中X（t）为AR（p）序列,Z（t）、为干扰噪声序列的未知参数φ₁,…,φ_p,σ_g²,σ_x²,谱密度f（λ）的估计问题,对所给估计建立了强收敛速度和渐近正态性,并给出了模型阶的一种强相容估计方法。

Abstract: In this paper, we disouss the estimation of autoregressive model with disturbing noise following Y（t）=X（t）+Z（t）, where X（t） is an AR（p）time series and Z（t） is an i. i. d. noise sequence. The paper gives the strong convergence rate of the estimators obtained and show that the estimtors are asymptotically normally distributed. A method of estimating order of the model is given and proven to be strongly consistent.