ASYMPTOTIC　CANONICAL　FORMS　AND　ITERATED　LOGARITHM　RATE　RESULTS　OF　LEAST　SQUARES　ESTIMATES　FOR　UNSTABLE　ARMA　MODELS  

作　　者：张虎明 

出　　处：《Acta Mathematicae Applicatae Sinica》1996年第3期257-277,共21页应用数学学报（英文版）

摘　　要：Herein we give the asymptotic canonical forms of the design mains Pn where is an unstable ARMA process B denotes the backshift operator such that B, and p is the order of the polynomial having all roots outside or on the unit circle. These asymptotic canonical forms for Pn, which behave a.s. approximately diagonally, are then used to obtain the itersted logarithm rates of almost sure convergence of the least-squares estimates to the unknown true parameter for an unstable time series.Herein we give the asymptotic canonical forms of the design mains Pn where is an unstable ARMA process B denotes the backshift operator such that B, and p is the order of the polynomial having all roots outside or on the unit circle. These asymptotic canonical forms for Pn, which behave a.s. approximately diagonally, are then used to obtain the itersted logarithm rates of almost sure convergence of the least-squares estimates to the unknown true parameter for an unstable time series.

关 键 词：Unstable ARMA models design matrices asymptotic canonical forms leastsquares estimates iterated logarithm rates 

分 类 号：O212.1[理学—概率论与数理统计]