STRICT STATIONARITY OF GENERALIZED AUTOREGRESSIVE PROCESSES

被引：273

作者：

BOUGEROL, P ^{[1
]}

PICARD, N ^{[1
]}

机构：

[1] UNIV NANCY 1, DEPT MATH, F-54506 VANDOEUVRE LES NANCY, FRANCE

来源：

ANNALS OF PROBABILITY | 1992年 / 20卷 / 04期

关键词：

AUTOREGRESSIVE MODEL; LINEAR STOCHASTIC SYSTEM; ARMA PROCESS; STRICT STATIONARITY; STATE SPACE SYSTEM; LYAPOUNOV EXPONENT; STOCHASTIC DIFFERENCE EQUATION;

D O I：

10.1214/aop/1176989526

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we consider the multivariate equation X(n+1) = A(n+1)X(n) + B(n+1) with i.i.d. coefficients which have only a logarithmic moment. We give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future. As an application we characterize the multivariate ARMA equations with general noise which have such a solution.

引用

页码：1714 / 1730

页数：17

共 26 条

[1] TIGHTNESS OF PRODUCTS OF RANDOM MATRICES AND STABILITY OF LINEAR STOCHASTIC-SYSTEMS
BOUGEROL, P
[J]. ANNALS OF PROBABILITY, 1987, 15 (01) : 40 - 74
[2] STATIONARITY OF GARCH PROCESSES AND OF SOME NONNEGATIVE TIME-SERIES
BOUGEROL, P
PICARD, N
[J]. JOURNAL OF ECONOMETRICS, 1992, 52 (1-2) : 115 - 127
[3] BOUGEROL P, 1985, PROGR PROBABILITY ST
[4] THE STOCHASTIC EQUATION YN+1=ANYN+BN WITH STATIONARY COEFFICIENTS
BRANDT, A
[J]. ADVANCES IN APPLIED PROBABILITY, 1986, 18 (01) : 211 - 220
[5] Caines P. E., 1988, LINEAR STOCHASTIC SY
[6] LINEAR PREDICTION OF ARMA PROCESSES WITH INFINITE VARIANCE
CLINE, DBH
BROCKWELL, PJ
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1985, 19 (02) : 281 - 296
[7] ELIE L, 1982, ANN SCI ECOLE NORM S, V15, P257
[8] Feigin P.D., 1985, J TIME SER ANAL, V6, DOI [10.1111/j.1467-9892.1985.tb00394.x, DOI 10.1111/j.1467-9892.1985.tb00394.x]
[9] PRODUCTS OF RANDOM MATRICES
FURSTENBERG, H
KESTEN, H
[J]. ANNALS OF MATHEMATICAL STATISTICS, 1960, 31 (02): : 457 - 469
[10] GFRANGER WJ, 1978, INTRO BILINEAR TIME

← 1 2 3 →