Tensorial products of functional ARMA processes

被引：4

作者：

Bosq, Denis ^{[1
]}

机构：

[1] Univ Paris 06, LSTA, Paris 6, France

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2010年 / 101卷 / 06期

关键词：

Autoregressive Hilbertian processes; Hilbertian moving averages; Tensorial products; Hilbert-Schmidt operators; Standard processes; Autocovariance operators;

D O I：

10.1016/j.jmva.2010.01.014

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：

We study the structure of tensorial products for the autoregressive and moving average processes (X-n), with values in a Hilbert space H and with innovations that are martingale differences. The obtained models are ARMA(H circle times H) processes, possibly non standard. We provide criteria for the standardness of these models, we specify the results in the real case, give some examples and consider some applications. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1352 / 1363

页数：12

共 14 条

[1]

[Anonymous], THEORY LINEAR OPERAT

[2]

[Anonymous], 1991, TIME SERIES THEORY M

[3]

[Anonymous], VECTEURS FONCTIONS D

[4] Linear functional processes and prediction [J].

Bosq, D .

COMPTES RENDUS MATHEMATIQUE, 2003, 337 (02) :115-118

[5]

Bosq D., 2000, LECT NOTES STAT, V149

[6]

BOSQ D, 2009, ANN L ISUP, V53, P31

[7]

Bosq D., 2007, Wiley Series in Probability and Statistics

[8] General linear processes in Hilbert spaces and prediction [J].

Bosq, Denis .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2007, 137 (03) :879-894

[9]

CHOI IB, 2003, STAT INFERENCE STOCH, V6, P43

[10]

Ferraty F., 2006, SPR S STAT

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