Asymptotic distribution of least squares estimators for purely unstable ARMAX(p,s,q) process

被引：0

作者：

Benaid, Brahim ^{[1
,2
]}

机构：

[1] IUT Pau & Pays Adours, Pau, France

[2] UPPA, UMR CNRS 5142, LMA, Dept Stat & Informat Decis, Pau, France

来源：

INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS | 2011年 / 21卷 / J11期

关键词：

Stochastic integrals; convergence in distribution; asymptotic statistics; least squares estimators; ARMAX model;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the limiting distribution of least squares estimators (phi) over cap (n), of the vector f of the autoregressive parameters in a purely unstable ARMAX( r,s,q). This extends the results obtained by Boutahar (1991) for the unstable ARX model. More precisely, it is shown that the asymptotic distribution (phi) over cap (n) - phi which are stochastic integrals with respect to Brownian motion differs from the purely unstable ARX by a decentring term due to the correlation between the (yt)'s and their MA part.

引用

页码：1 / 14

页数：14

共 50 条

[31] ASYMPTOTIC PROPERTIES OF LEAST-SQUARES ESTIMATORS FOR DISCRETE COMPOUND DISTRIBUTIONS
CHOI, K
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1978, 30 (01) : 45 - 50
[32] Consistency and asymptotic normality of least squares estimators in generalized STAR models
Borovkova, Svetlana
Lopuhaae, Hendrik P.
Ruchjana, Budi Nurani
STATISTICA NEERLANDICA, 2008, 62 (04) : 482 - 508
[33] Asymptotic efficiency of the ordinary least squares estimator for regressions with unstable regressors
Shin, DW
Oh, MS
ECONOMETRIC THEORY, 2002, 18 (05) : 1121 - 1138
[34] Asymptotic distribution of CLS estimators in the nearly unstable and unstable PINAR(1) model
Manaa, Abderrahmen
Bentarzi, Wissam
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 2024, 53 (01) : 1 - 29
[35] VARIANCE OF LEAST-SQUARES ESTIMATORS FOR A DAMPED SINUSOIDAL PROCESS
YAO, YX
PANDIT, SM
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1994, 42 (11) : 3016 - 3025
[36] FINITE SAMPLING DISTRIBUTION OF LEAST SQUARES ESTIMATORS WITH STOCHASTIC REGRESSORS
WEGGE, LL
ECONOMETRICA, 1971, 39 (02) : 241 - &
[37] Some asymptotic properties of the least squares estimators of a polynomial regression with a heteroskedastic error
Usami, Y
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2002, 31 (04) : 625 - 635
[38] On asymptotic behavior of least squares estimators and the confidence intervals of the superimposed exponential signals
Kundu, D
Mitra, A
SIGNAL PROCESSING, 1999, 72 (02) : 129 - 139
[39] Asymptotic properties of conditional least-squares estimators for array time series
Rajae Azrak
Guy Mélard
Statistical Inference for Stochastic Processes, 2021, 24 : 525 - 547
[40] Asymptotic properties of conditional least-squares estimators for array time series
Azrak, Rajae
Melard, Guy
STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES, 2021, 24 (03) : 525 - 547

← 1 2 3 4 5 →