Consistency and asymptotic normality of least squares estimators in generalized STAR models

被引:24
作者
Borovkova, Svetlana [1 ]
Lopuhaae, Hendrik P. [2 ]
Ruchjana, Budi Nurani [3 ]
机构
[1] Vrije Univ Amsterdam, Fac Econ, Dept Finance, NL-1081 HV Amsterdam, Netherlands
[2] Delft Univ Technol, Delft Inst Appl Math, Fac EEMCS, NL-2628 CD Delft, Netherlands
[3] Padjadjaran State Univ, Fac Math & Nat Sci, Dept Math, W Java 45363, Indonesia
关键词
space-time autoregressive models; least squares estimator; law of large numbers for dependent sequences; central limit theorem; multivariate time series;
D O I
10.1111/j.1467-9574.2008.00391.x
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
Space-time autoregressive (STAR) models, introduced by CLIFF and ORD [Spatial autocorrelation (1973) Pioneer, London] are successfully applied in many areas of science, particularly when there is prior information about spatial dependence. These models have significantly fewer parameters than vector autoregressive models, where all information about spatial and time dependence is deduced from the data. A more flexible class of models, generalized STAR models, has been introduced in BOROVKOVA et al. [Proc. 17th Int. Workshop Stat. Model. (2002), Chania, Greece] where the model parameters are allowed to vary per location. This paper establishes strong consistency and asymptotic normality of the least squares estimator in generalized STAR models. These results are obtained under minimal conditions on the sequence of innovations, which are assumed to form a martingale difference array. We investigate the quality of the normal approximation for finite samples by means of a numerical simulation study, and apply a generalized STAR model to a multivariate time series of monthly tea production in west Java, Indonesia.
引用
收藏
页码:482 / 508
页数:27
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