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

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  • Svetlana Borovkova
  • Hendrik P. Lopuhaä
  • Budi Nurani Ruchjana

Abstract

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 Borovkovaet 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.

Suggested Citation

  • Svetlana Borovkova & Hendrik P. Lopuhaä & Budi Nurani Ruchjana, 2008. "Consistency and asymptotic normality of least squares estimators in generalized STAR models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(4), pages 482-508, November.
    • Handle: RePEc:bla:stanee:v:62:y:2008:i:4:p:482-508
    DOI: 10.1111/j.1467-9574.2008.00391.x
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    5. Anderson, T. W. & Kunitomo, Naoto, 1992. "Asymptotic distributions of regression and autoregression coefficients with martingale difference disturbances," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 221-243, February.
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    Cited by:

    1. Gehman, Andrew & Wei, William W.S., 2020. "Optimal spatial aggregation of space–time models and applications," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    2. Ryan H. L. Ip & Dmitry Demskoi & Azizur Rahman & Lihong Zheng, 2021. "Evaluation of COVID-19 Mitigation Policies in Australia Using Generalised Space-Time Autoregressive Intervention Models," IJERPH, MDPI, vol. 18(14), pages 1-17, July.

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