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Central limit theorems for long range dependent spatial linear processes

Lahiri, S.N. and Robinson, Peter M. (2016) Central limit theorems for long range dependent spatial linear processes. Bernoulli, 22 (1). pp. 345-375. ISSN 1350-7265

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Identification Number: 10.3150/14-BEJ661

Abstract

Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a d d-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are established for the cases of positive strong dependence, short range dependence, and negative dependence. We provide approximations to asymptotic variances that reveal differential rates of convergence under the three types of dependence. Further, in contrast to the one dimensional (i.e., the time series) case, it is shown that the form of the asymptotic variance in dimensions d > 1 critically depends on the geometry of the sampling region under positive strong dependence and under negative dependence and that there can be non-trivial edge-effects under negative dependence for d > 1. Precise conditions for the presence of edge effects are also given.

Item Type: Article
Official URL: http://projecteuclid.org/info/euclid.bj
Additional Information: © 2016 ISI/BS
Subjects: H Social Sciences > HB Economic Theory
Sets: Departments > Economics
Date Deposited: 11 Feb 2016 12:39
Last Modified: 25 Sep 2017 11:06
Projects: DMS 1007703, DMS 1310068, ES/J007242/1, ES/J007242/1, DMS 1007703, DMS 1310068
Funders: National Science Foundation, Economic and Social Research Council, Economic and Social Research Council, National Science Foundation, National Science Foundation
URI: http://eprints.lse.ac.uk/id/eprint/65331

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