Testing stability in a spatial unilateral autoregressive model. Issue 4 (16th February 2016)

• Record Type: Journal Article
• Authors: Baran, Sándor; Pap, Gyula; Sikolya, Kinga
• Is Part Of: Communications in statistics. Volume 45:Issue 4(2016)
• Page Start: 933
• Page End: 949
• Publication Date: 2016-02-16
• Subjects: Spatial unilateral autoregressive process -- Unstable model -- Unit root test; Primary 62M10 -- Secondary 62F12; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2013.853792
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: Least squares estimator of the stability parameter ϱ ≔ |α| + |β| for a spatial unilateral autoregressive process X k, ℓ = α X k − 1, ℓ + β X k, ℓ − 1 + ϵ k, ℓ is investigated and asymptotic normality with a scaling factor n 5/4 is shown in the unstable case ϱ = 1. The result is in contrast to the unit root case of the AR(p) model Xk = α1 X k − 1 + ⋅⋅⋅ + α p X k − p + ϵ k, where the limiting distribution of the least squares estimator of the unit root parameter ϱ ≔ α1 + ⋅⋅⋅ + α p is not normal.