Testing stability in a spatial unilateral autoregressive model. Issue 4 (16th February 2016) - Baran, Sándor; Pap, Gyula; Sikolya, Kinga
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.