First-Order Spatial Gegenbauer Autoregressive (SGAR(1,1)) Model and some of its Properties

Document Type : Original Article


1 Department of Statistics, Hakim Sabzevari University, Sabzevar, Iran

2 School of Mathematical and Computer Sciences, Heriot-Watt University, Putrajaya, Malaysia


In this paper, we extend the idea of Gegenbauer process in the spatial domain by introducing a more general parameter and call this model as Spatial Gegenbauer Autoregressive (SGAR(1,1)) model. The spectral density and autocovariance functions of the model are introduced. The Yajima estimators of the Gegenbauer parameters, the log-periodogram regression estimators of the memory parameters and the Whittle's estimators of all parameters are discussed. The performance of these estimators are evaluated through a simulation study.


Volume 21, Issue 2
December 2022
Pages 73-88
  • Receive Date: 06 December 2021
  • Revise Date: 09 July 2023
  • Accept Date: 05 August 2023