Document Type : Original Article

Authors

• Alireza Ghodsi ¹
• Mahendran Shitan ²

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

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

Abstract

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.

Keywords

• Spatial Gegenbauer Autoregressive Model
• SGAR(1
• 1)
• Long Memory
• Log-Periodogram Estimation
• Whittle Estimation