Estimation of the Memory Parameters of the Fractionally Integrated Separable Spatial Autoregressive (FISSAR(1, 1)) Model: A Simulation Study

Abstract

In this article, we implement the Regression Method for estimating (d ₁, d ₂) of the FISSAR(1, 1) model. It is also possible to estimate d ₁ and d ₂ by Whittle's method. We also compute the estimated bias, standard error, and root mean square error by a simulation study. A comparison was made between the Regression Method of estimating d ₁ and d ₂ to that of the Whittle's method. It was found in this simulation study that the Regression Method of estimation was better when compare with the Whittle's estimator, in the sense that it had smaller root mean square errors (RMSE) values.

Keywords:

• Autoregressive process
• Fractional integration
• FISSAR
• Spatial model
• Separable process
• Whittle's estimation

Mathematics Subject Classification:

• 62M30

Acknowledgments

We would like to thank the reviewer(s) and the Editor for their useful comments and valuable suggestions to improve the quality of the article. The authors would also like to thank the Department of Mathematics, University Putra Malaysia and The Institute for Mathematical Research, University Putra Malaysia for their support. The first author would also like to thank the Department of Mathematics, Tarbiat Moallem University of Sabzevar, Iran for their financial support.