Journal of Probability and Statistics
Volume 2011 (2011), Article ID 691058, 11 pages
Review Article

The CSS and The Two-Staged Methods for Parameter Estimation in SARFIMA Models

1Department of Statistics, Ondokuz Mayis University, 55139 Samsun, Turkey
2Department of Statistics, Hacettepe University, Beytepe, 06800 Ankara, Turkey

Received 19 May 2011; Accepted 1 July 2011

Academic Editor: Mike Tsionas

Copyright © 2011 Erol Egrioglu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Seasonal Autoregressive Fractionally Integrated Moving Average (SARFIMA) models are used in the analysis of seasonal long memory-dependent time series. Two methods, which are conditional sum of squares (CSS) and two-staged methods introduced by Hosking (1984), are proposed to estimate the parameters of SARFIMA models. However, no simulation study has been conducted in the literature. Therefore, it is not known how these methods behave under different parameter settings and sample sizes in SARFIMA models. The aim of this study is to show the behavior of these methods by a simulation study. According to results of the simulation, advantages and disadvantages of both methods under different parameter settings and sample sizes are discussed by comparing the root mean square error (RMSE) obtained by the CSS and two-staged methods. As a result of the comparison, it is seen that CSS method produces better results than those obtained from the two-staged method.