Correlated Errors in the Parameters Estimation of the ARFIMA Model: A Simulated Study

Abstract

Processes with correlated errors have been widely used in economic time series. The fractionally integrated autoregressive moving-average processes—ARFIMA(p, d, q)—(Hosking, 1981) have been explored to model stationary and non stationary time series with long-memory property. This work uses the Monte Carlo simulation method to evaluate the performance of some parametric and semiparametric estimators for long and short-memory parameters of the ARFIMA model with conditional heteroskedastic (ARFIMA-GARCH model). The comparison is based on the empirical bias and the mean squared error of each estimator.

Keywords:

• Fractional differencing
• Long memory and GARCH models

Mathematics Subject Classification:

• 62M10
• 62M15

Acknowledgments

The author V. A. Reisen gratefully acknowledges partial financial support from CNPq/ Brazil. S.R.C. Lopes was partially supported by CNPq-Brazil, by Pronex Probabilidade e Processos Estocásticos (Convênio MCT/CNPq/FAPERJ - Edital 2003), and also by Fundaç cão de Amparo à Pesquisa no Estado do Rio Grande do Sul (FAPERGS Foundation). The authors wish to thank the editor and two anonymous referees for their valuable comments on the earlier version of this article.