A generalization of a Gaussian semiparametric estimator on multivariate long-range dependent processes

Abstract

In this paper, we propose and study a general class of Gaussian semiparametric estimators (GSE) of the fractional differencing parameter in the context of long-range dependent multivariate time series. We establish large sample properties of the estimator without assuming Gaussianity. The class of models considered here satisfies simple conditions on the spectral density function, restricted to a small neighbourhood of the zero frequency and includes important class of vector autoregressive fractionally integrated moving average processes. We also present a simulation study to assess the finite sample properties of the proposed estimator based on a smoothed version of the GSE which supports its competitiveness.

Keywords:

• fractional integration
• long-range dependence
• semiparametric estimation
• smoothed periodogram
• tapered periodogram
• VARFIMA processes

2010 Mathematical Subject Classification:

• Primary: 62H12
• 62F12
• 62M10
• 60G10
• 62M15

Acknowledgements

G. Pumi was partially supported by CAPES/Fulbright Grant BEX 2910/06-3 and by CNPq-Brazil. S.R.C. Lopes's research was partially supported by CNPq-Brazil, by CAPES-Brazil, by Pronex Probabilidade e Processos Estocásticos - E-26/170.008/2008 -APQ1 and also by INCT em Matemática. The authors are also grateful to the (Brazilian) National Center of Super Computing (CESUP-UFRGS) for the computational resources.