Asymptotic Properties of Self-Normalized Linear Processes with Long Memory

2010/06/08 by Peligrad, Magda, Sang, Hailin
#60F05 #60F17 #60G10 #60G22 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1006.1572

Abstract

In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem. The study is motivated by models arising in economical applications where often the linear processes have long memory, and the innovations have heavy tails.

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