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  • Ji Hyung Lee (a1), Oliver Linton (a2) and Yoon-Jae Whang (a3)


We develop the limit theory of the quantilogram and cross-quantilogram under long memory. We establish the sub-root-n central limit theorems for quantilograms that depend on nuisance parameters. We propose a moving block bootstrap (MBB) procedure for inference and establish its consistency, thereby enabling a consistent confidence interval construction for the quantilograms. The newly developed reduction principles for the quantilograms serve as the main technical devices used to derive the asymptotics and establish the validity of MBB. We report some simulation evidence that our methods work satisfactorily. We apply our method to quantile predictive relations between financial returns and long-memory predictors.


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*Address correspondence to Ji Hyung Lee, Department of Economics, University of Illinois, 1407 W. Gregory Dr., 214 David Kinley Hall, Urbana, IL 61801, USA; e-mail:


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We acknowledge helpful comments from Hongqi Chen, Rui Fan, Roger Koenker, Boyuan Zhang and participants from the seminars at University of Cambridge, UIUC, 2017 Asian meeting of the Econometric Society and Korea University. We thank the Co-Editor, Anna Mikusheva, and three anonymous referees for very constructive comments. We are also grateful for the vast amount of editorial input by the Editor, Peter Phillips, on the final version of the manuscript. Any errors are the responsibility of the authors.



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  • Ji Hyung Lee (a1), Oliver Linton (a2) and Yoon-Jae Whang (a3)


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