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Quantilograms Under Strong Dependence

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  • Lee, Ji Hyung
  • Linton, Oliver
  • Whang, Yoon-Jae

Abstract

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.

Suggested Citation

  • Lee, Ji Hyung & Linton, Oliver & Whang, Yoon-Jae, 2020. "Quantilograms Under Strong Dependence," Econometric Theory, Cambridge University Press, vol. 36(3), pages 457-487, June.
    • Handle: RePEc:cup:etheor:v:36:y:2020:i:3:p:457-487_4
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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