Quantilograms under Strong Dependence

Abstract

This paper studies 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. A moving block bootstrap (MBB) procedure is proposed and its consistency is proved, thereby enabling a consistent confidence interval construction for the quantilograms. The newly developed uniform reduction principles (URPs) for the quantilograms serve as the main technical devices used to derive asymptotics and MBB validity. Confirmatory simulation results are reported. Some empirical practices on quantile predictive relations between financial returns and long memory predictors are performed using the new methods.

Keywords: Long Memory, Moving Block Bootstrap, Nonlinear Dependence, Quantilogram and Cross-Quantilgoram, Uniform Reduction Principle

JEL Classification: C22