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Quantile Regression on Quantile Ranges – A Threshold Approach
Author(s) -
Kuan ChungMing,
Michalopoulos Christos,
Xiao Zhijie
Publication year - 2017
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12204
Subject(s) - mathematics , quantile , statistics , quantile regression , threshold model , range (aeronautics) , asymptotic distribution , complement (music) , statistic , econometrics , biochemistry , materials science , chemistry , estimator , composite material , gene , phenotype , complementation
We study, via quantile regression, time series models whose conditional distribution may change over different quantile range of a threshold variable. We derive the limiting distribution of the estimated threshold parameter under the frameworks of asymptotically shrinking and fixed regime change magnitude. We construct confidence intervals for the estimated threshold parameter via a likelihood‐ratio‐type statistic and tabulate critical values, and by extensive simulation, we investigate their coverage probabilities. We also derive the Bahadur representation allowing for serially correlated errors and discuss related inference problems on threshold effects. Our asymptotic and simulation results complement the existing literature of Caner (2002), Galvao et al (2011, 2014) on threshold regression models.