Quantile Regression on Quantile Ranges – A Threshold Approach

Abstract

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 (2011Galvao et al ( , 2014 on threshold regression models.

Quantile regression on the nonlinear relationship between land use and trip time

“…Figure 1 and Table 2 present the distributions of the subsamples and descriptive statistics of key land use variables according to five quantiles—Q10, Q25, Q50 (i.e., median), Q75, and Q90 (and the remaining Q100)—for a better understanding of the settings of the study area. One may or may not suspect the existence of a subset, and, if there is one, it is a rationale for conducting QR instead of OLS regression, which provides only one estimate for the sample mean, that is, for the homogeneous population (Chen, 2007; Koenker, 2005; Kuan, Michalopoulos, & Xiao, 2017). QR requires no assumptions regarding the distribution of the dependent variable, and, in a similar vein, it is insensitive to outliers.…”

The US debt–growth nexus along the business cycle

“…Nevertheless, it is worth mentioning that in our threshold regression model it is assumed that debt is exogenous and that this follows from the underlying mean regression speci…cation of Chudik et al (2017). Galvão et al (2014) and Kuan, Michalopoulos, and Xiao (2017) propose tests in threshold regression models with time series data but for a …xed threshold. This paper is structured as follows: In Section 2 we present the baseline model as in Chudik et al (2017) and the more general model that includes a dummy for the event of World War II, and more lagged and interaction terms between the threshold variable and the growth and debt covariates.…”

Spatial cluster detection with threshold quantile regression

“…There have been a number of studies on threshold quantile regression (Cai, 2010;Cai & Stander, 2008;Caner, 2002;Galvao et al, 2011Galvao et al, , 2014He & Zhu, 2003;Horowitz & Spokoiny, 2002;Lee et al, 2011;Otsu, 2008;Zheng, 1998). More recently, Zhang et al (2014) and Tang et al (2015) developed procedures for testing change points due to a covariate threshold, and Kuan et al (2017) and Su and Xu (2019) studied confidence intervals for the estimated threshold parameter in regression quantiles. Threshold quantile regression models consider piecewise effects in subregions divided by one threshold variable with jumps occurring at the unknown change points.…”