Optimal tests for parameter breaking process in conditional quantile models

Abstract

This paper proposes efficient tests for quantile parameter instability in parametric and semiparametric setups. In each setup, various types of unstable parameter processes are examined such as single structural break, multiple structural breaks, and random parameters, and the optimal test is suggested for each unstable process. In a parametric model, tick-exponential family of distributions is used to construct the likelihood ratio tests. The suggested tests have the best asymptotic weighted average power if the likelihood function is correctly specified and are asymptotically correct-sized even under misspecification. In a semiparametric setup in which the underlying distribution is unknown but is treated as an infinite-dimensional nuisance parameter, we show that semiparametric efficient tests are adaptive if the error term is conditionally iid. Non-adaptive efficient tests are suggested under weaker conditions as well. Monte Carlo simulation shows that the proposed tests have better finite sample powers than the existing tests under various circumstances.