Quantile Autoregression for Censored Data

• Activity Number: 181
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Seokwoo Choi* and Stephen Portnoy
• Companies: Michigan Technological University and University of Illinois at Urbana-Champaign
• Keywords: Censored time-series ; Autoregression ; Quantile ; Self-consistent ; Kaplan-Meier

Abstract

Quantile autoregression (QAR) provides an alternative way to study asymmetric dynamics and local persistence in time series. It is particularly attractive for censored data, where the classical autoregressive models are unidentifiable without further parametric assumptions on the distributions. However, unlike the standard regression models, the autoregressive models must take account of censoring on both response and regressors. In this paper, we first show that the existing censored quantile regression methods produce consistent estimators for QAR models when using only the fully observed regressors. A new algorithm is proposed to provide a censored quantile autoregression (CQAR) estimator by adopting imputation methods. The algorithm distributes probability mass of each censored point to any sufficiently large value appropriately, and iterates towards self-consistent solutions. Monte Carlo simulations are conducted to examine the empirical consistency of the CQAR estimator. Also, empirical applications of the algorithm to the Samish river water quality study demonstrate the merits of the proposed method.