Weighted quantile regression for AR model with infinite variance errors

Abstract

Autoregressive (AR) models with finite variance errors have been well studied. This paper is concerned with AR models with heavy-tailed errors, which is useful in various scientific research areas. Statistical estimation for AR models with infinite variance errors is very different from those for AR models with finite variance errors. In this paper, we consider a weighted quantile regression for AR models to deal with infinite variance errors. We further propose an induced smoothing method to deal with computational challenges in weighted quantile regression. We show that the difference between weighted quantile regression estimate and its smoothed version is negligible. We further propose a test for linear hypothesis on the regression coefficients. We conduct Monte Carlo simulation study to assess the finite sample performance of the proposed procedures. We illustrate the proposed methodology by an empirical analysis of a real-life data set.

Keywords:

• quantile regression
• autoregressive model
• infinite variance

Acknowledgements

Zhao Chen's research was partially supported by the National Institute on Drug Abuse (NIDA) grant R21-DA024260 as a graduate research assistant during his visit to Pennsylvania State University. Runze Li is the corresponding author and his research was supported by NIDA grant P50-DA10075 and the National Natural Science Foundation of China grants 11028103 and 10911120395. Yaohua Wu's research was supported by the National Natural Science Foundation of China grant 10871188. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIDA or the NIH.