A Nonparametric Measure of Heteroskedasticity

Song, Xiaojun; Taamouti, Abderrahim

Abstract

We introduce a nonparametric measure to quantify the degree of heteroskedasticity at a fixed quantile of the conditional distribution of a random variable. Our measure of heteroskedasticity is based on nonparametric quantile regressions and is expressed in terms of unrestricted and restricted expectations of quantile loss functions. It can be consistently estimated by replacing the unknown expectations by their nonparametric estimates. We derive a Bahadur-type representation for the nonparametric estimator of the measure. We provide the asymptotic distribution of this estimator, which one can use to build tests for the statistical significance of the measure. Thereafter, we establish the validity of a fixed regressor bootstrap that one can use in finite-sample settings to perform tests. A Monte Carlo simulation study reveals that the bootstrap-based test has a good finite sample size and power for a variety of data generating processes and different sample sizes. Finally, two empirical applications are provided to illustrate the importance of the proposed measure.

Citation

Song, X., & Taamouti, A. (2021). A Nonparametric Measure of Heteroskedasticity. Journal of Statistical Planning and Inference, 212, 45-68. https://doi.org/10.1016/j.jspi.2020.08.005

• Journal Article Type: Article
• Acceptance Date: Aug 20, 2020
• Online Publication Date: Nov 4, 2020
• Publication Date: 2021-05
• Deposit Date: Sep 16, 2020
• Publicly Available Date: Nov 4, 2021
• Journal: Journal of Statistical Planning and Inference
• Print ISSN: 0378-3758
• Electronic ISSN: 1873-1171
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 212
• Pages: 45-68
• DOI: https://doi.org/10.1016/j.jspi.2020.08.005
• Public URL: https://durham-repository.worktribe.com/output/1292198