QUANTILED CONDITIONAL VARIANCE, SKEWNESS, AND KURTOSIS BY CORNISH-FISHER EXPANSION

• 成果类型: Article
• 署名作者: Zhang, Ningning; Zhu, Ke
• 署名单位: University of Hong Kong
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157; 1941-7330
• DOI: 10.1214/25-AOAS2122
• 发表日期: 2026-03
• 页码: 131-147
• 关键词: Conditional moments; Cornish-Fisher expansion; news impact curve; quantiled conditional moments; REGRESSION ESTIMATION; volatility; heteroscedasticity; tests; fit

摘要

The conditional variance, skewness, and kurtosis play a central role in time series analysis. To learn the three conditional moments (CMs), the News Impact Curve (NIC) has been widely used. Since these CMs are unobserved, their NICs are typically assumed to have certain parametric forms and then learned within a parametric model, which accounts for the dynamics of all three CMs. However, this inevitably brings two issues: the risk of model misspecification and the instability of model estimation, where the latter issue results from a necessary nonlinear constraint (on the conditional skewness and kurtosis) that requires a complex restriction on the admission region of model parameters. To avoid the above two issues, we propose a novel method to estimate the three CMs via the so-called quantiled CMs (QCMs). Under certain high-level condition, we show the consistency of the QCMs. In an application to three major exchange rates, we give a data-driven method to propose the nonparametric NICs for the three CMs, based on the QCMs. Our obtained nonparametric NICs indicate that the existing parametric NICs for conditional skewness and kurtosis may miscapture the impact of large shocks (in absolute value).