Year: 2026
Type: article
Abstract: 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 mis-specification 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).
Source: The Annals of Applied Statistics
DOI: 10.1214/25-aoas2122
Authors: Ningning Zhang, Ke Zhu
Institution: University of Hong Kong
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7139071071