A0483
Title: Quantiled conditional variance, skewness, and kurtosis by Cornish-Fisher expansion
Authors: Ke Zhu - University of Hong Kong (Hong Kong) [presenting]
Abstract: The conditional variance, skewness, and kurtosis play a central role in time series analysis. Some parametric models often study these three conditional moments (CMs) but with two big issues: the risk of model misspecification and the instability of model estimation. To avoid the above two issues, a novel method is proposed to estimate these three CMs by the so-called quantized CMs (QCMs). The QCM method first adopts the idea of Cornish-Fisher expansion to construct a linear regression model based on n different estimated conditional quantiles. Next, it computes the QCMs simply and simultaneously by using this regression model's ordinary least squares estimator without any prior estimation of the conditional mean. Under certain conditions that allow estimated conditional quantiles to be biased, the QCMs are shown to be consistent with the convergence rate $n^{\frac{1}{2}}$. Simulation studies indicate that the QCMs perform well under different scenarios of estimated conditional quantiles. In the application, the study of QCMs for eight major stock indexes demonstrates the effectiveness of financial rescue plans during the COVID-19 pandemic outbreak. It unveils a new "non-zero kink" phenomenon in conditional kurtosis's "news impact curve" function.
