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Quantiled conditional variance, skewness, and kurtosis by Cornish-Fisher expansion

Ningning Zhang, Ke Zhu

arXiv 14 Feb 2023 · Statistics — Methodology · 1 citations (OpenAlex)

arXiv:2302.06799 · PDF · DOI · OpenAlex · Extracted main text

Abstract

The conditional variance, skewness, and kurtosis play a central role in time series analysis. These three conditional moments (CMs) are often studied by some parametric models but with two big issues: the risk of model mis-specification and the instability of model estimation. To avoid the above two issues, this paper proposes a novel method to estimate these three CMs by the so-called quantiled 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 the ordinary least squares estimator of this regression model, without any prior estimation of the conditional mean. Under certain conditions, the QCMs are shown to be consistent with the convergence rate $n^{-1/2}$. Simulation studies indicate that the QCMs perform well under different scenarios of Cornish-Fisher expansion errors and quantile estimation errors. In the application, the study of QCMs for three exchange rates demonstrates the effectiveness of financial rescue plans during the COVID-19 pandemic outbreak, and suggests that the existing “news impact curve” functions for the conditional skewness and kurtosis may not be suitable.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Bollerslev, T (1986) Generalized autoregressive conditional heteroskedasticity0.84333100%
2Lee, Y. S. and Lin, T. K (1992) Algorithm AS 269: High order Cornish-Fisher expansion0.84333100%
3Harvey, C. R. and Siddique, A (1999) Autoregressive conditional skewness0.81142100%
4León, Á., Rubio, G. and Serna, G (2005) Autoregresive conditional volatility, skewness and kurtosis0.81142100%
5Escanciano, J. C (2006) Goodness-of-fit tests for linear and nonlinear time series models0.73732100%
6Jondeau, E. and Rockinger, M (2003) Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements0.73732100%
7Engle, R. F. and Manganelli, S (2004) CAViaR: Conditional autoregressive value at risk by regression quantiles0.64441100%
8Cornish, E. A. and Fisher, R. A (1938) Moments and cumulants in the specification of distributions0.64422100%
9Engle, R. F. and Ng, V. K (1993) Measuring and testing the impact of news on volatility0.64422100%
10Andrews, D. W. K (1988) Laws of large numbers for dependent nonidentically distributed random variables0.40511100%

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