arXiv 14 Feb 2023 · Statistics — Methodology · 1 citations (OpenAlex)
arXiv:2302.06799 · PDF · DOI · OpenAlex · Extracted main text
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bollerslev, T (1986) Generalized autoregressive conditional heteroskedasticity | 0.843 | 3 | 3 | 100% |
| 2 | Lee, Y. S. and Lin, T. K (1992) Algorithm AS 269: High order Cornish-Fisher expansion | 0.843 | 3 | 3 | 100% |
| 3 | Harvey, C. R. and Siddique, A (1999) Autoregressive conditional skewness | 0.811 | 4 | 2 | 100% |
| 4 | León, Á., Rubio, G. and Serna, G (2005) Autoregresive conditional volatility, skewness and kurtosis | 0.811 | 4 | 2 | 100% |
| 5 | Escanciano, J. C (2006) Goodness-of-fit tests for linear and nonlinear time series models | 0.737 | 3 | 2 | 100% |
| 6 | Jondeau, E. and Rockinger, M (2003) Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements | 0.737 | 3 | 2 | 100% |
| 7 | Engle, R. F. and Manganelli, S (2004) CAViaR: Conditional autoregressive value at risk by regression quantiles | 0.644 | 4 | 1 | 100% |
| 8 | Cornish, E. A. and Fisher, R. A (1938) Moments and cumulants in the specification of distributions | 0.644 | 2 | 2 | 100% |
| 9 | Engle, R. F. and Ng, V. K (1993) Measuring and testing the impact of news on volatility | 0.644 | 2 | 2 | 100% |
| 10 | Andrews, D. W. K (1988) Laws of large numbers for dependent nonidentically distributed random variables | 0.405 | 1 | 1 | 100% |
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