半参数条件位置尺度模型中残差经验分布的适应性

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2022-02-01 DOI:10.3150/21-bej1357
C. Francq, J. Zakoian
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引用次数: 3

摘要

本文讨论了一类一般时间序列模型中残差的经验分布函数Fn的渐近分布问题,包括条件均值和条件异方差,其独立和同分布误差具有未知分布F,对于一大类时间序列模型(包括标准ARMA-GARCH),√n{Fn(·)−F(·)}的渐近分布受到估计的影响,但与模型参数无关。因此,它既不像纯线性模型那样无渐近估计,也不像一些非线性模型那样渐近依赖模型。建立了渐近随机等连续性。我们考虑一个应用于条件风险价值的估计。
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Adaptiveness of the empirical distribution of residuals in semi-parametric conditional location scale models
This paper addresses the problem of deriving the asymptotic distribution of the empirical distribution function F n of the residuals in a general class of time series models, including conditional mean and conditional heteroscedaticity, whose independent and identically distributed errors have unknown distribution F. We show that, for a large class of time series models (including the standard ARMA-GARCH), the asymptotic distribution of √ n{ F n (·) − F (·)} is impacted by the estimation but does not depend on the model parameters. It is thus neither asymptotically estimation free, as is the case for purely linear models, nor asymptotically model dependent, as is the case for some nonlinear models. The asymptotic stochastic equicontinuity is also established. We consider an application to the estimation of the conditional Value-at-Risk.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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