Adaptiveness of the empirical distribution of residuals in semi-parametric conditional location scale models

IF 1.5 2区 数学 Q2 STATISTICS & PROBABILITY
Bernoulli Pub Date : 2022-02-01 DOI:10.3150/21-bej1357
C. Francq, J. Zakoian
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引用次数: 3

Abstract

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.
半参数条件位置尺度模型中残差经验分布的适应性
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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来源期刊
Bernoulli
Bernoulli 数学-统计学与概率论
CiteScore
3.40
自引率
0.00%
发文量
116
审稿时长
6-12 weeks
期刊介绍: BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.
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