摘要翻译：
本文发展了GARCH(1,1）过程的极限理论，该过程在平稳和爆炸状态下适度偏离IGARCH过程。GARCH(1,1）过程由方程$u_t=\sigma_t\varepsilon_t$，$\sigma_t^2=\omega+\alpha_n u_{t-1}^2+\beta_n\sigma_t-1}^2$和$\alpha_n+\beta_n$等式定义。本文发展的渐近理论推广了Berkes等人。（2005）允许参数具有较慢的收敛速度。所得结果可应用于具有温和集成GARCH创新的过程的单位根检验（如Boswijk(2001)、Cavaliere和Taylor(2007，2009))和涉及温和集成GARCH过程的模型的估计量极限理论（如Jensen和Rahbek(2004)、Francq和Zako\\“Ian(2012，2013))。
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英文标题：
《Limit Theory for Moderate Deviation from Integrated GARCH Processes》
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作者：
Yubo Tao
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最新提交年份：
2018
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  This paper develops the limit theory of the GARCH(1,1) process that moderately deviates from IGARCH process towards both stationary and explosive regimes. The GARCH(1,1) process is defined by equations $u_t = \sigma_t \varepsilon_t$, $\sigma_t^2 = \omega + \alpha_n u_{t-1}^2 + \beta_n\sigma_{t-1}^2$ and $\alpha_n + \beta_n$ approaches to unity as sample size goes to infinity. The asymptotic theory developed in this paper extends Berkes et al. (2005) by allowing the parameters to have a slower convergence rate. The results can be applied to unit root test for processes with mildly-integrated GARCH innovations (e.g. Boswijk (2001), Cavaliere and Taylor (2007, 2009)) and deriving limit theory of estimators for models involving mildly-integrated GARCH processes (e.g. Jensen and Rahbek (2004), Francq and Zako\"ian (2012, 2013)).
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PDF链接：
https://arxiv.org/pdf/1806.01229