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摘要翻译：
本文讨论了一个半参数广义自回归条件异方差（S-GARCH）模型。对于该模型，首先用核估计器估计无条件方差的时变长期分量，然后用拟极大似然估计器(QMLE)估计GARCH型短期分量中的非时变参数。我们证明了QMLE在参数收敛速度下是渐近正态的。其次，我们构造了线性参数约束的Lagrange乘子检验和模型检验的portmanteau检验，并得到了它们的渐近零分布。我们的整个统计推断过程适用于非平稳数据，具有两个重要的特点：第一，我们的QMLE和两个检验对长期成分的未知形式是自适应的；第二，当S-GARCH模型平稳时，我们的QMLE和两个检验与方差目标法具有相同的效率和检验能力。
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英文标题：
《Adaptive inference for a semiparametric generalized autoregressive
conditional heteroskedasticity model》
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作者：
Feiyu Jiang, Dong Li, Ke Zhu
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最新提交年份：
2020
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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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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英文摘要：
This paper considers a semiparametric generalized autoregressive conditional heteroskedasticity (S-GARCH) model. For this model, we first estimate the time-varying long run component for unconditional variance by the kernel estimator, and then estimate the non-time-varying parameters in GARCH-type short run component by the quasi maximum likelihood estimator (QMLE). We show that the QMLE is asymptotically normal with the parametric convergence rate. Next, we construct a Lagrange multiplier test for linear parameter constraint and a portmanteau test for model checking, and obtain their asymptotic null distributions. Our entire statistical inference procedure works for the non-stationary data with two important features: first, our QMLE and two tests are adaptive to the unknown form of the long run component; second, our QMLE and two tests share the same efficiency and testing power as those in variance targeting method when the S-GARCH model is stationary.
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PDF链接：
https://arxiv.org/pdf/1907.04147
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