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摘要翻译：
针对时变已实现协方差(RCOV)矩阵，提出了一种新的条件BEKK矩阵-F(CBF)模型。这种CBF模型能够捕获重尾RCOV，这是一个重要的程式化事实，但不能被基于Wishart的模型充分处理。为了进一步模拟RCOV的长记忆特性，引入了一种特殊的条件异构自回归(HAR)结构CBF模型。此外，我们还系统地研究了CBF模型的概率性质和统计推断，包括探讨其平稳性，建立其最大似然估计量的渐近性，并对其模型检验给出了一些新的基于内积的检验。为了处理大维RCOV矩阵，我们构造了两个简化的CBF模型--方差-目标CBF模型（针对中维固定维RCOV矩阵）和因子CBF模型（针对高维RCOV矩阵）。对于这两种简化模型，导出了估计参数的渐近理论。仿真结果和两个实例说明了整个方法的重要性。
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英文标题：
《Time series models for realized covariance matrices based on the
matrix-F distribution》
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作者：
Jiayuan Zhou, Feiyu Jiang, Ke Zhu, Wai Keung Li
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最新提交年份：
2020
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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：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：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：
We propose a new Conditional BEKK matrix-F (CBF) model for the time-varying realized covariance (RCOV) matrices. This CBF model is capable of capturing heavy-tailed RCOV, which is an important stylized fact but could not be handled adequately by the Wishart-based models. To further mimic the long memory feature of the RCOV, a special CBF model with the conditional heterogeneous autoregressive (HAR) structure is introduced. Moreover, we give a systematical study on the probabilistic properties and statistical inferences of the CBF model, including exploring its stationarity, establishing the asymptotics of its maximum likelihood estimator, and giving some new inner-product-based tests for its model checking. In order to handle a large dimensional RCOV matrix, we construct two reduced CBF models -- the variance-target CBF model (for moderate but fixed dimensional RCOV matrix) and the factor CBF model (for high dimensional RCOV matrix). For both reduced models, the asymptotic theory of the estimated parameters is derived. The importance of our entire methodology is illustrated by simulation results and two real examples.
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PDF链接：
https://arxiv.org/pdf/1903.12077
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