Dependent and Independent Time Series
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AI 根据所提供的论文材料归类：摘要直接讨论相依时间序列、波动率建模及 ARCH、GARCH 等模型的比较。
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相依与独立时间序列
- 研究问题
- 在误差存在相依性的时间序列中，如何利用一般椭圆分布建立似然与波动率模型，并评价常见层级模型之间的差异证据？
- 方法与思路
- 作者在一般椭圆分布下讨论相依样本似然及独立情形，并通过修改 BIC 和引入差异证据等级来比较波动率模型。
- 材料陈述的贡献
- 摘要提出相依样本下的似然视角及模型比较准则，并称所考察示例未显示 ARCH、GARCH 等层级模型具有明显优势。
- 阅读关注点
- 应核对联合分布与相依结构的定义、似然是否可计算，以及修改 BIC 的推导、证据等级阈值和示例比较的有效性。
- 阅读边界
- 所据为 arXiv 预印本，同行评审及期刊接收均未核实；摘要表述较概括，未给出分布、准则公式或可推广的比较结论。
原文摘要
The time series theory is set in this work under the domain of general elliptically contoured distributions. The advent of a time series approach that is in accordance with the expected reality of dependence between errors, transfers the increasingly complex and difficult to handle correlation analysis into a discipline that models volatility from a new view of a likelihood based on dependent probabilistic samples. The equally important problem of model selection is strengthened, but at the same time criticized with the introduction of degrees of evidence of significant difference in the modified BIC criterion . The demanding scale of differentiation puts a well-known database in trouble by observing insignificant relevance between the hierarchical models most used in the theory of time series under independence, such as Arch, Garch, Tgarch and Egarch. For extreme cases where the probabilistic independence of the samples is exceptionally demonstrated by an expert, the article also proposes the theory of time series under elliptical models, but with the same demanding comparison of the degrees of evidence of differences of the modified BIC. The example studied under this approach also does not denote any advantage of the hierarchical models studied. Such a new perspective for a likelihood based on dependent probabilistic samples has arisen naturally in similar context in finance under the setting of multivector variate distributions.