Tests for the Gaussianity of a time series with application to financial time series

时间序列的高斯性检验及其在金融时间序列中的应用

• 批准号: 04630014
• 负责人: KARIYA Takeaki
• 金额: $ 0.77万
• 依托单位: Institute of Economic Research, Hitotsubashi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04630014/
• 关键词: Test for Multivariate Normality; Test for Gaussianity; Curved Family; Locally Best Invariant Test; Mardia's Test; 多変量光度; ガウス性の検定; エルミート多項式; 多変量正規性の検定; 曲分布族

In a view of testing multivariate normality, a new testing procedure for testing the Gaussianity of stationary time series process is proposed. The basic idea is that first standardizing p variates and then transforming them by Hermitian polynomials, the moment structure of the p-dim. multivariate normality is tested based on the transformed variates. The test statistic is shown to be asymptotically distributed as x^2-distribution. These results are applied to testing the Gaussianity of a univariate time series by considering lagged variates p-dim variates. The method is applied to returns of stocks and the Gaussianity is rejected.Also the problem of testing multivariate normality against a curved family is treated and the locally best invariant test and its distribution are derived. A curved family for which the Mardia test is locally best invariant is found.

从检验多元正态性的角度出发，提出了一种检验平稳时间序列过程高斯性的新方法。基本思想是首先标准化p变量然后用厄米多项式变换它们，p-dim的力矩结构。根据变换后的变量检验了多元正态性。检验统计量呈渐近分布，为x^2分布。这些结果被应用于测试一个单变量时间序列的高斯性，考虑滞后变量p-dim变量。将该方法应用于股票收益，并对其高斯性进行了否定。讨论了对曲线族进行多元正态性检验的问题，导出了局部最优不变检验及其分布。找到了一个Mardia检验为局部最优不变量的曲线族。

项目成果

Takeaki KARIYA: "LBI tests for multivariate normality in curved families and Mardia's test" Sankhya. (1994)

Takeaki KARIYA：“弯曲家庭中多元正态性的 LBI 测试和 Mardia 测试”Sankhya。

Takeaki KARIYA: "LBI tests for multivariate normality in curved families with μ known" Proceedings of the International Symposium on Multivariate Analysis and its Applications. (1994)

Takeaki KARIYA：“LBI 检验 μ 已知的曲线族中的多元正态性”多元分析及其应用国际研讨会论文集（1994 年）。

Takeaki KARIYA: "Tests for multinormality with application to time series" 一橋大学経済研究所ディスカッション・ペーパーNo.264.

Takeaki KARIYA：“应用于时间序列的多重正态性检验”一桥大学经济研究所讨论论文第 264 号。

T.KARIYA: "LBI Tests for Multivariate Normality in Curved Families with mu Known." Proceedings of the International Symposium on Multivariate Analysis and its Applications.(to appear). (1994)

T.KARIYA：“LBI 测试已知 mu 的弯曲家庭的多元正态性。”

Takeaki KARIYA: "Tests for multinormality with application to time series" 一橋大学経済研究所ディスカッション・ペーパーNo264.

Takeaki KARIYA：“应用于时间序列的多重正态性检验”一桥大学经济研究所讨论论文第 264 号。