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A misspecification test for the higher order co-moments of the factor model

机译：针对因子模型的高阶矩的误判检验

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摘要

The traditional estimation of higher order co-moments of non-normal random variables by the sample analog of the expectation faces a curse of dimensionality, as the number of parameters increases steeply when the dimension increases. Imposing a factor structure on the process solves this problem; however, it leads to the challenging task of selecting an appropriate factor model. This paper contributes by proposing a test that exploits the following feature: when the factor model is correctly specified, the higher order co-moments of the unexplained return variation are sparse. It recommends a general to specific approach for selecting the factor model by choosing the most parsimonious specification for which the sparsity assumption is satisfied. This approach uses a Wald or Gumbel test statistic for testing the joint statistical significance of the co-moments that are zero when the factor model is correctly specified. The asymptotic distribution of the test is derived. An extensive simulation study confirms the good finite sample properties of the approach. This paper illustrates the practical usefulness of factor selection on daily returns of random subsets of S&P 100 constituents.
机译：通过期望的样本模拟对非正常随机变量的高阶共矩的传统估计面临着维数的诅咒，因为随着维数的增加，参数的数量急剧增加。在过程中强加因子结构可以解决此问题；然而，这导致了选择合适的因子模型的艰巨任务。本文通过提出一项利用以下功能的测试做出了贡献：正确地指定因子模型后，无法解释的收益变化的高阶共矩稀疏。它建议通过选择满足稀疏性假设的最简约规范来选择因子模型的通用方法。当正确指定因子模型时，此方法使用Wald或Gumbel检验统计量来检验共矩的联合统计显着性为零。得出测试的渐近分布。广泛的仿真研究证实了该方法的良好有限样本性质。本文阐述了因子选择对标普100成分随机子集的每日收益的实际实用性。

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  • 来源
    《Statistics》 |2019年第3期|471-488|共18页
  • 作者

    Lu Wanbo; Yang Dong; Boudt Kris;

  • 作者单位

    Southwestern Univ Finance & Econ, Sch Stat, Chengdu, Sichuan, Peoples R China;

    Southwestern Univ Finance & Econ, Sch Stat, Chengdu, Sichuan, Peoples R China|Vrije Univ Brussel, Solvay Business Sch, Brussels, Belgium;

    Vrije Univ Brussel, Solvay Business Sch, Brussels, Belgium|Vrije Univ Amsterdam, Sch Business & Econ, Amsterdam, Netherlands;

  • 收录信息 美国《科学引文索引》(SCI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Factor models; higher order co-moments; sparsity; curse of dimensionality; diagnostic test;

    机译：因子模型;高阶矩;稀疏性;维数诅咒;诊断检验;

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