On Extreme Value Asymptotics of Projected Sample Covariances in High Dimensions with Applications in Finance and Convolutional Networks

• URL: http://arxiv.org/abs/2310.08150v1
• Date: Thu, 12 Oct 2023 09:17:46 GMT
• Title: On Extreme Value Asymptotics of Projected Sample Covariances in High Dimensions with Applications in Finance and Convolutional Networks
• Authors: Ansgar Steland
• Abstract summary: We show that Gumbel-type extreme values holds true within a linear time series framework. As applications we discuss long-only mimimal-variance portfolio optimization and sub-portfolio analysis with respect to idiosyncratic risks.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a data set has been collected under normal conditions. The approach generalizes the case of the maximal deviation of the sample autocovariances function from its assumed values. Within a linear time series framework it is shown that Gumbel-type extreme value asymptotics holds true. As applications we discuss long-only mimimal-variance portfolio optimization and subportfolio analysis with respect to idiosyncratic risks, ETF index tracking by sparse tracking portfolios, convolutional deep learners for image analysis and the analysis of array-of-sensors data.

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