Abstract
In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen stochastically based on the random projection method. Randomness of factors has the consequence that correlation and covariance matrices are well preserved in a linear factor representation. It also enables derivation of probabilistic bounds for the accuracy of the random factor representation of time-series, their cross-correlations and covariances. As an application, we analyze reproduction of time-series and their cross-correlation coefficients in the well-diversified Russell 3,000 equity index.
Publication types
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Research Support, Non-U.S. Gov't
Associated data
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figshare/10.6084/m9.figshare.7286150.v1
Grants and funding
The research of J. Lukkarinen has been supported by the Academy of Finland (
http://www.aka.fi/en) via the Centre of Excellence in Analysis and Dynamics Research (projects 271983 and 307333) and from an Academy Project (project 258302). This work has also benefited from the support of the project EDNHS ANR-14-CE25-0011 of the French National Research Agency (ANR;
http://www.agence-nationale-recherche.fr/en/). Antti J. Tanskanen is affiliated with the Confederation of Finnish Industries EK. Kari Vatanen is affiliated with Varma Mutual Pension Insurance Company. The funders provided support in the form of salaries for authors AJT and KV, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the ‘author contributions’ section.