Random selection of factors preserves the correlation structure in a linear factor model to a high degree

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http://hdl.handle.net/10138/288726

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Tanskanen , A J , Lukkarinen , J & Vatanen , K 2018 , ' Random selection of factors preserves the correlation structure in a linear factor model to a high degree ' , PLoS One , vol. 13 , no. 12 , 0206551 . https://doi.org/10.1371/journal.pone.0206551

Julkaisun nimi: Random selection of factors preserves the correlation structure in a linear factor model to a high degree
Tekijä: Tanskanen, Antti J.; Lukkarinen, Jani; Vatanen, Kari
Muu tekijä: University of Helsinki, Confederation of Finnish Industries (EK)
University of Helsinki, Department of Mathematics and Statistics
Päiväys: 2018-12-21
Kieli: eng
Sivumäärä: 22
Kuuluu julkaisusarjaan: PLoS One
ISSN: 1932-6203
URI: http://hdl.handle.net/10138/288726
Tiivistelmä: 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.
Avainsanat: JOHNSON-LINDENSTRAUSS
MATRIX
NOISE
RANDOM PROJECTION
111 Mathematics
112 Statistics and probability
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