Random selection of factors preserves the correlation structure in a linear factor model to a high degree
arXiv:1604.05896 · doi:10.1371/journal.pone.0206551
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 at random based on the random projection method. Randomness of factors has the consequence that covariance matrix is 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.
27 pages, 7 figures, ver 2: includes major revision of the abstract, introduction and discussion, ver 3: title changed to match the final published version (available as an open access file following the DOI link)