  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.
