Before revision:  Random selection of factors has the important consequence that the factors are almost orthogonal with respect to each other. The developed random factor model is expected to preserve covariance between time-series. We derive probabilistic bounds for the accuracy of the random factor representation of time-series, their cross-correlations and covariances.
After revision:  Random selection 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.