The paper discusses the identification of the empirical, partially intelligible white noise processes generated by deterministic numerical algorithms. The introduced fuzzy-random complementary approach can identify the inner hidden correlational patterns of the empirical white noise process if the process has a real hidden structure of this kind. We have shown how the characteristics of autocorrelated white noise processes change as the order of autocorrelation increases. Based on this approach, the original empirical white noise process transformed by the autocorrelation operator can be considered to be random data series (randomlikeness), and at the same time, it has function-like characteristics (functionlikeness), as well. We approach the analysis of the mentioned complementarity by modeling the autocorrelation functions of the empirical white noise processes using tensor product (TP) model transformation.