Is the quantum theory predictably complete?

Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability distributions extracted from these time series were shown to be consistent with the probabilistic predictions of QT. However it was not proven that the time series of existing experimental data did not contain some stochastic fine structures, which could have been averaged out by describing them in terms of the empirical probability distributions. In this paper we advocate various statistical tests which could be used to search for such fine structures in the data and to answer the title question of this paper. In our opinion a proper understanding of the statistical character of QT and of its limitations is crucial in the domains such as: quantum optics and quantum information.