Time Series, Stochastic Processes and Completeness of Quantum Theory

Most of physical experiments are usually described as repeated measurements of some random variables. The experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared with the probabilities provided by the algorithms of quantum theory (QT). In spite of statistical predictions of QT a claim was made that the theory provided the most complete description of the data and of the underlying physical phenomena. This claim could be easily rejected if some fine structures, averaged out in standard statistical descriptive analysis, were found in the time series of experimental data. To search for these structures one has to use more subtle statistical tools which were developed to study time series produced by various stochastic processes. In this talk we review some of these tools. As an example we show how the standard descriptive statistical analysis of the data is unable to reveal a fine structure in a simulated sample of AR(2) stochastic process. We emphasize once again that the violation of Bell inequalities gives no information on the completeness or the non locality of QT. The appropriate way to test the completeness of quantum theory is to search for fine structures in time series of experimental data by means of the purity tests or by studying the autocorrelation and partial autocorrelation functions.