The existence of long-range dependencies in many natural systems was a very important discovery that introduced many interesting challenges and explanations about the systems behaviour. In the case of man-made systems such dependencies can also be visible, and one example is computer systems. Because the studies focused on long-range statistical dependencies in computer systems, particularly in the context of system performance counters, are not very common in the literature, this paper undertook an investigation of statistical long-range dependencies present in cache memory data represented as time series. Based on the time series collected during computer system processing by internal system tools, it will be seen that in the case of cache memory modelling, statistical models with long-term dependencies should be used. The following paper sections show how to collect data, analyse, and build an appropriate model.