This paper presents the concept of complexity index for generic random processes. This is based on the notion of small-ball probability and the possibility that this probability can be decomposed as a factorization of two functions. One of these two factors carries information regarding the complexity of the process, which coincides with the number of random sources characterizing the process or, equivalently, its degrees of freedom. This factor has been studied in literature and this paper shows some statistical results on how it can be exploited to make inference on the degrees of freedom of the random process.