In my statistics textbook I find the following line:
We now consider a general sequence of random variables that we denote by $\{Y_{n}\}_{n \ge 1}$ or simply $Y_{n}$. Note that in many applications $Y_{n}$ will be a statistic and thus a function of another sequence $X_{1} , X_{2} , .. ,X_{n}$ of underlying random variables. Why is a statistic that is a function of another sequence a sequence in itself? I can't find anything on the properties of functions of random sequences.