  In this paper we study the self-similar processes with stationary increments
in a discrete-time setting. Different from the continuous-time case, it is
shown that the scaling function of such a process may not take the form of a
power function $b(a)=a^H$. More precisely, its scaling function can belong to
one of three types, among which one type is degenerate, one type has a
continuous-time counterpart, while the other type is new and unique for the
discrete-time setting. We then focus on this last type of processes, construct
two classes of examples, and prove a special spectral representation result for
the processes of this type. We also derive basic properties of discrete-time
self-similar processes with stationary increments of different types.
