5. Stochastic Processes in Discrete Time

A stochastic process or random process consists of chronologically ordered random variables $ \{ X_t;\, \, t \ge 0 \}.$ For simplicity we assume that the process starts at time $ t=0$ in $ X_0=0.$ In this chapter, we consider exclusively processes in discrete time, i.e. processes which are observed at equally spaced points of time $ t =
0, 1,2, \ldots \, .$ Typical examples are daily, monthly or yearly observed economic data as stock prices, rates of unemployment or sales amount.