If the value of the time series at time \( t \) is the value of the series at time \( t -1\) plus a completely random movement determined by a white noise process \(w_t\); e.i. if   $$x_t=x_{t-1}+w_t$$ or equivalently $$x_t=\sum\limits_{j = 1}^t {{w_j}},   t=1,2,....$$then the generating process is called random walk.