Let xt = a + b t for t = 1; 2 with a and b constants. Show that the sample autocorrelations of this sequence ^_(k) satisfy ^_(k) ! 1 as n ! 1 for each _xed k. Let St, t = 0; 1; 2; a random walk...

Let xt = a + b t for t = 1; 2 with a and b constants. Show that the

sample autocorrelations of this sequence ^_(k) satisfy ^_(k) ! 1 as n ! 1 for

each _xed k.

Let St, t = 0; 1; 2; a random walk with constant jump _ de_ned as

S0 = 0 and St = _+St􀀀1 +xt, t = 1; 2; where x1; x2; are i.i.d. random

variables with zero-mean and variance _2.

(a) Is the process fStg stationary?

(b) Is the sequence frStg stationary?