Consider the following processes zt de_ned by (i) zt = _0 + _1_t, (ii) zt = _0 + _1t + _t, (iii) zt = _t0 e_t , _0 > 0 (iv) zt = _0 + _t + _1_t􀀀1, where _0 and _1 are constant and f_tg is a white...

Consider the following processes zt de_ned by

(i) zt = _0 + _1_t,

(ii) zt = _0 + _1t + _t,

(iii) zt = _t0 e_t , _0 > 0

(iv) zt = _0 + _t + _1_t􀀀1,

where _0 and _1 are constant and f_tg is a white noise process with zero-mean

and variance _2 de_ne a new process yt (as a function of zt) that is stationary.

Provide E(yt), Var(yt) and Cov(yt,yt+k) for k = 1; 2.