Let yt be an ARMA(1,2) time series where Var "t = _2 " and yt 􀀀 0:5yt􀀀1 = "t 􀀀 "t􀀀1 + 0:24"t􀀀2: (a) Verify if this model is causal, stationary and invertible. (b) Find the _rst _ve terms of the...

Let yt be an ARMA(1,2) time series where Var "t = _2 " and

yt 􀀀 0:5yt􀀀1 = "t 􀀀 "t􀀀1 + 0:24"t􀀀2:

(a) Verify if this model is causal, stationary and invertible.

(b) Find the _rst _ve terms of the Wold expansion of this process,

15.

(c) Find the ACF.

Show that an ARFIMA model satis_es the de_nition of a long-memory

process described in this chapter and discuss alternative de_nitions of strongly

dependent time series models.