Consider the linear process yt = _yt􀀀1+"t where j_j 1 and "t is white noise. (a) Find a minimal state space representation of the process yt. (b) Verify that the system is stable. (c) Find the Hankel...

Consider the linear process yt = _yt􀀀1+"t where j_j 1 and "t is white noise.

(a) Find a minimal state space representation of the process yt.

(b) Verify that the system is stable.

(c) Find the Hankel matrix representing this process.

(d) What is the rank of this Hankel matrix?

Provide another state space representation based on the in_nite autoregressive

expansion of an ARFIMA process. Discuss the advantages or

disadvantages of this AR(1) with respect to the MA(1) representation.