Consider the AR(3) model

where {et} and {at} are independent and the initial values of xj with j ≤ 0 are independent of et and at for t > 0.

(a) Convert the model into a state-space form.

(b) If E(et) =

c, which is not zero, what is the corresponding statespace form for the system?

Transcribed Image Text:

x = 1x11 + 2x1-2+3x1-3+ at, a ~N(0,0) and suppose that the observed data are y = x + e, e~ N(0, 0)