4.3 In d = 1 dimension, consider the SAR model

∑

S s=−S dsXt−s = ????t, where d0 > 0, ds = d−s and {????t} is a white noise process. Assume that

∑dsei????s ≠ 0 for all ???? ∈ [−????, ????).

Show that it is possible to find a unilateral representation

∑2S s=0 asXt−s = ????′

t, in terms of another white noise process {????′

t

} for which the coefficients {as}

satisfy the stability conditions

∑2S s=0 aszs ≠ 0, for all |z| ≤ 1, where z is a complex number.