4.3 In d = 1 dimension, consider the SAR model S s=S dsXts = ????t, where...
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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.
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