how to generate error terms for idploy or ARMAX models

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Dear Experts,
I would like to convert ARMAX model of idploy form to classical time series equation as given below.
y(t)=[a1 a2 .... an]*[y(t−1)+y(t-2)+...+y(t−n)] + [b1 b2 .... bn]*[u(t−1)+u(t-2)+...+u(t−n)] + [c1 c2 .... cn]*[e(t−1)+e(t-2)+...+e(t−n)] + e(t)
As idploy provides a1...an, b1....bn and c1... cn, please let me know how to generate e(t−1), e(t-2),...,e(t−n)],e(t) terms
Thanking you in advance,
Kind Regards, Kushan

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