Derive three step-ahead forecasts for an ARMA

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Derive three step-ahead forecasts for an ARMA(1,1) model at the forecast origin h (for a general positive integer h), i.e, compute rh+3|h = rh(3) = E(rh+3|Ih), where rt = φ0 + φ1rt−1 + at −θ1at−1 with at is iid (0,σ2a).

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