Computing Forecasts and Forecast Standard Errors Using a Regression Package. This is based on Salkever (1976). From equations (7.23) and (7.24), show that

(a) δ



OLS = (β



OLS, γ



OLS) where β



OLS = (XX)−1Xy, and γ



OLS = yo −XoβOLS. Hint: Set up the OLS normal equations and solve two equations in two unknowns. Alternatively, one can use the FWL Theorem to residual out the additional To dummy variables.

(b) e∗

OLS = (e

OLS, 0) and s∗2 = s2.

(c) s∗2(X∗X∗)−1 is given by the expression in (7.25). Hint: Use partitioned inverse.

(d) Replace yo by 0 and ITo by −ITo in (7.23) and show that γ = yo = XoβOLS whereas all the results in parts (a),

(b) and

(c) remain the same.