Question

The forecast for the month of June is 150 units and $\alpha =0.2$ in an exponential smoothing model is constant at 140 units for June, July and August. Determine the mean forecast error ?

Answer 1

$F_{\text{jun}}=150\text{units},\alpha =0.2$

$D_{\text{jun}}=140\text{units},D_{\text{july}}=140\text{units}$

$D_{\text{aug}}=140\text{units}$

$F_{\text{july}}=F_{\text{jun}}+\alpha (D_{\text{jun}}-F_{\text{jun}})$

$=150+0.2(140-150)=148\text{units}$

$F_{\text{aug}}=F_{\text{july}}+\alpha (D_{\text{july}}-F_{\text{july}})$

$=148+0.2(140-148)$

$=146.4\text{units}$

$F_i$	$D_i$	$D_i-F_i$
150	140	-10
148	140	-8
146.4	140	-6.4
		$\Sigma \left(D_i{F}_i\right)=-24.4\text{units}$

$\text{Mean forecast error}=\frac{\Sigma D_i-F_i}{n}$

$=-\frac{24.4}{3}=-8.13\text{units}$