Question

Suppose that simple exponential smoothing is used to forecast demand from a constant process $Y_t = \mu + \epsilon_t$, where $Var(\epsilon_t) = \sigma^2$. Show that the variance of the forecast $F_{t, t+\tau}$ is $(\alpha/(2 - \alpha))\sigma^2$ for large values of $t$. Also find the variance of the forecast error $Y_{t+\tau} - F_{t, t+\tau}$. Plot these variance terms as a function of $\alpha$. Observe that we would like to choose a small $\alpha$ value in order to have a stable forecasting model.

          Suppose that simple exponential smoothing is used to forecast demand from a constant process $Y_t = \mu + \epsilon_t$, where $Var(\epsilon_t) = \sigma^2$. Show that the variance of the forecast $F_{t, t+\tau}$ is $(\alpha/(2 - \alpha))\sigma^2$ for large values of $t$. Also find the variance of the forecast error $Y_{t+\tau} - F_{t, t+\tau}$. Plot these variance terms as a function of $\alpha$. Observe that we would like to choose a small $\alpha$ value in order to have a stable forecasting model.

Suppose that simple exponential smoothing is used to forecast demand from a constant process Yt = μ +, where Var() = σ^2. Show that the variance of the forecast Ft, t+τ is (α/(2 - α))σ^2 for large values of t. Also find the variance of the forecast error Yt+τ - Ft, t+τ. Plot these variance terms as a function of α. Observe that we would like to choose a small α value in order to have a stable forecasting model.

Added by Jasmine J.

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