= Brown's double exponential smoothing
{c}
{title2=$a_t=2s_t^{(1)}-s_t^{(2)},\quad b_t=\frac{\alpha}{1-\alpha}(s_t^{(1)}-s_t^{(2)})$}
For $0<\alpha<1$, set $s_t^{(1)}=\alpha X_t+(1-\alpha)s_{t-1}^{(1)}$ and $s_t^{(2)}=\alpha s_t^{(1)}+(1-\alpha)s_{t-1}^{(2)}$. Use the displayed corrected level and slope, then forecast $a_t+hb_t$. For an exact linear trend after initialization transients, the first and second smooths have lags $(1-\alpha)/\alpha$ and twice that lag; their difference recovers the slope and the corrected level removes the lag. This is distinct from <Holt's linear trend method>.
Back to article page
