Brown's double exponential smoothing ($a_t=2s_t^{(1)}-s_t^{(2)},b_t=\frac{\alpha }{1-\alpha }(s_t^{(1)}-s_t^{(2)})$)

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 $a_t+h{b}_t$. 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.