= Holt's linear trend method
{c}
{title2=$\widehat X_{t+h\mid t}=\ell_t+hb_t$}
Update the level and slope by $\ell_t=\alpha X_t+(1-\alpha)(\ell_{t-1}+b_{t-1})$ and $b_t=\beta(\ell_t-\ell_{t-1})+(1-\beta)b_{t-1}$, with gains in $(0,1)$. The first update compares the new observation with the previous level extrapolated one step; the second smooths the latest level increment. The displayed forecast extrapolates that local slope. This is a <double exponential smoothing> method for a nonseasonal trending <time series>.
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