Forecasting - Holt’s Linear Trend Forecasting

Holt's Forecasting method

Holt (1957) extended simple exponential smoothing to allow the forecasting of data with a trend. This method involves a forecast equation and two smoothing equations (one for the level and one for the trend):

Forecast equation: ŷ = l + h * b
Level equation: l = alpha * y + (1 - alpha) * (l + b)
Trend equation: b = beta * (l - l) + (1 - beta) * b

l (or l) denotes an estimate of the level of the series at time t,
b (or b) denotes an estimate of the trend (slope) of the series at time t,
alpha is the smoothing parameter for the level, 0 ≤ alpha ≤ 1, and
beta is the smoothing parameter for the trend, 0 ≤ beta ≤ 1.

As with simple exponential smoothing, the level equation here shows that l is a weighted average of observation y and the one-step-ahead training forecast for time t, here given by l+b. The trend equation shows that b is a weighted average of the estimated trend at time t based on l-l and b, the previous estimate of the trend.

The forecast function is not flat but trending. The h-step-ahead forecast is equal to the last estimated level plus h times the last estimated trend value. Hence the forecasts are a linear function of h.
הערות שחרור: Minor fix in documentation.
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UPD: use f instead of forecast The line forecast = l + b may be removed.
+1 השב
in the code need to change to extend.right in order for it to apear
capissimo RafaelZioni
@RafaelZioni, thx for you suggestion, but I left it as such deliberately as a short-term forecast.
Anyway, you can update in the Inputes section:
ex = input(true, "Extend Right")
And then in the Main section:
fl :=, close, time + 60 * 60 * 24 * 6, f,
xloc.bar_time, extend=ex ? extend.right : extend.none, style=line.style_solid,, width=2)