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I have the following table

t    Demand    Level    Trend    Forecast
.
.
.
8    121,63    119,04    12.52    118,4
9                                 131.56

I want to calculate the Demand, Level and Trend for t=9 with the following formulas

$$ L_{t} = \alpha D_{t} + (1-\alpha)(L_{t-1}-T_{t-1})$$ $$ T_{t} = \beta(L_{t}-L_{t-1})+(1-\beta)T_{t-1} $$ $$ F_{t+1} = L_{t} + T_{t} $$ $$ \alpha = 0.2, \beta = 0.4 $$

but I have no formula to calculate $D_{t}$

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The demand $D_t$ is the observed data. It doesn't have to be calculated. See https://www.otexts.org/fpp/7/2 for a discussion of this forecasting method.

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Well, if I correctly understand your model, Dt is simply Ft+1, that is forecast for next period when t=8.

Remember that many times in forecast models you simply use a window of some periods of the demand to forecast next period demand, putting yourself on the actual period and looking back at a bunch of hystorical data.

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Exactly. As @Vincenzo Maggio pointed out Ft+1 is nothing but the one step ahead foracast of Dt or the Demand.

What you are using is called Double Exponential Smoothing, or Holt's Smoothing

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