Demand forecasting : Double exponential smoothing
The drawback of simple exponential smoothing is that it can only see a level (the average value around which the demand varies over time) and is unable to identify and project a trend. Double exponential smoothing brings together "level" and "trend" to generate forecasts. For a given period, "t" with demand, d, the "Level" and "Trend" can be expressed as: $$ a_{t}, b_{t}$$ The "Level", which is a function of demand and forecast, can be calculated as: $$ a_{t}=\alpha d_{t}+(1-\alpha)(a_{t-1}+b_{t-1})$$ and the "Trend", which is a function of the difference in levels as well as the previous trend, can be calculated as: $$ b_{t}=\beta (a_{t}-a_{t-1}) + (1-\beta) b_{t-1}$$ Forecast = Level + Trend $$f_{t+1}=a_{t}+b_{t}$$ for a generalised forecast, the expression can be written as: $$f_{t+\lambda}=a_{t}+\lambda b_{t}$$ Now moving on to the implementation of the Double Exponential smoothing model. The simplest way to ini...