# Exponential smoothing

Simple exponential smoothing is forecasting method using historical demand discounted with its weight. The weights exponentially decreases as data is further in the past. The forecast mathematically is computed as follows:

where F(t+1) -forecast in room demand in period t+1, alpha – is exponential smoothing parameter and , xt- is the number of rooms sold in period t, Ft- the most recent period’s forecast (the output of smoothing in last period) (Phumchusri and Mongkolkul, 2012). Simple exponential smoothing can be expanded and used as recursive formula:

where F(t+1)forecast for period is combination of all previous observations with the weights exponentially decreasing at the rate of (1-alpha). Smaller values of leads to bigger stability of the forecast, while bigger leads to better responsive to recent changes but it is also more sensitive to noises. Talluri and Van Ryzin (2004) suggest that the most typical alpha is between 0.05 and 0.3 in RM. The expanded simple exponential smoothing are double exponential smoothing sometimes referred as Holt’s model and two additional methods which include both trend and seasonality. Those are Additive Model and Multiplicative Model usually called Holt-Winter methods.

The application of this method on our data set is available here: Exponential Smoothing

Example

This method is extremely efficient with stable demand as it corrects previous forecast with information from market. In our application we achieved the smallest for MAPE of 6%. However, as following example will show, it is basically completely inefficient when the fluctuations of demand are significant. In this example (model 15 ->  alpha = 0,05) MAPE accounted to 53%

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