Single Exponential Smooting (SES)
Single Exponential Smooting (SES) use a single parameter 'alpha' in its forecasts. The exponentially smoohed value is actually a weigthted moving average of all past actual values.
The equation is:
Ft = α * At-1 + (1 - α) * Ft-1
where
Ft = Exponentially smoothed forecast for period t
At-1 = Actual value in the prior period
Ft-1 = Exponentially smoothed forecast of the prior period
α = Smooting constant, called alpha, greater than or equal to 0 and less than or equal to 1.
The next forecast is: a fraction (weight 1) of the current value added to a fraction (weight 2) of the current forecast.
Another way to see to equation is:
Ft = Ft-1 + α * (At-1 - Ft-1)
We formulate that the next forecast is the current forecast added with the fraction of the difference of the current value minus the current forecast.
The basic exponential smoothing model is:
Ft = α * At-1 + (1 - α) * Ft-1
Following equations:
Ft-1 = α * At-2 + (1 - α) * Ft-2
Ft-2 = α * At-3 + (1 - α) * Ft-3
Ft-3 = α * At-4 + (1 - α) * Ft-4
Ft-4 = α * At-5 + (1 - α) * Ft-5
Substituting:
Ft = α * At-1 + (1 - α) * Ft-1
Ft = α * At-1 + (1 - α) * [α * At-2 + (1 - α) * Ft-2]
Ft = α * At-1 + (1 - α) * [α * At-2 + (1 - α) * (α * At-3 + (1 - α) * Ft-3)]
etc.
F(t) = α * At-1 + α * (1 - α)1 * At-2 + α * (1 - α)2 * At-3 + α * (1 - α)3 * At-4 + ... + α * (1 - α)n * Ft-n
Where:
Ft-n = Initial forecast in period t - 1
The forecast in period t is equal to a weigthted moving average of all past actual values and one initial forecast.
When α is close to 1, then the most recent values have more weight for the forecast.
When α is close to 0, then the forecast will be more smoothed.