# Exponential smoothing

Exponential smoothing method for finding the trend and seasonality of the data and doing forecast. simple exponential smoothing is for the data which doesn’t have seasonality. for data which has seasonality exponential smoothing has three formula as we could see in the figure below:

at is level, bt is the trend and Ft is seasonality. alpha, beta and gamma are the damping ratio in appropriate with level, trend and seasonality respectively.

this is Holt – winter method to do exponential smoothing for the data which include seasonality.

finding the values of alpha, beta and gamma will be done by considering an objective.

for this reason, we can have our own objective for estimating these ratios, otherwise, we can estimate them by minimizing the followings:

MSE: Mean squared error.

MAE: Mean absolute error.

MAPE: MEAN absolute percentage error.

if we want to minimize one of these objectives using excel. we could use solver.

the following formula is used to find the forecast after m steps.

at is level in period t, bt is trend in period t.

Ft+m-s: is the seasonality in period t + m – s.

for example if we want to calculate the forecast at 1 next step, we will have:

Forecast(t+1) = (at + bt) * Ft+1-s

s in the above formula is the number of points that each season took. for example if our data has repeated fluctuations after 3 points. then s = 3.

if our data is based on monthly seasonality : s =12.

The image below is an example of holt-winter method which is done for calculating the exponential smoothing and doing forecast using excel.