Exponential smoothing is based on three terms,

• Currently observed value at time Yi
• The previously computed exponentially smoothed value Ei and
• The weight or smoothing coefficient assigned.

for the first observation in the series.

E1 = Y1
Ei = WYi + (1 – W) Ei-1 i = 2, 3, 4 …
Ei = Exponentially smooth series at time i
W = Weight or smoothing coefficient (where 0 < W < 1)
Ei-1 = Exponentially smooth series at time i-1

This method has below two advantages over Moving Average method.

• We can use it to get the short-term (one period into the future) forecast when it is questionable whether long-term trend is present in the series or not.
• Throughout the series each smoothing calculations is dependent on all previously observed values.(1 – W),Ei-1). Moving average does not consider all observed values.

Forecasting using Exponential Smoothing can be done as follow:

Ŷi+1 = Ei
Ŷi+2 = E2000 = WYi-1 + (1 – W) Ŷi-1

For example, we have revenue till 1999 and we want to make forecast for the year 2000 and 2001.

Ŷ2000 = E1999
Ŷ2001 = WY2000 + (1 – W) Ŷ2000

The choice of weight (W) is subjective. If you want to smooth the series by eliminating cyclical and irregular patterns, choose weight (W) close to 0. If you want to make the forecast, choose the weight (W) close to 1.

Let’s implement the Exponential Smoothing method using Cabot Corporation revenues using Python.