Process or Product Monitoring and Control
6.4. Introduction to Time Series Analysis
6.4.3. What is Exponential Smoothing?
|Double exponential smoothing uses two constants and is better at handling trends||
As was previously
observed, Single Smoothing does not excel in following the data when
there is a trend. This situation can be improved by the introduction
of a second equation with a second constant,
, which must
be chosen in conjunction with
Here are the two equations associated with Double Exponential Smoothing:
|Several methods to choose the initial values||
As in the case for single smoothing, there are a variety of schemes
to set initial values for St and
bt in double smoothing.
S1 is in general set to y1. Here are three suggestions for b1:
b1 = [(y2 - y1) + (y3 - y2) + (y4 - y3)]/3
b1 = (yn - y1)/(n - 1)
|Meaning of the smoothing equations||
The first smoothing equation adjusts St directly
for the trend of the previous period, bt-1,
by adding it to the last smoothed value, St-1.
This helps to eliminate the lag and brings St to
the appropriate base of the current value.
The second smoothing equation then updates the trend, which is expressed as the difference between the last two values. The equation is similar to the basic form of single smoothing, but here applied to the updating of the trend.
|Non-linear optimization techniques can be used||The values for and can be obtained via non-linear optimization techniques, such as the Marquardt Algorithm.|