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The value of D can also be calculated directly from the past data values using
the sum squared prediction errors (SSE) for different values of D The value of D
which minimizes the SSE is taken for forecasting. For instance, given the value of
search step
' , the following algorithm can be used to select the best value
for starting with any initial value of D within 0 < D <1:
0.1
Algorithm 2.1. Algorithm for selection of best smoothing constant
Given a time series X = { X 1 , X 2 , X 3 ,…., X n },
for
t ={1, 2, 3, …, n }.
Set :
ˆ (1,1)
X X
eXX
1
ˆ (1,1)
2
2
Then :
ˆ
ˆ
X
(2,1)
X
X
(1,1)
3
ˆ (2,1)
eXX
3
3
...
...
...
...
...
ˆ (
eXXn
, )
n
n
Calculate :
n
2
SSE
¦
e
i
i
2
Repeat :
the same procedure for other values
of 0 < D<1 , say in steps of 0.1
Select :
the value for which SSE computed
is the minimum
End :
Because the surface of SSE near its minimum is quite flat, the choice of D is not
very critical and can be found very easily.
The considerable disadvantage of so-called single exponential smoothing
described above is that it does not work efficiently when a remarkable trend
component is present in the time series pattern. This can be improved by upgrading
the single exponential smoothing algorithm to the double exponential smoothing
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