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In-Depth Information
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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