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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 10 Jan 2014 17:15:28 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jan/10/t1389392163o46d0nhmir44lni.htm/, Retrieved Tue, 28 May 2024 07:01:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232881, Retrieved Tue, 28 May 2024 07:01:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-01-10 22:15:28] [3c7daf9c150a57900c7784703a011e78] [Current]
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Dataseries X:
102,78
102,78
102,78
102,78
102,78
102,78
102,78
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
104,47
104,47
104,47
104,47
104,47
104,47
104,47
104,47
105,5
105,5
105,5
105,5
106,61
106,61
106,61
106,61
106,61
106,61
106,61
106,61
112,06
112,06
112,06
112,06
111,18
111,18
111,18
111,18
111,18
111,18
111,18
111,18
117,21
117,21
117,21
117,21
107,98
107,98
107,98
107,98
107,98




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232881&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232881&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232881&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232881&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232881&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232881&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3102.78102.780
4102.78102.780
5102.78102.780
6102.78102.780
7102.78102.780
8101.67102.78-1.11
9101.67101.670
10101.67101.670
11101.67101.670
12101.67101.670
13101.67101.670
14101.67101.670
15101.67101.670
16101.67101.670
17101.67101.670
18101.67101.670
19101.67101.670
20105.79101.674.12
21105.79105.790
22105.79105.790
23105.79105.790
24105.79105.790
25105.79105.790
26105.79105.790
27105.79105.790
28105.79105.790
29105.79105.790
30105.79105.790
31105.79105.790
32104.47105.79-1.32000000000001
33104.47104.470
34104.47104.470
35104.47104.470
36104.47104.470
37104.47104.470
38104.47104.470
39104.47104.470
40105.5104.471.03
41105.5105.50
42105.5105.50
43105.5105.50
44106.61105.51.11
45106.61106.610
46106.61106.610
47106.61106.610
48106.61106.610
49106.61106.610
50106.61106.610
51106.61106.610
52112.06106.615.45
53112.06112.060
54112.06112.060
55112.06112.060
56111.18112.06-0.879999999999995
57111.18111.180
58111.18111.180
59111.18111.180
60111.18111.180
61111.18111.180
62111.18111.180
63111.18111.180
64117.21111.186.02999999999999
65117.21117.210
66117.21117.210
67117.21117.210
68107.98117.21-9.22999999999999
69107.98107.980
70107.98107.980
71107.98107.980
72107.98107.980

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 102.78 & 102.78 & 0 \tabularnewline
4 & 102.78 & 102.78 & 0 \tabularnewline
5 & 102.78 & 102.78 & 0 \tabularnewline
6 & 102.78 & 102.78 & 0 \tabularnewline
7 & 102.78 & 102.78 & 0 \tabularnewline
8 & 101.67 & 102.78 & -1.11 \tabularnewline
9 & 101.67 & 101.67 & 0 \tabularnewline
10 & 101.67 & 101.67 & 0 \tabularnewline
11 & 101.67 & 101.67 & 0 \tabularnewline
12 & 101.67 & 101.67 & 0 \tabularnewline
13 & 101.67 & 101.67 & 0 \tabularnewline
14 & 101.67 & 101.67 & 0 \tabularnewline
15 & 101.67 & 101.67 & 0 \tabularnewline
16 & 101.67 & 101.67 & 0 \tabularnewline
17 & 101.67 & 101.67 & 0 \tabularnewline
18 & 101.67 & 101.67 & 0 \tabularnewline
19 & 101.67 & 101.67 & 0 \tabularnewline
20 & 105.79 & 101.67 & 4.12 \tabularnewline
21 & 105.79 & 105.79 & 0 \tabularnewline
22 & 105.79 & 105.79 & 0 \tabularnewline
23 & 105.79 & 105.79 & 0 \tabularnewline
24 & 105.79 & 105.79 & 0 \tabularnewline
25 & 105.79 & 105.79 & 0 \tabularnewline
26 & 105.79 & 105.79 & 0 \tabularnewline
27 & 105.79 & 105.79 & 0 \tabularnewline
28 & 105.79 & 105.79 & 0 \tabularnewline
29 & 105.79 & 105.79 & 0 \tabularnewline
30 & 105.79 & 105.79 & 0 \tabularnewline
31 & 105.79 & 105.79 & 0 \tabularnewline
32 & 104.47 & 105.79 & -1.32000000000001 \tabularnewline
33 & 104.47 & 104.47 & 0 \tabularnewline
34 & 104.47 & 104.47 & 0 \tabularnewline
35 & 104.47 & 104.47 & 0 \tabularnewline
36 & 104.47 & 104.47 & 0 \tabularnewline
37 & 104.47 & 104.47 & 0 \tabularnewline
38 & 104.47 & 104.47 & 0 \tabularnewline
39 & 104.47 & 104.47 & 0 \tabularnewline
40 & 105.5 & 104.47 & 1.03 \tabularnewline
41 & 105.5 & 105.5 & 0 \tabularnewline
42 & 105.5 & 105.5 & 0 \tabularnewline
43 & 105.5 & 105.5 & 0 \tabularnewline
44 & 106.61 & 105.5 & 1.11 \tabularnewline
45 & 106.61 & 106.61 & 0 \tabularnewline
46 & 106.61 & 106.61 & 0 \tabularnewline
47 & 106.61 & 106.61 & 0 \tabularnewline
48 & 106.61 & 106.61 & 0 \tabularnewline
49 & 106.61 & 106.61 & 0 \tabularnewline
50 & 106.61 & 106.61 & 0 \tabularnewline
51 & 106.61 & 106.61 & 0 \tabularnewline
52 & 112.06 & 106.61 & 5.45 \tabularnewline
53 & 112.06 & 112.06 & 0 \tabularnewline
54 & 112.06 & 112.06 & 0 \tabularnewline
55 & 112.06 & 112.06 & 0 \tabularnewline
56 & 111.18 & 112.06 & -0.879999999999995 \tabularnewline
57 & 111.18 & 111.18 & 0 \tabularnewline
58 & 111.18 & 111.18 & 0 \tabularnewline
59 & 111.18 & 111.18 & 0 \tabularnewline
60 & 111.18 & 111.18 & 0 \tabularnewline
61 & 111.18 & 111.18 & 0 \tabularnewline
62 & 111.18 & 111.18 & 0 \tabularnewline
63 & 111.18 & 111.18 & 0 \tabularnewline
64 & 117.21 & 111.18 & 6.02999999999999 \tabularnewline
65 & 117.21 & 117.21 & 0 \tabularnewline
66 & 117.21 & 117.21 & 0 \tabularnewline
67 & 117.21 & 117.21 & 0 \tabularnewline
68 & 107.98 & 117.21 & -9.22999999999999 \tabularnewline
69 & 107.98 & 107.98 & 0 \tabularnewline
70 & 107.98 & 107.98 & 0 \tabularnewline
71 & 107.98 & 107.98 & 0 \tabularnewline
72 & 107.98 & 107.98 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232881&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]102.78[/C][C]102.78[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]102.78[/C][C]102.78[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]102.78[/C][C]102.78[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]102.78[/C][C]102.78[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]102.78[/C][C]102.78[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]101.67[/C][C]102.78[/C][C]-1.11[/C][/ROW]
[ROW][C]9[/C][C]101.67[/C][C]101.67[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]101.67[/C][C]101.67[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]101.67[/C][C]101.67[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]101.67[/C][C]101.67[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]101.67[/C][C]101.67[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]101.67[/C][C]101.67[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]101.67[/C][C]101.67[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]101.67[/C][C]101.67[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]101.67[/C][C]101.67[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]101.67[/C][C]101.67[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]101.67[/C][C]101.67[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]105.79[/C][C]101.67[/C][C]4.12[/C][/ROW]
[ROW][C]21[/C][C]105.79[/C][C]105.79[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]105.79[/C][C]105.79[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]105.79[/C][C]105.79[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]105.79[/C][C]105.79[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]105.79[/C][C]105.79[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]105.79[/C][C]105.79[/C][C]0[/C][/ROW]
[ROW][C]27[/C][C]105.79[/C][C]105.79[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]105.79[/C][C]105.79[/C][C]0[/C][/ROW]
[ROW][C]29[/C][C]105.79[/C][C]105.79[/C][C]0[/C][/ROW]
[ROW][C]30[/C][C]105.79[/C][C]105.79[/C][C]0[/C][/ROW]
[ROW][C]31[/C][C]105.79[/C][C]105.79[/C][C]0[/C][/ROW]
[ROW][C]32[/C][C]104.47[/C][C]105.79[/C][C]-1.32000000000001[/C][/ROW]
[ROW][C]33[/C][C]104.47[/C][C]104.47[/C][C]0[/C][/ROW]
[ROW][C]34[/C][C]104.47[/C][C]104.47[/C][C]0[/C][/ROW]
[ROW][C]35[/C][C]104.47[/C][C]104.47[/C][C]0[/C][/ROW]
[ROW][C]36[/C][C]104.47[/C][C]104.47[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]104.47[/C][C]104.47[/C][C]0[/C][/ROW]
[ROW][C]38[/C][C]104.47[/C][C]104.47[/C][C]0[/C][/ROW]
[ROW][C]39[/C][C]104.47[/C][C]104.47[/C][C]0[/C][/ROW]
[ROW][C]40[/C][C]105.5[/C][C]104.47[/C][C]1.03[/C][/ROW]
[ROW][C]41[/C][C]105.5[/C][C]105.5[/C][C]0[/C][/ROW]
[ROW][C]42[/C][C]105.5[/C][C]105.5[/C][C]0[/C][/ROW]
[ROW][C]43[/C][C]105.5[/C][C]105.5[/C][C]0[/C][/ROW]
[ROW][C]44[/C][C]106.61[/C][C]105.5[/C][C]1.11[/C][/ROW]
[ROW][C]45[/C][C]106.61[/C][C]106.61[/C][C]0[/C][/ROW]
[ROW][C]46[/C][C]106.61[/C][C]106.61[/C][C]0[/C][/ROW]
[ROW][C]47[/C][C]106.61[/C][C]106.61[/C][C]0[/C][/ROW]
[ROW][C]48[/C][C]106.61[/C][C]106.61[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]106.61[/C][C]106.61[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]106.61[/C][C]106.61[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]106.61[/C][C]106.61[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]112.06[/C][C]106.61[/C][C]5.45[/C][/ROW]
[ROW][C]53[/C][C]112.06[/C][C]112.06[/C][C]0[/C][/ROW]
[ROW][C]54[/C][C]112.06[/C][C]112.06[/C][C]0[/C][/ROW]
[ROW][C]55[/C][C]112.06[/C][C]112.06[/C][C]0[/C][/ROW]
[ROW][C]56[/C][C]111.18[/C][C]112.06[/C][C]-0.879999999999995[/C][/ROW]
[ROW][C]57[/C][C]111.18[/C][C]111.18[/C][C]0[/C][/ROW]
[ROW][C]58[/C][C]111.18[/C][C]111.18[/C][C]0[/C][/ROW]
[ROW][C]59[/C][C]111.18[/C][C]111.18[/C][C]0[/C][/ROW]
[ROW][C]60[/C][C]111.18[/C][C]111.18[/C][C]0[/C][/ROW]
[ROW][C]61[/C][C]111.18[/C][C]111.18[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]111.18[/C][C]111.18[/C][C]0[/C][/ROW]
[ROW][C]63[/C][C]111.18[/C][C]111.18[/C][C]0[/C][/ROW]
[ROW][C]64[/C][C]117.21[/C][C]111.18[/C][C]6.02999999999999[/C][/ROW]
[ROW][C]65[/C][C]117.21[/C][C]117.21[/C][C]0[/C][/ROW]
[ROW][C]66[/C][C]117.21[/C][C]117.21[/C][C]0[/C][/ROW]
[ROW][C]67[/C][C]117.21[/C][C]117.21[/C][C]0[/C][/ROW]
[ROW][C]68[/C][C]107.98[/C][C]117.21[/C][C]-9.22999999999999[/C][/ROW]
[ROW][C]69[/C][C]107.98[/C][C]107.98[/C][C]0[/C][/ROW]
[ROW][C]70[/C][C]107.98[/C][C]107.98[/C][C]0[/C][/ROW]
[ROW][C]71[/C][C]107.98[/C][C]107.98[/C][C]0[/C][/ROW]
[ROW][C]72[/C][C]107.98[/C][C]107.98[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232881&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232881&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3102.78102.780
4102.78102.780
5102.78102.780
6102.78102.780
7102.78102.780
8101.67102.78-1.11
9101.67101.670
10101.67101.670
11101.67101.670
12101.67101.670
13101.67101.670
14101.67101.670
15101.67101.670
16101.67101.670
17101.67101.670
18101.67101.670
19101.67101.670
20105.79101.674.12
21105.79105.790
22105.79105.790
23105.79105.790
24105.79105.790
25105.79105.790
26105.79105.790
27105.79105.790
28105.79105.790
29105.79105.790
30105.79105.790
31105.79105.790
32104.47105.79-1.32000000000001
33104.47104.470
34104.47104.470
35104.47104.470
36104.47104.470
37104.47104.470
38104.47104.470
39104.47104.470
40105.5104.471.03
41105.5105.50
42105.5105.50
43105.5105.50
44106.61105.51.11
45106.61106.610
46106.61106.610
47106.61106.610
48106.61106.610
49106.61106.610
50106.61106.610
51106.61106.610
52112.06106.615.45
53112.06112.060
54112.06112.060
55112.06112.060
56111.18112.06-0.879999999999995
57111.18111.180
58111.18111.180
59111.18111.180
60111.18111.180
61111.18111.180
62111.18111.180
63111.18111.180
64117.21111.186.02999999999999
65117.21117.210
66117.21117.210
67117.21117.210
68107.98117.21-9.22999999999999
69107.98107.980
70107.98107.980
71107.98107.980
72107.98107.980







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73107.98104.868597138689111.091402861311
74107.98103.579811875527112.380188124473
75107.98102.590892161394113.369107838606
76107.98101.757194277378114.202805722622
77107.98101.022691696721114.937308303279
78107.98100.358650605552115.601349394448
79107.9899.7480018004362116.211998199564
80107.9899.1796237510549116.780376248945
81107.9898.6457914160669117.314208583933
82107.9898.1408802398921117.819119760108
83107.9897.660644137393118.299355862607
84107.9897.2017843227882118.758215677212

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 107.98 & 104.868597138689 & 111.091402861311 \tabularnewline
74 & 107.98 & 103.579811875527 & 112.380188124473 \tabularnewline
75 & 107.98 & 102.590892161394 & 113.369107838606 \tabularnewline
76 & 107.98 & 101.757194277378 & 114.202805722622 \tabularnewline
77 & 107.98 & 101.022691696721 & 114.937308303279 \tabularnewline
78 & 107.98 & 100.358650605552 & 115.601349394448 \tabularnewline
79 & 107.98 & 99.7480018004362 & 116.211998199564 \tabularnewline
80 & 107.98 & 99.1796237510549 & 116.780376248945 \tabularnewline
81 & 107.98 & 98.6457914160669 & 117.314208583933 \tabularnewline
82 & 107.98 & 98.1408802398921 & 117.819119760108 \tabularnewline
83 & 107.98 & 97.660644137393 & 118.299355862607 \tabularnewline
84 & 107.98 & 97.2017843227882 & 118.758215677212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232881&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]107.98[/C][C]104.868597138689[/C][C]111.091402861311[/C][/ROW]
[ROW][C]74[/C][C]107.98[/C][C]103.579811875527[/C][C]112.380188124473[/C][/ROW]
[ROW][C]75[/C][C]107.98[/C][C]102.590892161394[/C][C]113.369107838606[/C][/ROW]
[ROW][C]76[/C][C]107.98[/C][C]101.757194277378[/C][C]114.202805722622[/C][/ROW]
[ROW][C]77[/C][C]107.98[/C][C]101.022691696721[/C][C]114.937308303279[/C][/ROW]
[ROW][C]78[/C][C]107.98[/C][C]100.358650605552[/C][C]115.601349394448[/C][/ROW]
[ROW][C]79[/C][C]107.98[/C][C]99.7480018004362[/C][C]116.211998199564[/C][/ROW]
[ROW][C]80[/C][C]107.98[/C][C]99.1796237510549[/C][C]116.780376248945[/C][/ROW]
[ROW][C]81[/C][C]107.98[/C][C]98.6457914160669[/C][C]117.314208583933[/C][/ROW]
[ROW][C]82[/C][C]107.98[/C][C]98.1408802398921[/C][C]117.819119760108[/C][/ROW]
[ROW][C]83[/C][C]107.98[/C][C]97.660644137393[/C][C]118.299355862607[/C][/ROW]
[ROW][C]84[/C][C]107.98[/C][C]97.2017843227882[/C][C]118.758215677212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232881&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232881&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73107.98104.868597138689111.091402861311
74107.98103.579811875527112.380188124473
75107.98102.590892161394113.369107838606
76107.98101.757194277378114.202805722622
77107.98101.022691696721114.937308303279
78107.98100.358650605552115.601349394448
79107.9899.7480018004362116.211998199564
80107.9899.1796237510549116.780376248945
81107.9898.6457914160669117.314208583933
82107.9898.1408802398921117.819119760108
83107.9897.660644137393118.299355862607
84107.9897.2017843227882118.758215677212



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')