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Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Dec 2016 22:29:44 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/19/t1482183010ph6rx584szi39gu.htm/, Retrieved Fri, 01 Nov 2024 03:38:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301528, Retrieved Fri, 01 Nov 2024 03:38:32 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-19 21:29:44] [2e11ca31a00cf8de75c33c1af2d59434] [Current]
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Dataseries X:
2298.3
2424.67
2584.65
2639.42
2452.02
2537.49
2726.36
2843.85
2615.11
2778.08
2918.75
3023.41
2733.07
2933.31
3089.19
3256.6
2968.74
3101.7
3277.21
3420.1
3097.55
3286.21
3491.96
3608.53
3259.04
3492.27
3665.64
3808.02
3397.47
3644.83
3812.8
3958.78
3602.73
3845.49
4022.27
4195.29
3867.28
4142.62
4217.79
4487.61
4089.69
4431.36
4629.82
4832.81




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301528&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301528&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301528&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.330867342573275
beta0.359136037376688
gamma0.524181187375416

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.330867342573275 \tabularnewline
beta & 0.359136037376688 \tabularnewline
gamma & 0.524181187375416 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301528&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]0.330867342573275[/C][/ROW]
[ROW][C]beta[/C][C]0.359136037376688[/C][/ROW]
[ROW][C]gamma[/C][C]0.524181187375416[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301528&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301528&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
alpha0.330867342573275
beta0.359136037376688
gamma0.524181187375416







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
52452.022391.0780416150160.9419583849926
62537.492496.058145089241.4318549108043
72726.362716.925582570699.43441742930736
82843.852792.6909397479251.1590602520773
92615.112653.93763442137-38.8276344213741
102778.082729.075295468349.0047045317037
112918.752962.36756643977-43.6175664397738
123023.413040.11611232451-16.7061123245089
132733.072824.18556561934-91.1155656193368
142933.312905.0581100965128.2518899034867
153089.193090.66209310472-1.47209310472044
163256.63183.9530360976572.6469639023503
172968.742954.5398959329614.200104067037
183101.73133.41891249195-31.7189124919514
193277.213303.32968123795-26.1196812379499
203420.13422.68022766252-2.58022766252179
213097.553124.08616211536-26.5361621153643
223286.213268.5392887609817.6707112390168
233491.963459.0913148426532.8686851573534
243608.533613.67593708215-5.14593708214807
253259.043288.29009961517-29.2500996151743
263492.273456.1324432558736.1375567441328
273665.643670.43383661941-4.79383661940665
283808.023803.102149858814.91785014118614
293397.473452.947063441-55.4770634410024
303644.833640.445518065154.38448193484783
313812.83829.6977469178-16.8977469177985
323958.783957.280455064941.49954493505902
333602.733560.3861162720642.3438837279368
343845.493814.0380689985631.4519310014402
354022.274019.214874649153.05512535085018
364195.294175.2652000509720.0247999490321
373867.283786.129439063781.1505609363007
384142.624077.2308279642765.3891720357319
394217.794314.22499406687-96.4349940668726
404487.614460.1143889297127.4956110702897
414089.694075.9128172644613.7771827355423
424431.364352.8794922600278.4805077399787
434629.824545.7731106792684.0468893207426
444832.814832.447424148270.362575851733709

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 2452.02 & 2391.07804161501 & 60.9419583849926 \tabularnewline
6 & 2537.49 & 2496.0581450892 & 41.4318549108043 \tabularnewline
7 & 2726.36 & 2716.92558257069 & 9.43441742930736 \tabularnewline
8 & 2843.85 & 2792.69093974792 & 51.1590602520773 \tabularnewline
9 & 2615.11 & 2653.93763442137 & -38.8276344213741 \tabularnewline
10 & 2778.08 & 2729.0752954683 & 49.0047045317037 \tabularnewline
11 & 2918.75 & 2962.36756643977 & -43.6175664397738 \tabularnewline
12 & 3023.41 & 3040.11611232451 & -16.7061123245089 \tabularnewline
13 & 2733.07 & 2824.18556561934 & -91.1155656193368 \tabularnewline
14 & 2933.31 & 2905.05811009651 & 28.2518899034867 \tabularnewline
15 & 3089.19 & 3090.66209310472 & -1.47209310472044 \tabularnewline
16 & 3256.6 & 3183.95303609765 & 72.6469639023503 \tabularnewline
17 & 2968.74 & 2954.53989593296 & 14.200104067037 \tabularnewline
18 & 3101.7 & 3133.41891249195 & -31.7189124919514 \tabularnewline
19 & 3277.21 & 3303.32968123795 & -26.1196812379499 \tabularnewline
20 & 3420.1 & 3422.68022766252 & -2.58022766252179 \tabularnewline
21 & 3097.55 & 3124.08616211536 & -26.5361621153643 \tabularnewline
22 & 3286.21 & 3268.53928876098 & 17.6707112390168 \tabularnewline
23 & 3491.96 & 3459.09131484265 & 32.8686851573534 \tabularnewline
24 & 3608.53 & 3613.67593708215 & -5.14593708214807 \tabularnewline
25 & 3259.04 & 3288.29009961517 & -29.2500996151743 \tabularnewline
26 & 3492.27 & 3456.13244325587 & 36.1375567441328 \tabularnewline
27 & 3665.64 & 3670.43383661941 & -4.79383661940665 \tabularnewline
28 & 3808.02 & 3803.10214985881 & 4.91785014118614 \tabularnewline
29 & 3397.47 & 3452.947063441 & -55.4770634410024 \tabularnewline
30 & 3644.83 & 3640.44551806515 & 4.38448193484783 \tabularnewline
31 & 3812.8 & 3829.6977469178 & -16.8977469177985 \tabularnewline
32 & 3958.78 & 3957.28045506494 & 1.49954493505902 \tabularnewline
33 & 3602.73 & 3560.38611627206 & 42.3438837279368 \tabularnewline
34 & 3845.49 & 3814.03806899856 & 31.4519310014402 \tabularnewline
35 & 4022.27 & 4019.21487464915 & 3.05512535085018 \tabularnewline
36 & 4195.29 & 4175.26520005097 & 20.0247999490321 \tabularnewline
37 & 3867.28 & 3786.1294390637 & 81.1505609363007 \tabularnewline
38 & 4142.62 & 4077.23082796427 & 65.3891720357319 \tabularnewline
39 & 4217.79 & 4314.22499406687 & -96.4349940668726 \tabularnewline
40 & 4487.61 & 4460.11438892971 & 27.4956110702897 \tabularnewline
41 & 4089.69 & 4075.91281726446 & 13.7771827355423 \tabularnewline
42 & 4431.36 & 4352.87949226002 & 78.4805077399787 \tabularnewline
43 & 4629.82 & 4545.77311067926 & 84.0468893207426 \tabularnewline
44 & 4832.81 & 4832.44742414827 & 0.362575851733709 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301528&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]5[/C][C]2452.02[/C][C]2391.07804161501[/C][C]60.9419583849926[/C][/ROW]
[ROW][C]6[/C][C]2537.49[/C][C]2496.0581450892[/C][C]41.4318549108043[/C][/ROW]
[ROW][C]7[/C][C]2726.36[/C][C]2716.92558257069[/C][C]9.43441742930736[/C][/ROW]
[ROW][C]8[/C][C]2843.85[/C][C]2792.69093974792[/C][C]51.1590602520773[/C][/ROW]
[ROW][C]9[/C][C]2615.11[/C][C]2653.93763442137[/C][C]-38.8276344213741[/C][/ROW]
[ROW][C]10[/C][C]2778.08[/C][C]2729.0752954683[/C][C]49.0047045317037[/C][/ROW]
[ROW][C]11[/C][C]2918.75[/C][C]2962.36756643977[/C][C]-43.6175664397738[/C][/ROW]
[ROW][C]12[/C][C]3023.41[/C][C]3040.11611232451[/C][C]-16.7061123245089[/C][/ROW]
[ROW][C]13[/C][C]2733.07[/C][C]2824.18556561934[/C][C]-91.1155656193368[/C][/ROW]
[ROW][C]14[/C][C]2933.31[/C][C]2905.05811009651[/C][C]28.2518899034867[/C][/ROW]
[ROW][C]15[/C][C]3089.19[/C][C]3090.66209310472[/C][C]-1.47209310472044[/C][/ROW]
[ROW][C]16[/C][C]3256.6[/C][C]3183.95303609765[/C][C]72.6469639023503[/C][/ROW]
[ROW][C]17[/C][C]2968.74[/C][C]2954.53989593296[/C][C]14.200104067037[/C][/ROW]
[ROW][C]18[/C][C]3101.7[/C][C]3133.41891249195[/C][C]-31.7189124919514[/C][/ROW]
[ROW][C]19[/C][C]3277.21[/C][C]3303.32968123795[/C][C]-26.1196812379499[/C][/ROW]
[ROW][C]20[/C][C]3420.1[/C][C]3422.68022766252[/C][C]-2.58022766252179[/C][/ROW]
[ROW][C]21[/C][C]3097.55[/C][C]3124.08616211536[/C][C]-26.5361621153643[/C][/ROW]
[ROW][C]22[/C][C]3286.21[/C][C]3268.53928876098[/C][C]17.6707112390168[/C][/ROW]
[ROW][C]23[/C][C]3491.96[/C][C]3459.09131484265[/C][C]32.8686851573534[/C][/ROW]
[ROW][C]24[/C][C]3608.53[/C][C]3613.67593708215[/C][C]-5.14593708214807[/C][/ROW]
[ROW][C]25[/C][C]3259.04[/C][C]3288.29009961517[/C][C]-29.2500996151743[/C][/ROW]
[ROW][C]26[/C][C]3492.27[/C][C]3456.13244325587[/C][C]36.1375567441328[/C][/ROW]
[ROW][C]27[/C][C]3665.64[/C][C]3670.43383661941[/C][C]-4.79383661940665[/C][/ROW]
[ROW][C]28[/C][C]3808.02[/C][C]3803.10214985881[/C][C]4.91785014118614[/C][/ROW]
[ROW][C]29[/C][C]3397.47[/C][C]3452.947063441[/C][C]-55.4770634410024[/C][/ROW]
[ROW][C]30[/C][C]3644.83[/C][C]3640.44551806515[/C][C]4.38448193484783[/C][/ROW]
[ROW][C]31[/C][C]3812.8[/C][C]3829.6977469178[/C][C]-16.8977469177985[/C][/ROW]
[ROW][C]32[/C][C]3958.78[/C][C]3957.28045506494[/C][C]1.49954493505902[/C][/ROW]
[ROW][C]33[/C][C]3602.73[/C][C]3560.38611627206[/C][C]42.3438837279368[/C][/ROW]
[ROW][C]34[/C][C]3845.49[/C][C]3814.03806899856[/C][C]31.4519310014402[/C][/ROW]
[ROW][C]35[/C][C]4022.27[/C][C]4019.21487464915[/C][C]3.05512535085018[/C][/ROW]
[ROW][C]36[/C][C]4195.29[/C][C]4175.26520005097[/C][C]20.0247999490321[/C][/ROW]
[ROW][C]37[/C][C]3867.28[/C][C]3786.1294390637[/C][C]81.1505609363007[/C][/ROW]
[ROW][C]38[/C][C]4142.62[/C][C]4077.23082796427[/C][C]65.3891720357319[/C][/ROW]
[ROW][C]39[/C][C]4217.79[/C][C]4314.22499406687[/C][C]-96.4349940668726[/C][/ROW]
[ROW][C]40[/C][C]4487.61[/C][C]4460.11438892971[/C][C]27.4956110702897[/C][/ROW]
[ROW][C]41[/C][C]4089.69[/C][C]4075.91281726446[/C][C]13.7771827355423[/C][/ROW]
[ROW][C]42[/C][C]4431.36[/C][C]4352.87949226002[/C][C]78.4805077399787[/C][/ROW]
[ROW][C]43[/C][C]4629.82[/C][C]4545.77311067926[/C][C]84.0468893207426[/C][/ROW]
[ROW][C]44[/C][C]4832.81[/C][C]4832.44742414827[/C][C]0.362575851733709[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301528&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301528&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
52452.022391.0780416150160.9419583849926
62537.492496.058145089241.4318549108043
72726.362716.925582570699.43441742930736
82843.852792.6909397479251.1590602520773
92615.112653.93763442137-38.8276344213741
102778.082729.075295468349.0047045317037
112918.752962.36756643977-43.6175664397738
123023.413040.11611232451-16.7061123245089
132733.072824.18556561934-91.1155656193368
142933.312905.0581100965128.2518899034867
153089.193090.66209310472-1.47209310472044
163256.63183.9530360976572.6469639023503
172968.742954.5398959329614.200104067037
183101.73133.41891249195-31.7189124919514
193277.213303.32968123795-26.1196812379499
203420.13422.68022766252-2.58022766252179
213097.553124.08616211536-26.5361621153643
223286.213268.5392887609817.6707112390168
233491.963459.0913148426532.8686851573534
243608.533613.67593708215-5.14593708214807
253259.043288.29009961517-29.2500996151743
263492.273456.1324432558736.1375567441328
273665.643670.43383661941-4.79383661940665
283808.023803.102149858814.91785014118614
293397.473452.947063441-55.4770634410024
303644.833640.445518065154.38448193484783
313812.83829.6977469178-16.8977469177985
323958.783957.280455064941.49954493505902
333602.733560.3861162720642.3438837279368
343845.493814.0380689985631.4519310014402
354022.274019.214874649153.05512535085018
364195.294175.2652000509720.0247999490321
373867.283786.129439063781.1505609363007
384142.624077.2308279642765.3891720357319
394217.794314.22499406687-96.4349940668726
404487.614460.1143889297127.4956110702897
414089.694075.9128172644613.7771827355423
424431.364352.8794922600278.4805077399787
434629.824545.7731106792684.0468893207426
444832.814832.447424148270.362575851733709







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
454418.327824715764360.915086229114475.74056320241
464751.47001860534681.478689947954821.46134726265
474937.715092873974851.304561751355024.12562399659
485177.69097307985086.998619085035268.38332707457
494728.212903957634594.944238535944861.48156937931
505078.977905918054922.81297848745235.1428333487
515272.294969183335092.54427640695452.04566195976
525522.687385200855335.215289634635710.15948076706
535038.097983199494810.325302869575265.87066352942
545406.48579323085145.681768991395667.28981747021
555606.874845492695315.637501762345898.11218922303
565867.683797321895564.861563114916170.50603152888
575347.983062441365009.631601261455686.33452362127
585733.993680543555352.35137229196115.63598879521
595941.454721802055522.787715449026360.12172815507
606212.680209442945778.133417121386647.2270017645
615657.868141683235194.845023583466120.891259783
626061.501567856315544.643634199246578.35950151337

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
45 & 4418.32782471576 & 4360.91508622911 & 4475.74056320241 \tabularnewline
46 & 4751.4700186053 & 4681.47868994795 & 4821.46134726265 \tabularnewline
47 & 4937.71509287397 & 4851.30456175135 & 5024.12562399659 \tabularnewline
48 & 5177.6909730798 & 5086.99861908503 & 5268.38332707457 \tabularnewline
49 & 4728.21290395763 & 4594.94423853594 & 4861.48156937931 \tabularnewline
50 & 5078.97790591805 & 4922.8129784874 & 5235.1428333487 \tabularnewline
51 & 5272.29496918333 & 5092.5442764069 & 5452.04566195976 \tabularnewline
52 & 5522.68738520085 & 5335.21528963463 & 5710.15948076706 \tabularnewline
53 & 5038.09798319949 & 4810.32530286957 & 5265.87066352942 \tabularnewline
54 & 5406.4857932308 & 5145.68176899139 & 5667.28981747021 \tabularnewline
55 & 5606.87484549269 & 5315.63750176234 & 5898.11218922303 \tabularnewline
56 & 5867.68379732189 & 5564.86156311491 & 6170.50603152888 \tabularnewline
57 & 5347.98306244136 & 5009.63160126145 & 5686.33452362127 \tabularnewline
58 & 5733.99368054355 & 5352.3513722919 & 6115.63598879521 \tabularnewline
59 & 5941.45472180205 & 5522.78771544902 & 6360.12172815507 \tabularnewline
60 & 6212.68020944294 & 5778.13341712138 & 6647.2270017645 \tabularnewline
61 & 5657.86814168323 & 5194.84502358346 & 6120.891259783 \tabularnewline
62 & 6061.50156785631 & 5544.64363419924 & 6578.35950151337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301528&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]45[/C][C]4418.32782471576[/C][C]4360.91508622911[/C][C]4475.74056320241[/C][/ROW]
[ROW][C]46[/C][C]4751.4700186053[/C][C]4681.47868994795[/C][C]4821.46134726265[/C][/ROW]
[ROW][C]47[/C][C]4937.71509287397[/C][C]4851.30456175135[/C][C]5024.12562399659[/C][/ROW]
[ROW][C]48[/C][C]5177.6909730798[/C][C]5086.99861908503[/C][C]5268.38332707457[/C][/ROW]
[ROW][C]49[/C][C]4728.21290395763[/C][C]4594.94423853594[/C][C]4861.48156937931[/C][/ROW]
[ROW][C]50[/C][C]5078.97790591805[/C][C]4922.8129784874[/C][C]5235.1428333487[/C][/ROW]
[ROW][C]51[/C][C]5272.29496918333[/C][C]5092.5442764069[/C][C]5452.04566195976[/C][/ROW]
[ROW][C]52[/C][C]5522.68738520085[/C][C]5335.21528963463[/C][C]5710.15948076706[/C][/ROW]
[ROW][C]53[/C][C]5038.09798319949[/C][C]4810.32530286957[/C][C]5265.87066352942[/C][/ROW]
[ROW][C]54[/C][C]5406.4857932308[/C][C]5145.68176899139[/C][C]5667.28981747021[/C][/ROW]
[ROW][C]55[/C][C]5606.87484549269[/C][C]5315.63750176234[/C][C]5898.11218922303[/C][/ROW]
[ROW][C]56[/C][C]5867.68379732189[/C][C]5564.86156311491[/C][C]6170.50603152888[/C][/ROW]
[ROW][C]57[/C][C]5347.98306244136[/C][C]5009.63160126145[/C][C]5686.33452362127[/C][/ROW]
[ROW][C]58[/C][C]5733.99368054355[/C][C]5352.3513722919[/C][C]6115.63598879521[/C][/ROW]
[ROW][C]59[/C][C]5941.45472180205[/C][C]5522.78771544902[/C][C]6360.12172815507[/C][/ROW]
[ROW][C]60[/C][C]6212.68020944294[/C][C]5778.13341712138[/C][C]6647.2270017645[/C][/ROW]
[ROW][C]61[/C][C]5657.86814168323[/C][C]5194.84502358346[/C][C]6120.891259783[/C][/ROW]
[ROW][C]62[/C][C]6061.50156785631[/C][C]5544.64363419924[/C][C]6578.35950151337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301528&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301528&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
454418.327824715764360.915086229114475.74056320241
464751.47001860534681.478689947954821.46134726265
474937.715092873974851.304561751355024.12562399659
485177.69097307985086.998619085035268.38332707457
494728.212903957634594.944238535944861.48156937931
505078.977905918054922.81297848745235.1428333487
515272.294969183335092.54427640695452.04566195976
525522.687385200855335.215289634635710.15948076706
535038.097983199494810.325302869575265.87066352942
545406.48579323085145.681768991395667.28981747021
555606.874845492695315.637501762345898.11218922303
565867.683797321895564.861563114916170.50603152888
575347.983062441365009.631601261455686.33452362127
585733.993680543555352.35137229196115.63598879521
595941.454721802055522.787715449026360.12172815507
606212.680209442945778.133417121386647.2270017645
615657.868141683235194.845023583466120.891259783
626061.501567856315544.643634199246578.35950151337



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')