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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Nov 2011 09:02:40 -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/2011/Nov/26/t13223162840yfvkaoez5v42yk.htm/, Retrieved Mon, 30 Jan 2023 01:22:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147404, Retrieved Mon, 30 Jan 2023 01:22:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [WS 8 - Exponentia...] [2011-11-26 14:02:40] [e598b5cd83fcb010b35e92a01f5e81e9] [Current]
- RMP     [Structural Time Series Models] [WS 8 - Structural...] [2011-11-29 15:08:10] [ae1339cb5a7cf28362d01e7220b4a16c]
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Dataseries X:
6827
6178
7084
8162
8462
9644
10466
10748
9963
8194
6848
7027
7269
6775
7819
8371
9069
10248
11030
10882
10333
9109
7685
7602
8350
7829
8829
9948
10638
11253
11424
11391
10665
9396
7775
7933
8186
7444
8484
9864
10252
12282
11637
11577
12417
9637
8094
9280
8334
7899
9994
10078
10801
12950
12222
12246
13281
10366
8730
9614
8639
8772
10894
10455
11179
10588
10794
12770
13812
10857
9290
10925
9491
8919
11607
8852
12537
14759
13667
13731
15110
12185
10645
12161
10840
10436
13589
13402
13103
14933
14147
14057
16234
12389
11595
12772




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147404&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147404&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147404&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.195810608415622
beta0
gamma0.414899767975478

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.195810608415622 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.414899767975478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147404&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]0.195810608415622[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.414899767975478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147404&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147404&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
alpha0.195810608415622
beta0
gamma0.414899767975478







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1372696992.55582264958276.444177350424
1467756567.29885038434207.701149615657
1578197674.66459736737144.335402632632
1683718245.08099221427125.919007785729
1790698938.43292824804130.567071751957
181024810127.8616711817120.138328818333
191103010919.7900222831110.209977716891
201088211223.7742969148-341.774296914818
211033310360.0469224033-27.0469224032659
2291098590.11317324654518.886826753464
2376857355.41237700014329.587622999858
2476027592.186455160839.8135448391713
2583507923.37485229639426.625147703614
2678297504.58824661208324.411753387922
2788298613.66468002985215.335319970154
2899489191.838834564756.161165436
291063810010.149734626627.850265374005
301125311293.4721688315-40.4721688315403
311142412050.6386069781-626.638606978078
321139112059.5319464518-668.531946451816
331066511236.8332615796-571.833261579588
3493969542.37972638817-146.37972638817
3577758114.25148940533-339.251489405333
3679338113.3645972285-180.364597228501
3781868546.38661910277-360.386619102774
3874447939.39044462936-495.390444629358
3984848851.54668712675-367.546687126745
4098649496.03722682397367.962773176028
411025210195.522806248256.4771937518308
421228211143.97321027711138.02678972293
431163711936.3231297992-299.323129799228
441157711995.3302644772-418.330264477199
451241711253.88801220031163.11198779971
46963710041.111134089-404.11113408898
4780948498.16314819912-404.163148199121
4892808537.57974601575742.42025398425
4983349091.22704471256-757.227044712556
5078998361.4801997222-462.480199722202
5199949322.73670871305671.263291286954
521007810416.0458719162-338.045871916167
531080110873.3578160378-72.3578160377965
541295012157.4486248295792.551375170513
551222212402.5675053199-180.567505319863
561224612445.1205694924-199.120569492363
571328112274.26274728291006.73725271714
581036610507.9495173254-141.949517325365
5987309016.31820219367-286.318202193666
6096149461.37680619265152.623193807354
6186399399.16627733801-760.16627733801
6287728767.188539859944.81146014006117
631089410198.2282897027695.771710297275
641045510959.5723926655-504.572392665526
651117911472.9256206585-293.925620658458
661058813002.2149668028-2414.21496680282
671079412294.7260872056-1500.72608720563
681277012072.5877181172697.41228188284
691381212479.62463856781332.37536143216
701085710393.8062836986463.193716301434
7192908972.49866782445317.501332175545
72109259682.247847006661242.75215299334
7394919528.93663086188-37.936630861881
7489199293.62005566991-374.620055669913
751160710880.9074991531726.092500846938
76885211247.6843314854-2395.68433148539
771253711461.02175912021075.97824087979
781475912551.10132821922207.89867178083
791366713053.4641976186613.535802381371
801373113978.7471697971-247.747169797149
811511014412.5723490664697.427650933634
821218511912.4150943149272.584905685055
831064510405.1728229309239.827177069081
841216111408.4299094924752.570090507586
851084010731.8237974897108.176202510338
861043610412.780549644423.2194503556457
871358912445.23073020511143.76926979491
881340211852.18731551081549.81268448919
891310313996.4428770617-893.442877061658
901493315078.5631968818-145.563196881771
911414714588.1213524094-441.121352409407
921405715019.5173184176-962.517318417647
931623415628.7480527601605.251947239869
941238912968.7896401018-579.789640101788
951159511283.7135123575311.286487642472
961277212472.0438608975299.956139102467

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7269 & 6992.55582264958 & 276.444177350424 \tabularnewline
14 & 6775 & 6567.29885038434 & 207.701149615657 \tabularnewline
15 & 7819 & 7674.66459736737 & 144.335402632632 \tabularnewline
16 & 8371 & 8245.08099221427 & 125.919007785729 \tabularnewline
17 & 9069 & 8938.43292824804 & 130.567071751957 \tabularnewline
18 & 10248 & 10127.8616711817 & 120.138328818333 \tabularnewline
19 & 11030 & 10919.7900222831 & 110.209977716891 \tabularnewline
20 & 10882 & 11223.7742969148 & -341.774296914818 \tabularnewline
21 & 10333 & 10360.0469224033 & -27.0469224032659 \tabularnewline
22 & 9109 & 8590.11317324654 & 518.886826753464 \tabularnewline
23 & 7685 & 7355.41237700014 & 329.587622999858 \tabularnewline
24 & 7602 & 7592.18645516083 & 9.8135448391713 \tabularnewline
25 & 8350 & 7923.37485229639 & 426.625147703614 \tabularnewline
26 & 7829 & 7504.58824661208 & 324.411753387922 \tabularnewline
27 & 8829 & 8613.66468002985 & 215.335319970154 \tabularnewline
28 & 9948 & 9191.838834564 & 756.161165436 \tabularnewline
29 & 10638 & 10010.149734626 & 627.850265374005 \tabularnewline
30 & 11253 & 11293.4721688315 & -40.4721688315403 \tabularnewline
31 & 11424 & 12050.6386069781 & -626.638606978078 \tabularnewline
32 & 11391 & 12059.5319464518 & -668.531946451816 \tabularnewline
33 & 10665 & 11236.8332615796 & -571.833261579588 \tabularnewline
34 & 9396 & 9542.37972638817 & -146.37972638817 \tabularnewline
35 & 7775 & 8114.25148940533 & -339.251489405333 \tabularnewline
36 & 7933 & 8113.3645972285 & -180.364597228501 \tabularnewline
37 & 8186 & 8546.38661910277 & -360.386619102774 \tabularnewline
38 & 7444 & 7939.39044462936 & -495.390444629358 \tabularnewline
39 & 8484 & 8851.54668712675 & -367.546687126745 \tabularnewline
40 & 9864 & 9496.03722682397 & 367.962773176028 \tabularnewline
41 & 10252 & 10195.5228062482 & 56.4771937518308 \tabularnewline
42 & 12282 & 11143.9732102771 & 1138.02678972293 \tabularnewline
43 & 11637 & 11936.3231297992 & -299.323129799228 \tabularnewline
44 & 11577 & 11995.3302644772 & -418.330264477199 \tabularnewline
45 & 12417 & 11253.8880122003 & 1163.11198779971 \tabularnewline
46 & 9637 & 10041.111134089 & -404.11113408898 \tabularnewline
47 & 8094 & 8498.16314819912 & -404.163148199121 \tabularnewline
48 & 9280 & 8537.57974601575 & 742.42025398425 \tabularnewline
49 & 8334 & 9091.22704471256 & -757.227044712556 \tabularnewline
50 & 7899 & 8361.4801997222 & -462.480199722202 \tabularnewline
51 & 9994 & 9322.73670871305 & 671.263291286954 \tabularnewline
52 & 10078 & 10416.0458719162 & -338.045871916167 \tabularnewline
53 & 10801 & 10873.3578160378 & -72.3578160377965 \tabularnewline
54 & 12950 & 12157.4486248295 & 792.551375170513 \tabularnewline
55 & 12222 & 12402.5675053199 & -180.567505319863 \tabularnewline
56 & 12246 & 12445.1205694924 & -199.120569492363 \tabularnewline
57 & 13281 & 12274.2627472829 & 1006.73725271714 \tabularnewline
58 & 10366 & 10507.9495173254 & -141.949517325365 \tabularnewline
59 & 8730 & 9016.31820219367 & -286.318202193666 \tabularnewline
60 & 9614 & 9461.37680619265 & 152.623193807354 \tabularnewline
61 & 8639 & 9399.16627733801 & -760.16627733801 \tabularnewline
62 & 8772 & 8767.18853985994 & 4.81146014006117 \tabularnewline
63 & 10894 & 10198.2282897027 & 695.771710297275 \tabularnewline
64 & 10455 & 10959.5723926655 & -504.572392665526 \tabularnewline
65 & 11179 & 11472.9256206585 & -293.925620658458 \tabularnewline
66 & 10588 & 13002.2149668028 & -2414.21496680282 \tabularnewline
67 & 10794 & 12294.7260872056 & -1500.72608720563 \tabularnewline
68 & 12770 & 12072.5877181172 & 697.41228188284 \tabularnewline
69 & 13812 & 12479.6246385678 & 1332.37536143216 \tabularnewline
70 & 10857 & 10393.8062836986 & 463.193716301434 \tabularnewline
71 & 9290 & 8972.49866782445 & 317.501332175545 \tabularnewline
72 & 10925 & 9682.24784700666 & 1242.75215299334 \tabularnewline
73 & 9491 & 9528.93663086188 & -37.936630861881 \tabularnewline
74 & 8919 & 9293.62005566991 & -374.620055669913 \tabularnewline
75 & 11607 & 10880.9074991531 & 726.092500846938 \tabularnewline
76 & 8852 & 11247.6843314854 & -2395.68433148539 \tabularnewline
77 & 12537 & 11461.0217591202 & 1075.97824087979 \tabularnewline
78 & 14759 & 12551.1013282192 & 2207.89867178083 \tabularnewline
79 & 13667 & 13053.4641976186 & 613.535802381371 \tabularnewline
80 & 13731 & 13978.7471697971 & -247.747169797149 \tabularnewline
81 & 15110 & 14412.5723490664 & 697.427650933634 \tabularnewline
82 & 12185 & 11912.4150943149 & 272.584905685055 \tabularnewline
83 & 10645 & 10405.1728229309 & 239.827177069081 \tabularnewline
84 & 12161 & 11408.4299094924 & 752.570090507586 \tabularnewline
85 & 10840 & 10731.8237974897 & 108.176202510338 \tabularnewline
86 & 10436 & 10412.7805496444 & 23.2194503556457 \tabularnewline
87 & 13589 & 12445.2307302051 & 1143.76926979491 \tabularnewline
88 & 13402 & 11852.1873155108 & 1549.81268448919 \tabularnewline
89 & 13103 & 13996.4428770617 & -893.442877061658 \tabularnewline
90 & 14933 & 15078.5631968818 & -145.563196881771 \tabularnewline
91 & 14147 & 14588.1213524094 & -441.121352409407 \tabularnewline
92 & 14057 & 15019.5173184176 & -962.517318417647 \tabularnewline
93 & 16234 & 15628.7480527601 & 605.251947239869 \tabularnewline
94 & 12389 & 12968.7896401018 & -579.789640101788 \tabularnewline
95 & 11595 & 11283.7135123575 & 311.286487642472 \tabularnewline
96 & 12772 & 12472.0438608975 & 299.956139102467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147404&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]13[/C][C]7269[/C][C]6992.55582264958[/C][C]276.444177350424[/C][/ROW]
[ROW][C]14[/C][C]6775[/C][C]6567.29885038434[/C][C]207.701149615657[/C][/ROW]
[ROW][C]15[/C][C]7819[/C][C]7674.66459736737[/C][C]144.335402632632[/C][/ROW]
[ROW][C]16[/C][C]8371[/C][C]8245.08099221427[/C][C]125.919007785729[/C][/ROW]
[ROW][C]17[/C][C]9069[/C][C]8938.43292824804[/C][C]130.567071751957[/C][/ROW]
[ROW][C]18[/C][C]10248[/C][C]10127.8616711817[/C][C]120.138328818333[/C][/ROW]
[ROW][C]19[/C][C]11030[/C][C]10919.7900222831[/C][C]110.209977716891[/C][/ROW]
[ROW][C]20[/C][C]10882[/C][C]11223.7742969148[/C][C]-341.774296914818[/C][/ROW]
[ROW][C]21[/C][C]10333[/C][C]10360.0469224033[/C][C]-27.0469224032659[/C][/ROW]
[ROW][C]22[/C][C]9109[/C][C]8590.11317324654[/C][C]518.886826753464[/C][/ROW]
[ROW][C]23[/C][C]7685[/C][C]7355.41237700014[/C][C]329.587622999858[/C][/ROW]
[ROW][C]24[/C][C]7602[/C][C]7592.18645516083[/C][C]9.8135448391713[/C][/ROW]
[ROW][C]25[/C][C]8350[/C][C]7923.37485229639[/C][C]426.625147703614[/C][/ROW]
[ROW][C]26[/C][C]7829[/C][C]7504.58824661208[/C][C]324.411753387922[/C][/ROW]
[ROW][C]27[/C][C]8829[/C][C]8613.66468002985[/C][C]215.335319970154[/C][/ROW]
[ROW][C]28[/C][C]9948[/C][C]9191.838834564[/C][C]756.161165436[/C][/ROW]
[ROW][C]29[/C][C]10638[/C][C]10010.149734626[/C][C]627.850265374005[/C][/ROW]
[ROW][C]30[/C][C]11253[/C][C]11293.4721688315[/C][C]-40.4721688315403[/C][/ROW]
[ROW][C]31[/C][C]11424[/C][C]12050.6386069781[/C][C]-626.638606978078[/C][/ROW]
[ROW][C]32[/C][C]11391[/C][C]12059.5319464518[/C][C]-668.531946451816[/C][/ROW]
[ROW][C]33[/C][C]10665[/C][C]11236.8332615796[/C][C]-571.833261579588[/C][/ROW]
[ROW][C]34[/C][C]9396[/C][C]9542.37972638817[/C][C]-146.37972638817[/C][/ROW]
[ROW][C]35[/C][C]7775[/C][C]8114.25148940533[/C][C]-339.251489405333[/C][/ROW]
[ROW][C]36[/C][C]7933[/C][C]8113.3645972285[/C][C]-180.364597228501[/C][/ROW]
[ROW][C]37[/C][C]8186[/C][C]8546.38661910277[/C][C]-360.386619102774[/C][/ROW]
[ROW][C]38[/C][C]7444[/C][C]7939.39044462936[/C][C]-495.390444629358[/C][/ROW]
[ROW][C]39[/C][C]8484[/C][C]8851.54668712675[/C][C]-367.546687126745[/C][/ROW]
[ROW][C]40[/C][C]9864[/C][C]9496.03722682397[/C][C]367.962773176028[/C][/ROW]
[ROW][C]41[/C][C]10252[/C][C]10195.5228062482[/C][C]56.4771937518308[/C][/ROW]
[ROW][C]42[/C][C]12282[/C][C]11143.9732102771[/C][C]1138.02678972293[/C][/ROW]
[ROW][C]43[/C][C]11637[/C][C]11936.3231297992[/C][C]-299.323129799228[/C][/ROW]
[ROW][C]44[/C][C]11577[/C][C]11995.3302644772[/C][C]-418.330264477199[/C][/ROW]
[ROW][C]45[/C][C]12417[/C][C]11253.8880122003[/C][C]1163.11198779971[/C][/ROW]
[ROW][C]46[/C][C]9637[/C][C]10041.111134089[/C][C]-404.11113408898[/C][/ROW]
[ROW][C]47[/C][C]8094[/C][C]8498.16314819912[/C][C]-404.163148199121[/C][/ROW]
[ROW][C]48[/C][C]9280[/C][C]8537.57974601575[/C][C]742.42025398425[/C][/ROW]
[ROW][C]49[/C][C]8334[/C][C]9091.22704471256[/C][C]-757.227044712556[/C][/ROW]
[ROW][C]50[/C][C]7899[/C][C]8361.4801997222[/C][C]-462.480199722202[/C][/ROW]
[ROW][C]51[/C][C]9994[/C][C]9322.73670871305[/C][C]671.263291286954[/C][/ROW]
[ROW][C]52[/C][C]10078[/C][C]10416.0458719162[/C][C]-338.045871916167[/C][/ROW]
[ROW][C]53[/C][C]10801[/C][C]10873.3578160378[/C][C]-72.3578160377965[/C][/ROW]
[ROW][C]54[/C][C]12950[/C][C]12157.4486248295[/C][C]792.551375170513[/C][/ROW]
[ROW][C]55[/C][C]12222[/C][C]12402.5675053199[/C][C]-180.567505319863[/C][/ROW]
[ROW][C]56[/C][C]12246[/C][C]12445.1205694924[/C][C]-199.120569492363[/C][/ROW]
[ROW][C]57[/C][C]13281[/C][C]12274.2627472829[/C][C]1006.73725271714[/C][/ROW]
[ROW][C]58[/C][C]10366[/C][C]10507.9495173254[/C][C]-141.949517325365[/C][/ROW]
[ROW][C]59[/C][C]8730[/C][C]9016.31820219367[/C][C]-286.318202193666[/C][/ROW]
[ROW][C]60[/C][C]9614[/C][C]9461.37680619265[/C][C]152.623193807354[/C][/ROW]
[ROW][C]61[/C][C]8639[/C][C]9399.16627733801[/C][C]-760.16627733801[/C][/ROW]
[ROW][C]62[/C][C]8772[/C][C]8767.18853985994[/C][C]4.81146014006117[/C][/ROW]
[ROW][C]63[/C][C]10894[/C][C]10198.2282897027[/C][C]695.771710297275[/C][/ROW]
[ROW][C]64[/C][C]10455[/C][C]10959.5723926655[/C][C]-504.572392665526[/C][/ROW]
[ROW][C]65[/C][C]11179[/C][C]11472.9256206585[/C][C]-293.925620658458[/C][/ROW]
[ROW][C]66[/C][C]10588[/C][C]13002.2149668028[/C][C]-2414.21496680282[/C][/ROW]
[ROW][C]67[/C][C]10794[/C][C]12294.7260872056[/C][C]-1500.72608720563[/C][/ROW]
[ROW][C]68[/C][C]12770[/C][C]12072.5877181172[/C][C]697.41228188284[/C][/ROW]
[ROW][C]69[/C][C]13812[/C][C]12479.6246385678[/C][C]1332.37536143216[/C][/ROW]
[ROW][C]70[/C][C]10857[/C][C]10393.8062836986[/C][C]463.193716301434[/C][/ROW]
[ROW][C]71[/C][C]9290[/C][C]8972.49866782445[/C][C]317.501332175545[/C][/ROW]
[ROW][C]72[/C][C]10925[/C][C]9682.24784700666[/C][C]1242.75215299334[/C][/ROW]
[ROW][C]73[/C][C]9491[/C][C]9528.93663086188[/C][C]-37.936630861881[/C][/ROW]
[ROW][C]74[/C][C]8919[/C][C]9293.62005566991[/C][C]-374.620055669913[/C][/ROW]
[ROW][C]75[/C][C]11607[/C][C]10880.9074991531[/C][C]726.092500846938[/C][/ROW]
[ROW][C]76[/C][C]8852[/C][C]11247.6843314854[/C][C]-2395.68433148539[/C][/ROW]
[ROW][C]77[/C][C]12537[/C][C]11461.0217591202[/C][C]1075.97824087979[/C][/ROW]
[ROW][C]78[/C][C]14759[/C][C]12551.1013282192[/C][C]2207.89867178083[/C][/ROW]
[ROW][C]79[/C][C]13667[/C][C]13053.4641976186[/C][C]613.535802381371[/C][/ROW]
[ROW][C]80[/C][C]13731[/C][C]13978.7471697971[/C][C]-247.747169797149[/C][/ROW]
[ROW][C]81[/C][C]15110[/C][C]14412.5723490664[/C][C]697.427650933634[/C][/ROW]
[ROW][C]82[/C][C]12185[/C][C]11912.4150943149[/C][C]272.584905685055[/C][/ROW]
[ROW][C]83[/C][C]10645[/C][C]10405.1728229309[/C][C]239.827177069081[/C][/ROW]
[ROW][C]84[/C][C]12161[/C][C]11408.4299094924[/C][C]752.570090507586[/C][/ROW]
[ROW][C]85[/C][C]10840[/C][C]10731.8237974897[/C][C]108.176202510338[/C][/ROW]
[ROW][C]86[/C][C]10436[/C][C]10412.7805496444[/C][C]23.2194503556457[/C][/ROW]
[ROW][C]87[/C][C]13589[/C][C]12445.2307302051[/C][C]1143.76926979491[/C][/ROW]
[ROW][C]88[/C][C]13402[/C][C]11852.1873155108[/C][C]1549.81268448919[/C][/ROW]
[ROW][C]89[/C][C]13103[/C][C]13996.4428770617[/C][C]-893.442877061658[/C][/ROW]
[ROW][C]90[/C][C]14933[/C][C]15078.5631968818[/C][C]-145.563196881771[/C][/ROW]
[ROW][C]91[/C][C]14147[/C][C]14588.1213524094[/C][C]-441.121352409407[/C][/ROW]
[ROW][C]92[/C][C]14057[/C][C]15019.5173184176[/C][C]-962.517318417647[/C][/ROW]
[ROW][C]93[/C][C]16234[/C][C]15628.7480527601[/C][C]605.251947239869[/C][/ROW]
[ROW][C]94[/C][C]12389[/C][C]12968.7896401018[/C][C]-579.789640101788[/C][/ROW]
[ROW][C]95[/C][C]11595[/C][C]11283.7135123575[/C][C]311.286487642472[/C][/ROW]
[ROW][C]96[/C][C]12772[/C][C]12472.0438608975[/C][C]299.956139102467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147404&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147404&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
1372696992.55582264958276.444177350424
1467756567.29885038434207.701149615657
1578197674.66459736737144.335402632632
1683718245.08099221427125.919007785729
1790698938.43292824804130.567071751957
181024810127.8616711817120.138328818333
191103010919.7900222831110.209977716891
201088211223.7742969148-341.774296914818
211033310360.0469224033-27.0469224032659
2291098590.11317324654518.886826753464
2376857355.41237700014329.587622999858
2476027592.186455160839.8135448391713
2583507923.37485229639426.625147703614
2678297504.58824661208324.411753387922
2788298613.66468002985215.335319970154
2899489191.838834564756.161165436
291063810010.149734626627.850265374005
301125311293.4721688315-40.4721688315403
311142412050.6386069781-626.638606978078
321139112059.5319464518-668.531946451816
331066511236.8332615796-571.833261579588
3493969542.37972638817-146.37972638817
3577758114.25148940533-339.251489405333
3679338113.3645972285-180.364597228501
3781868546.38661910277-360.386619102774
3874447939.39044462936-495.390444629358
3984848851.54668712675-367.546687126745
4098649496.03722682397367.962773176028
411025210195.522806248256.4771937518308
421228211143.97321027711138.02678972293
431163711936.3231297992-299.323129799228
441157711995.3302644772-418.330264477199
451241711253.88801220031163.11198779971
46963710041.111134089-404.11113408898
4780948498.16314819912-404.163148199121
4892808537.57974601575742.42025398425
4983349091.22704471256-757.227044712556
5078998361.4801997222-462.480199722202
5199949322.73670871305671.263291286954
521007810416.0458719162-338.045871916167
531080110873.3578160378-72.3578160377965
541295012157.4486248295792.551375170513
551222212402.5675053199-180.567505319863
561224612445.1205694924-199.120569492363
571328112274.26274728291006.73725271714
581036610507.9495173254-141.949517325365
5987309016.31820219367-286.318202193666
6096149461.37680619265152.623193807354
6186399399.16627733801-760.16627733801
6287728767.188539859944.81146014006117
631089410198.2282897027695.771710297275
641045510959.5723926655-504.572392665526
651117911472.9256206585-293.925620658458
661058813002.2149668028-2414.21496680282
671079412294.7260872056-1500.72608720563
681277012072.5877181172697.41228188284
691381212479.62463856781332.37536143216
701085710393.8062836986463.193716301434
7192908972.49866782445317.501332175545
72109259682.247847006661242.75215299334
7394919528.93663086188-37.936630861881
7489199293.62005566991-374.620055669913
751160710880.9074991531726.092500846938
76885211247.6843314854-2395.68433148539
771253711461.02175912021075.97824087979
781475912551.10132821922207.89867178083
791366713053.4641976186613.535802381371
801373113978.7471697971-247.747169797149
811511014412.5723490664697.427650933634
821218511912.4150943149272.584905685055
831064510405.1728229309239.827177069081
841216111408.4299094924752.570090507586
851084010731.8237974897108.176202510338
861043610412.780549644423.2194503556457
871358912445.23073020511143.76926979491
881340211852.18731551081549.81268448919
891310313996.4428770617-893.442877061658
901493315078.5631968818-145.563196881771
911414714588.1213524094-441.121352409407
921405715019.5173184176-962.517318417647
931623415628.7480527601605.251947239869
941238912968.7896401018-579.789640101788
951159511283.7135123575311.286487642472
961277212472.0438608975299.956139102467







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9711491.803964981510052.758581532212930.8493484308
9811123.23216977789656.8584853303512589.6058542252
9913525.016138301312031.814226551515018.218050051
10012843.490197403611323.933644962614363.0467498446
10113869.064249721412323.602414903215414.5260845396
10215375.666195212613804.726206004616946.6061844205
10314815.111828198913219.100356903616411.1232994941
10415158.916103564413538.220949218916779.61125791
10516479.716684698914834.708189239918124.7251801579
10613305.844923565511636.877243547314974.8126035838
10712031.612429484210339.024681756213724.2001772121
10813155.209120145111439.326417110914871.0918231793

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 11491.8039649815 & 10052.7585815322 & 12930.8493484308 \tabularnewline
98 & 11123.2321697778 & 9656.85848533035 & 12589.6058542252 \tabularnewline
99 & 13525.0161383013 & 12031.8142265515 & 15018.218050051 \tabularnewline
100 & 12843.4901974036 & 11323.9336449626 & 14363.0467498446 \tabularnewline
101 & 13869.0642497214 & 12323.6024149032 & 15414.5260845396 \tabularnewline
102 & 15375.6661952126 & 13804.7262060046 & 16946.6061844205 \tabularnewline
103 & 14815.1118281989 & 13219.1003569036 & 16411.1232994941 \tabularnewline
104 & 15158.9161035644 & 13538.2209492189 & 16779.61125791 \tabularnewline
105 & 16479.7166846989 & 14834.7081892399 & 18124.7251801579 \tabularnewline
106 & 13305.8449235655 & 11636.8772435473 & 14974.8126035838 \tabularnewline
107 & 12031.6124294842 & 10339.0246817562 & 13724.2001772121 \tabularnewline
108 & 13155.2091201451 & 11439.3264171109 & 14871.0918231793 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147404&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]97[/C][C]11491.8039649815[/C][C]10052.7585815322[/C][C]12930.8493484308[/C][/ROW]
[ROW][C]98[/C][C]11123.2321697778[/C][C]9656.85848533035[/C][C]12589.6058542252[/C][/ROW]
[ROW][C]99[/C][C]13525.0161383013[/C][C]12031.8142265515[/C][C]15018.218050051[/C][/ROW]
[ROW][C]100[/C][C]12843.4901974036[/C][C]11323.9336449626[/C][C]14363.0467498446[/C][/ROW]
[ROW][C]101[/C][C]13869.0642497214[/C][C]12323.6024149032[/C][C]15414.5260845396[/C][/ROW]
[ROW][C]102[/C][C]15375.6661952126[/C][C]13804.7262060046[/C][C]16946.6061844205[/C][/ROW]
[ROW][C]103[/C][C]14815.1118281989[/C][C]13219.1003569036[/C][C]16411.1232994941[/C][/ROW]
[ROW][C]104[/C][C]15158.9161035644[/C][C]13538.2209492189[/C][C]16779.61125791[/C][/ROW]
[ROW][C]105[/C][C]16479.7166846989[/C][C]14834.7081892399[/C][C]18124.7251801579[/C][/ROW]
[ROW][C]106[/C][C]13305.8449235655[/C][C]11636.8772435473[/C][C]14974.8126035838[/C][/ROW]
[ROW][C]107[/C][C]12031.6124294842[/C][C]10339.0246817562[/C][C]13724.2001772121[/C][/ROW]
[ROW][C]108[/C][C]13155.2091201451[/C][C]11439.3264171109[/C][C]14871.0918231793[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147404&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147404&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
9711491.803964981510052.758581532212930.8493484308
9811123.23216977789656.8584853303512589.6058542252
9913525.016138301312031.814226551515018.218050051
10012843.490197403611323.933644962614363.0467498446
10113869.064249721412323.602414903215414.5260845396
10215375.666195212613804.726206004616946.6061844205
10314815.111828198913219.100356903616411.1232994941
10415158.916103564413538.220949218916779.61125791
10516479.716684698914834.708189239918124.7251801579
10613305.844923565511636.877243547314974.8126035838
10712031.612429484210339.024681756213724.2001772121
10813155.209120145111439.326417110914871.0918231793



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')