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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 14:35:24 +0000
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/Nov/30/t1417358158gjsltfvbx9alka8.htm/, Retrieved Sun, 19 May 2024 15:25:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261477, Retrieved Sun, 19 May 2024 15:25:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [eigen reeks decom...] [2014-11-30 14:35:24] [6e93958bb59fd6ca90246553243cf8d9] [Current]
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Dataseries X:
389.09
391.76
390.96
391.76
392.8
393.06
393.06
393.26
393.87
394.47
394.57
394.57
394.57
399.57
406.13
407.03
409.46
409.9
409.9
410.14
410.54
410.69
410.79
410.97
410.97
413.8
423.31
423.85
426.6
426.26
426.26
426.32
427.14
427.55
428.29
428.8
428.8
434.87
435.66
440.75
440.99
441.04
441.04
441.88
441.92
442.48
442.81
442.81
442.81
447.19
446.52
448.57
448.71
448.73
449.07
449.03
448.68
450.08
449.96
449.96
449.96
452.56
455.31
456.2
456.75
457.63
457.63
457.65
458.32
459.64
460.16
459.89




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261477&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261477&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261477&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.799705137423186
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.799705137423186 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261477&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]0.799705137423186[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261477&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261477&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
alpha0.799705137423186
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13394.57387.0390331196587.53096688034191
14399.57397.9654234362191.60457656378122
15406.13405.7195323035840.410467696415765
16407.03406.8862061750750.143793824925069
17409.46409.3883695815180.0716304184821297
18409.9409.8353235410950.0646764589054101
19409.9408.1492163834721.75078361652754
20410.14410.504414448713-0.364414448713262
21410.54411.174327754513-0.634327754513436
22410.69411.307556669673-0.617556669673093
23410.79410.892114174206-0.102114174206292
24410.97410.7234570237440.24654297625608
25410.97412.334536764074-1.36453676407427
26413.8414.960121582197-1.16012158219661
27423.31420.2641132673093.04588673269143
28423.85423.4849318749290.365068125071332
29426.6426.1495955164020.45040448359822
30426.26426.898064199397-0.638064199396695
31426.26424.987690328481.27230967152002
32426.32426.536587015975-0.216587015974937
33427.14427.270656430695-0.130656430695183
34427.55427.810033053218-0.260033053218308
35428.29427.7837445143760.506255485623683
36428.8428.1714379423710.628562057629381
37428.8429.765329309479-0.965329309479102
38434.87432.7511056907022.11889430929841
39435.66441.519785087362-5.85978508736179
40440.75437.0817379936743.66826200632619
41440.99442.405075186095-1.41507518609529
42441.04441.443695508198-0.403695508198098
43441.04440.103385555630.936614444370377
44441.88441.0856066879520.794393312048328
45441.92442.645373719596-0.725373719595609
46442.48442.683238398042-0.203238398041719
47442.81442.855852494304-0.0458524943042562
48442.81442.82651971237-0.0165197123699841
49442.81443.585287621615-0.775287621614609
50447.19447.340795462826-0.150795462826125
51446.52452.696303795063-6.17630379506295
52448.57449.913553947991-1.34355394799132
53448.71450.210749849538-1.50074984953795
54448.73449.383429856736-0.653429856736068
55449.07448.1118632604110.958136739589179
56449.03449.082809720634-0.0528097206345137
57448.68449.66066260585-0.980662605849602
58450.08449.5989524729080.481047527091562
59449.96450.350317126927-0.390317126927016
60449.96450.05138941415-0.0913894141502283
61449.96450.598306324134-0.638306324134021
62452.56454.588441383797-2.02844138379652
63455.31457.235508263411-1.92550826341085
64456.2458.820116407624-2.62011640762427
65456.75458.064953220463-1.31495322046294
66457.63457.5559295879650.074070412034871
67457.63457.1889372039970.441062796002882
68457.65457.5438895927840.106110407215795
69458.32458.0629875545460.25701244545445
70459.64459.2838255487970.356174451202662
71460.16459.7607986988710.399201301129267
72459.89460.153126614252-0.263126614251917

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 394.57 & 387.039033119658 & 7.53096688034191 \tabularnewline
14 & 399.57 & 397.965423436219 & 1.60457656378122 \tabularnewline
15 & 406.13 & 405.719532303584 & 0.410467696415765 \tabularnewline
16 & 407.03 & 406.886206175075 & 0.143793824925069 \tabularnewline
17 & 409.46 & 409.388369581518 & 0.0716304184821297 \tabularnewline
18 & 409.9 & 409.835323541095 & 0.0646764589054101 \tabularnewline
19 & 409.9 & 408.149216383472 & 1.75078361652754 \tabularnewline
20 & 410.14 & 410.504414448713 & -0.364414448713262 \tabularnewline
21 & 410.54 & 411.174327754513 & -0.634327754513436 \tabularnewline
22 & 410.69 & 411.307556669673 & -0.617556669673093 \tabularnewline
23 & 410.79 & 410.892114174206 & -0.102114174206292 \tabularnewline
24 & 410.97 & 410.723457023744 & 0.24654297625608 \tabularnewline
25 & 410.97 & 412.334536764074 & -1.36453676407427 \tabularnewline
26 & 413.8 & 414.960121582197 & -1.16012158219661 \tabularnewline
27 & 423.31 & 420.264113267309 & 3.04588673269143 \tabularnewline
28 & 423.85 & 423.484931874929 & 0.365068125071332 \tabularnewline
29 & 426.6 & 426.149595516402 & 0.45040448359822 \tabularnewline
30 & 426.26 & 426.898064199397 & -0.638064199396695 \tabularnewline
31 & 426.26 & 424.98769032848 & 1.27230967152002 \tabularnewline
32 & 426.32 & 426.536587015975 & -0.216587015974937 \tabularnewline
33 & 427.14 & 427.270656430695 & -0.130656430695183 \tabularnewline
34 & 427.55 & 427.810033053218 & -0.260033053218308 \tabularnewline
35 & 428.29 & 427.783744514376 & 0.506255485623683 \tabularnewline
36 & 428.8 & 428.171437942371 & 0.628562057629381 \tabularnewline
37 & 428.8 & 429.765329309479 & -0.965329309479102 \tabularnewline
38 & 434.87 & 432.751105690702 & 2.11889430929841 \tabularnewline
39 & 435.66 & 441.519785087362 & -5.85978508736179 \tabularnewline
40 & 440.75 & 437.081737993674 & 3.66826200632619 \tabularnewline
41 & 440.99 & 442.405075186095 & -1.41507518609529 \tabularnewline
42 & 441.04 & 441.443695508198 & -0.403695508198098 \tabularnewline
43 & 441.04 & 440.10338555563 & 0.936614444370377 \tabularnewline
44 & 441.88 & 441.085606687952 & 0.794393312048328 \tabularnewline
45 & 441.92 & 442.645373719596 & -0.725373719595609 \tabularnewline
46 & 442.48 & 442.683238398042 & -0.203238398041719 \tabularnewline
47 & 442.81 & 442.855852494304 & -0.0458524943042562 \tabularnewline
48 & 442.81 & 442.82651971237 & -0.0165197123699841 \tabularnewline
49 & 442.81 & 443.585287621615 & -0.775287621614609 \tabularnewline
50 & 447.19 & 447.340795462826 & -0.150795462826125 \tabularnewline
51 & 446.52 & 452.696303795063 & -6.17630379506295 \tabularnewline
52 & 448.57 & 449.913553947991 & -1.34355394799132 \tabularnewline
53 & 448.71 & 450.210749849538 & -1.50074984953795 \tabularnewline
54 & 448.73 & 449.383429856736 & -0.653429856736068 \tabularnewline
55 & 449.07 & 448.111863260411 & 0.958136739589179 \tabularnewline
56 & 449.03 & 449.082809720634 & -0.0528097206345137 \tabularnewline
57 & 448.68 & 449.66066260585 & -0.980662605849602 \tabularnewline
58 & 450.08 & 449.598952472908 & 0.481047527091562 \tabularnewline
59 & 449.96 & 450.350317126927 & -0.390317126927016 \tabularnewline
60 & 449.96 & 450.05138941415 & -0.0913894141502283 \tabularnewline
61 & 449.96 & 450.598306324134 & -0.638306324134021 \tabularnewline
62 & 452.56 & 454.588441383797 & -2.02844138379652 \tabularnewline
63 & 455.31 & 457.235508263411 & -1.92550826341085 \tabularnewline
64 & 456.2 & 458.820116407624 & -2.62011640762427 \tabularnewline
65 & 456.75 & 458.064953220463 & -1.31495322046294 \tabularnewline
66 & 457.63 & 457.555929587965 & 0.074070412034871 \tabularnewline
67 & 457.63 & 457.188937203997 & 0.441062796002882 \tabularnewline
68 & 457.65 & 457.543889592784 & 0.106110407215795 \tabularnewline
69 & 458.32 & 458.062987554546 & 0.25701244545445 \tabularnewline
70 & 459.64 & 459.283825548797 & 0.356174451202662 \tabularnewline
71 & 460.16 & 459.760798698871 & 0.399201301129267 \tabularnewline
72 & 459.89 & 460.153126614252 & -0.263126614251917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261477&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]394.57[/C][C]387.039033119658[/C][C]7.53096688034191[/C][/ROW]
[ROW][C]14[/C][C]399.57[/C][C]397.965423436219[/C][C]1.60457656378122[/C][/ROW]
[ROW][C]15[/C][C]406.13[/C][C]405.719532303584[/C][C]0.410467696415765[/C][/ROW]
[ROW][C]16[/C][C]407.03[/C][C]406.886206175075[/C][C]0.143793824925069[/C][/ROW]
[ROW][C]17[/C][C]409.46[/C][C]409.388369581518[/C][C]0.0716304184821297[/C][/ROW]
[ROW][C]18[/C][C]409.9[/C][C]409.835323541095[/C][C]0.0646764589054101[/C][/ROW]
[ROW][C]19[/C][C]409.9[/C][C]408.149216383472[/C][C]1.75078361652754[/C][/ROW]
[ROW][C]20[/C][C]410.14[/C][C]410.504414448713[/C][C]-0.364414448713262[/C][/ROW]
[ROW][C]21[/C][C]410.54[/C][C]411.174327754513[/C][C]-0.634327754513436[/C][/ROW]
[ROW][C]22[/C][C]410.69[/C][C]411.307556669673[/C][C]-0.617556669673093[/C][/ROW]
[ROW][C]23[/C][C]410.79[/C][C]410.892114174206[/C][C]-0.102114174206292[/C][/ROW]
[ROW][C]24[/C][C]410.97[/C][C]410.723457023744[/C][C]0.24654297625608[/C][/ROW]
[ROW][C]25[/C][C]410.97[/C][C]412.334536764074[/C][C]-1.36453676407427[/C][/ROW]
[ROW][C]26[/C][C]413.8[/C][C]414.960121582197[/C][C]-1.16012158219661[/C][/ROW]
[ROW][C]27[/C][C]423.31[/C][C]420.264113267309[/C][C]3.04588673269143[/C][/ROW]
[ROW][C]28[/C][C]423.85[/C][C]423.484931874929[/C][C]0.365068125071332[/C][/ROW]
[ROW][C]29[/C][C]426.6[/C][C]426.149595516402[/C][C]0.45040448359822[/C][/ROW]
[ROW][C]30[/C][C]426.26[/C][C]426.898064199397[/C][C]-0.638064199396695[/C][/ROW]
[ROW][C]31[/C][C]426.26[/C][C]424.98769032848[/C][C]1.27230967152002[/C][/ROW]
[ROW][C]32[/C][C]426.32[/C][C]426.536587015975[/C][C]-0.216587015974937[/C][/ROW]
[ROW][C]33[/C][C]427.14[/C][C]427.270656430695[/C][C]-0.130656430695183[/C][/ROW]
[ROW][C]34[/C][C]427.55[/C][C]427.810033053218[/C][C]-0.260033053218308[/C][/ROW]
[ROW][C]35[/C][C]428.29[/C][C]427.783744514376[/C][C]0.506255485623683[/C][/ROW]
[ROW][C]36[/C][C]428.8[/C][C]428.171437942371[/C][C]0.628562057629381[/C][/ROW]
[ROW][C]37[/C][C]428.8[/C][C]429.765329309479[/C][C]-0.965329309479102[/C][/ROW]
[ROW][C]38[/C][C]434.87[/C][C]432.751105690702[/C][C]2.11889430929841[/C][/ROW]
[ROW][C]39[/C][C]435.66[/C][C]441.519785087362[/C][C]-5.85978508736179[/C][/ROW]
[ROW][C]40[/C][C]440.75[/C][C]437.081737993674[/C][C]3.66826200632619[/C][/ROW]
[ROW][C]41[/C][C]440.99[/C][C]442.405075186095[/C][C]-1.41507518609529[/C][/ROW]
[ROW][C]42[/C][C]441.04[/C][C]441.443695508198[/C][C]-0.403695508198098[/C][/ROW]
[ROW][C]43[/C][C]441.04[/C][C]440.10338555563[/C][C]0.936614444370377[/C][/ROW]
[ROW][C]44[/C][C]441.88[/C][C]441.085606687952[/C][C]0.794393312048328[/C][/ROW]
[ROW][C]45[/C][C]441.92[/C][C]442.645373719596[/C][C]-0.725373719595609[/C][/ROW]
[ROW][C]46[/C][C]442.48[/C][C]442.683238398042[/C][C]-0.203238398041719[/C][/ROW]
[ROW][C]47[/C][C]442.81[/C][C]442.855852494304[/C][C]-0.0458524943042562[/C][/ROW]
[ROW][C]48[/C][C]442.81[/C][C]442.82651971237[/C][C]-0.0165197123699841[/C][/ROW]
[ROW][C]49[/C][C]442.81[/C][C]443.585287621615[/C][C]-0.775287621614609[/C][/ROW]
[ROW][C]50[/C][C]447.19[/C][C]447.340795462826[/C][C]-0.150795462826125[/C][/ROW]
[ROW][C]51[/C][C]446.52[/C][C]452.696303795063[/C][C]-6.17630379506295[/C][/ROW]
[ROW][C]52[/C][C]448.57[/C][C]449.913553947991[/C][C]-1.34355394799132[/C][/ROW]
[ROW][C]53[/C][C]448.71[/C][C]450.210749849538[/C][C]-1.50074984953795[/C][/ROW]
[ROW][C]54[/C][C]448.73[/C][C]449.383429856736[/C][C]-0.653429856736068[/C][/ROW]
[ROW][C]55[/C][C]449.07[/C][C]448.111863260411[/C][C]0.958136739589179[/C][/ROW]
[ROW][C]56[/C][C]449.03[/C][C]449.082809720634[/C][C]-0.0528097206345137[/C][/ROW]
[ROW][C]57[/C][C]448.68[/C][C]449.66066260585[/C][C]-0.980662605849602[/C][/ROW]
[ROW][C]58[/C][C]450.08[/C][C]449.598952472908[/C][C]0.481047527091562[/C][/ROW]
[ROW][C]59[/C][C]449.96[/C][C]450.350317126927[/C][C]-0.390317126927016[/C][/ROW]
[ROW][C]60[/C][C]449.96[/C][C]450.05138941415[/C][C]-0.0913894141502283[/C][/ROW]
[ROW][C]61[/C][C]449.96[/C][C]450.598306324134[/C][C]-0.638306324134021[/C][/ROW]
[ROW][C]62[/C][C]452.56[/C][C]454.588441383797[/C][C]-2.02844138379652[/C][/ROW]
[ROW][C]63[/C][C]455.31[/C][C]457.235508263411[/C][C]-1.92550826341085[/C][/ROW]
[ROW][C]64[/C][C]456.2[/C][C]458.820116407624[/C][C]-2.62011640762427[/C][/ROW]
[ROW][C]65[/C][C]456.75[/C][C]458.064953220463[/C][C]-1.31495322046294[/C][/ROW]
[ROW][C]66[/C][C]457.63[/C][C]457.555929587965[/C][C]0.074070412034871[/C][/ROW]
[ROW][C]67[/C][C]457.63[/C][C]457.188937203997[/C][C]0.441062796002882[/C][/ROW]
[ROW][C]68[/C][C]457.65[/C][C]457.543889592784[/C][C]0.106110407215795[/C][/ROW]
[ROW][C]69[/C][C]458.32[/C][C]458.062987554546[/C][C]0.25701244545445[/C][/ROW]
[ROW][C]70[/C][C]459.64[/C][C]459.283825548797[/C][C]0.356174451202662[/C][/ROW]
[ROW][C]71[/C][C]460.16[/C][C]459.760798698871[/C][C]0.399201301129267[/C][/ROW]
[ROW][C]72[/C][C]459.89[/C][C]460.153126614252[/C][C]-0.263126614251917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261477&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261477&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
13394.57387.0390331196587.53096688034191
14399.57397.9654234362191.60457656378122
15406.13405.7195323035840.410467696415765
16407.03406.8862061750750.143793824925069
17409.46409.3883695815180.0716304184821297
18409.9409.8353235410950.0646764589054101
19409.9408.1492163834721.75078361652754
20410.14410.504414448713-0.364414448713262
21410.54411.174327754513-0.634327754513436
22410.69411.307556669673-0.617556669673093
23410.79410.892114174206-0.102114174206292
24410.97410.7234570237440.24654297625608
25410.97412.334536764074-1.36453676407427
26413.8414.960121582197-1.16012158219661
27423.31420.2641132673093.04588673269143
28423.85423.4849318749290.365068125071332
29426.6426.1495955164020.45040448359822
30426.26426.898064199397-0.638064199396695
31426.26424.987690328481.27230967152002
32426.32426.536587015975-0.216587015974937
33427.14427.270656430695-0.130656430695183
34427.55427.810033053218-0.260033053218308
35428.29427.7837445143760.506255485623683
36428.8428.1714379423710.628562057629381
37428.8429.765329309479-0.965329309479102
38434.87432.7511056907022.11889430929841
39435.66441.519785087362-5.85978508736179
40440.75437.0817379936743.66826200632619
41440.99442.405075186095-1.41507518609529
42441.04441.443695508198-0.403695508198098
43441.04440.103385555630.936614444370377
44441.88441.0856066879520.794393312048328
45441.92442.645373719596-0.725373719595609
46442.48442.683238398042-0.203238398041719
47442.81442.855852494304-0.0458524943042562
48442.81442.82651971237-0.0165197123699841
49442.81443.585287621615-0.775287621614609
50447.19447.340795462826-0.150795462826125
51446.52452.696303795063-6.17630379506295
52448.57449.913553947991-1.34355394799132
53448.71450.210749849538-1.50074984953795
54448.73449.383429856736-0.653429856736068
55449.07448.1118632604110.958136739589179
56449.03449.082809720634-0.0528097206345137
57448.68449.66066260585-0.980662605849602
58450.08449.5989524729080.481047527091562
59449.96450.350317126927-0.390317126927016
60449.96450.05138941415-0.0913894141502283
61449.96450.598306324134-0.638306324134021
62452.56454.588441383797-2.02844138379652
63455.31457.235508263411-1.92550826341085
64456.2458.820116407624-2.62011640762427
65456.75458.064953220463-1.31495322046294
66457.63457.5559295879650.074070412034871
67457.63457.1889372039970.441062796002882
68457.65457.5438895927840.106110407215795
69458.32458.0629875545460.25701244545445
70459.64459.2838255487970.356174451202662
71460.16459.7607986988710.399201301129267
72459.89460.153126614252-0.263126614251917







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73460.453159755702456.856168135118464.050151376285
74464.675314751285460.06958039425469.281049108321
75468.965153601686463.534939129254474.395368074118
76471.95047415351465.80542171552478.095526591499
77473.552048999385466.767057494993480.337040503777
78474.37281451035467.003245325947481.742383694753
79474.02009432646466.109026749152481.931161903768
80473.955237288675465.537432915695482.373041661656
81474.419703115664465.523981070164483.315425161164
82475.454868577218466.10562738021484.804109774226
83475.655625245839465.873869206719485.437381284959
84475.596048951049465.400109001349485.791988900749

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 460.453159755702 & 456.856168135118 & 464.050151376285 \tabularnewline
74 & 464.675314751285 & 460.06958039425 & 469.281049108321 \tabularnewline
75 & 468.965153601686 & 463.534939129254 & 474.395368074118 \tabularnewline
76 & 471.95047415351 & 465.80542171552 & 478.095526591499 \tabularnewline
77 & 473.552048999385 & 466.767057494993 & 480.337040503777 \tabularnewline
78 & 474.37281451035 & 467.003245325947 & 481.742383694753 \tabularnewline
79 & 474.02009432646 & 466.109026749152 & 481.931161903768 \tabularnewline
80 & 473.955237288675 & 465.537432915695 & 482.373041661656 \tabularnewline
81 & 474.419703115664 & 465.523981070164 & 483.315425161164 \tabularnewline
82 & 475.454868577218 & 466.10562738021 & 484.804109774226 \tabularnewline
83 & 475.655625245839 & 465.873869206719 & 485.437381284959 \tabularnewline
84 & 475.596048951049 & 465.400109001349 & 485.791988900749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261477&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]460.453159755702[/C][C]456.856168135118[/C][C]464.050151376285[/C][/ROW]
[ROW][C]74[/C][C]464.675314751285[/C][C]460.06958039425[/C][C]469.281049108321[/C][/ROW]
[ROW][C]75[/C][C]468.965153601686[/C][C]463.534939129254[/C][C]474.395368074118[/C][/ROW]
[ROW][C]76[/C][C]471.95047415351[/C][C]465.80542171552[/C][C]478.095526591499[/C][/ROW]
[ROW][C]77[/C][C]473.552048999385[/C][C]466.767057494993[/C][C]480.337040503777[/C][/ROW]
[ROW][C]78[/C][C]474.37281451035[/C][C]467.003245325947[/C][C]481.742383694753[/C][/ROW]
[ROW][C]79[/C][C]474.02009432646[/C][C]466.109026749152[/C][C]481.931161903768[/C][/ROW]
[ROW][C]80[/C][C]473.955237288675[/C][C]465.537432915695[/C][C]482.373041661656[/C][/ROW]
[ROW][C]81[/C][C]474.419703115664[/C][C]465.523981070164[/C][C]483.315425161164[/C][/ROW]
[ROW][C]82[/C][C]475.454868577218[/C][C]466.10562738021[/C][C]484.804109774226[/C][/ROW]
[ROW][C]83[/C][C]475.655625245839[/C][C]465.873869206719[/C][C]485.437381284959[/C][/ROW]
[ROW][C]84[/C][C]475.596048951049[/C][C]465.400109001349[/C][C]485.791988900749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261477&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261477&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
73460.453159755702456.856168135118464.050151376285
74464.675314751285460.06958039425469.281049108321
75468.965153601686463.534939129254474.395368074118
76471.95047415351465.80542171552478.095526591499
77473.552048999385466.767057494993480.337040503777
78474.37281451035467.003245325947481.742383694753
79474.02009432646466.109026749152481.931161903768
80473.955237288675465.537432915695482.373041661656
81474.419703115664465.523981070164483.315425161164
82475.454868577218466.10562738021484.804109774226
83475.655625245839465.873869206719485.437381284959
84475.596048951049465.400109001349485.791988900749



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')