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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 computationTue, 21 Dec 2010 15:32:41 +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/2010/Dec/21/t1292945580ogr85u9h7cdatm8.htm/, Retrieved Sun, 19 May 2024 18:06:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113681, Retrieved Sun, 19 May 2024 18:06:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [paper- exponentia...] [2010-12-21 15:32:41] [5398da98f4f83c6a353e4d3806d4bcaa] [Current]
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Dataseries X:
631 923
654 294
671 833
586 840
600 969
625 568
558 110
630 577
628 654
603 184
656 255
600 730
670 326
678 423
641 502
625 311
628 177
589 767
582 471
636 248
599 885
621 694
637 406
595 994
696 308
674 201
648 861
649 605
672 392
598 396
613 177
638 104
615 632
634 465
638 686
604 243
706 669
677 185
644 328
644 825
605 707
600 136
612 166
599 659
634 210
618 234
613 576
627 200
668 973
651 479
619 661
644 260
579 936
601 752
595 376
588 902
634 341
594 305
606 200
610 926
633 685
639 696
659 451
593 248
606 677
599 434
569 578
629 873
613 438
604 172
658 328
612 633
707 372
739 770
777 535
685 030
730 234
714 154
630 872
719 492
677 023
679 272
718 317
645 672




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113681&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113681&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113681&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.372612088044863
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.372612088044863 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113681&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]0.372612088044863[/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=113681&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113681&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
alpha0.372612088044863
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13670326668237.2198183762088.78018162376
14678423676144.0439397752278.95606022526
15641502641317.479892395184.520107605262
16625311625905.5453581-594.545358099393
17628177628846.98828057-669.988280570717
18589767591452.903591505-1685.90359150525
19582471562903.35991048919567.6400895109
20636248640338.851852142-4090.85185214237
21599885637432.82037809-37547.8203780904
22621694597915.734668623778.2653313997
23637406657393.031473608-19987.0314736081
24595994595061.516318865932.48368113453
25696308667074.965823529233.0341765003
26674201685215.38115173-11014.3811517294
27648861644121.535169684739.46483031951
28649605629918.0518436419686.9481563602
29672392640369.29243560132022.7075643989
30598396614519.528423495-16123.5284234949
31613177593924.56759910319252.4324008974
32638104656399.557486453-18295.5574864526
33615632627210.183362094-11578.1833620943
34634465635844.94318856-1379.94318856043
35638686658490.169206887-19804.1692068871
36604243609351.44167522-5108.44167521992
37706669696869.3926515689799.60734843183
38677185682517.936367155-5332.93636715494
39644328653424.837925338-9096.83792533842
40644825643443.65129161381.34870839992
41605707654813.310587734-49106.3105877343
42600136568527.52725598831608.4727440118
43612166587912.53724820324253.4627517974
44599659628693.81652344-29034.8165234402
45634210599717.26399095834492.7360090421
46618234631916.85789054-13682.8578905402
47613576638418.732481697-24842.7324816969
48627200596622.49717821130577.5028217891
49668973706790.592195716-37817.5921957165
50651479665202.416758017-13723.4167580174
51619661630621.497558669-10960.4975586688
52644260626519.77645076817740.2235492324
53579936612309.603114105-32373.6031141051
54601752582898.10823116718853.8917688327
55595376592916.1628126582459.83718734165
56588902592144.451494083-3242.45149408269
57634341612634.86448577921706.1355142212
58594305609845.231212133-15540.2312121327
59606200608653.455634225-2453.45563422504
60610926609969.721233806956.278766193544
61633685666190.334254506-32505.3342545058
62639696641697.964758653-2001.96475865284
63659451613218.02237108546232.9776289148
64593248648433.766962864-55185.7669628644
65606677575609.67895835731067.3210416434
66599434601976.550341887-2542.55034188682
67569578593736.600279411-24158.6002794114
68629873579468.99040665350404.009593347
69613438635601.165189725-22163.1651897246
70604172593097.37993135111074.6200686492
71658328610033.10446622848294.8955337722
72612633632398.045305151-19765.0453051509
73707372659904.23097286547467.7690271351
74739770684348.2517738155421.7482261892
75777535707527.09877262770007.9012273734
76685030687972.772886987-2942.77288698684
77730234688729.20077363841504.7992263619
78714154697898.77566910516255.2243308946
79630872683101.45524303-52229.4552430304
80719492705153.98560706914338.0143929311
81677023702319.766347463-25296.7663474628
82679272679501.348109869-229.348109868704
83718317715576.6283650142740.37163498602
84645672678267.418763399-32595.4187633987

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 670326 & 668237.219818376 & 2088.78018162376 \tabularnewline
14 & 678423 & 676144.043939775 & 2278.95606022526 \tabularnewline
15 & 641502 & 641317.479892395 & 184.520107605262 \tabularnewline
16 & 625311 & 625905.5453581 & -594.545358099393 \tabularnewline
17 & 628177 & 628846.98828057 & -669.988280570717 \tabularnewline
18 & 589767 & 591452.903591505 & -1685.90359150525 \tabularnewline
19 & 582471 & 562903.359910489 & 19567.6400895109 \tabularnewline
20 & 636248 & 640338.851852142 & -4090.85185214237 \tabularnewline
21 & 599885 & 637432.82037809 & -37547.8203780904 \tabularnewline
22 & 621694 & 597915.7346686 & 23778.2653313997 \tabularnewline
23 & 637406 & 657393.031473608 & -19987.0314736081 \tabularnewline
24 & 595994 & 595061.516318865 & 932.48368113453 \tabularnewline
25 & 696308 & 667074.9658235 & 29233.0341765003 \tabularnewline
26 & 674201 & 685215.38115173 & -11014.3811517294 \tabularnewline
27 & 648861 & 644121.53516968 & 4739.46483031951 \tabularnewline
28 & 649605 & 629918.05184364 & 19686.9481563602 \tabularnewline
29 & 672392 & 640369.292435601 & 32022.7075643989 \tabularnewline
30 & 598396 & 614519.528423495 & -16123.5284234949 \tabularnewline
31 & 613177 & 593924.567599103 & 19252.4324008974 \tabularnewline
32 & 638104 & 656399.557486453 & -18295.5574864526 \tabularnewline
33 & 615632 & 627210.183362094 & -11578.1833620943 \tabularnewline
34 & 634465 & 635844.94318856 & -1379.94318856043 \tabularnewline
35 & 638686 & 658490.169206887 & -19804.1692068871 \tabularnewline
36 & 604243 & 609351.44167522 & -5108.44167521992 \tabularnewline
37 & 706669 & 696869.392651568 & 9799.60734843183 \tabularnewline
38 & 677185 & 682517.936367155 & -5332.93636715494 \tabularnewline
39 & 644328 & 653424.837925338 & -9096.83792533842 \tabularnewline
40 & 644825 & 643443.6512916 & 1381.34870839992 \tabularnewline
41 & 605707 & 654813.310587734 & -49106.3105877343 \tabularnewline
42 & 600136 & 568527.527255988 & 31608.4727440118 \tabularnewline
43 & 612166 & 587912.537248203 & 24253.4627517974 \tabularnewline
44 & 599659 & 628693.81652344 & -29034.8165234402 \tabularnewline
45 & 634210 & 599717.263990958 & 34492.7360090421 \tabularnewline
46 & 618234 & 631916.85789054 & -13682.8578905402 \tabularnewline
47 & 613576 & 638418.732481697 & -24842.7324816969 \tabularnewline
48 & 627200 & 596622.497178211 & 30577.5028217891 \tabularnewline
49 & 668973 & 706790.592195716 & -37817.5921957165 \tabularnewline
50 & 651479 & 665202.416758017 & -13723.4167580174 \tabularnewline
51 & 619661 & 630621.497558669 & -10960.4975586688 \tabularnewline
52 & 644260 & 626519.776450768 & 17740.2235492324 \tabularnewline
53 & 579936 & 612309.603114105 & -32373.6031141051 \tabularnewline
54 & 601752 & 582898.108231167 & 18853.8917688327 \tabularnewline
55 & 595376 & 592916.162812658 & 2459.83718734165 \tabularnewline
56 & 588902 & 592144.451494083 & -3242.45149408269 \tabularnewline
57 & 634341 & 612634.864485779 & 21706.1355142212 \tabularnewline
58 & 594305 & 609845.231212133 & -15540.2312121327 \tabularnewline
59 & 606200 & 608653.455634225 & -2453.45563422504 \tabularnewline
60 & 610926 & 609969.721233806 & 956.278766193544 \tabularnewline
61 & 633685 & 666190.334254506 & -32505.3342545058 \tabularnewline
62 & 639696 & 641697.964758653 & -2001.96475865284 \tabularnewline
63 & 659451 & 613218.022371085 & 46232.9776289148 \tabularnewline
64 & 593248 & 648433.766962864 & -55185.7669628644 \tabularnewline
65 & 606677 & 575609.678958357 & 31067.3210416434 \tabularnewline
66 & 599434 & 601976.550341887 & -2542.55034188682 \tabularnewline
67 & 569578 & 593736.600279411 & -24158.6002794114 \tabularnewline
68 & 629873 & 579468.990406653 & 50404.009593347 \tabularnewline
69 & 613438 & 635601.165189725 & -22163.1651897246 \tabularnewline
70 & 604172 & 593097.379931351 & 11074.6200686492 \tabularnewline
71 & 658328 & 610033.104466228 & 48294.8955337722 \tabularnewline
72 & 612633 & 632398.045305151 & -19765.0453051509 \tabularnewline
73 & 707372 & 659904.230972865 & 47467.7690271351 \tabularnewline
74 & 739770 & 684348.25177381 & 55421.7482261892 \tabularnewline
75 & 777535 & 707527.098772627 & 70007.9012273734 \tabularnewline
76 & 685030 & 687972.772886987 & -2942.77288698684 \tabularnewline
77 & 730234 & 688729.200773638 & 41504.7992263619 \tabularnewline
78 & 714154 & 697898.775669105 & 16255.2243308946 \tabularnewline
79 & 630872 & 683101.45524303 & -52229.4552430304 \tabularnewline
80 & 719492 & 705153.985607069 & 14338.0143929311 \tabularnewline
81 & 677023 & 702319.766347463 & -25296.7663474628 \tabularnewline
82 & 679272 & 679501.348109869 & -229.348109868704 \tabularnewline
83 & 718317 & 715576.628365014 & 2740.37163498602 \tabularnewline
84 & 645672 & 678267.418763399 & -32595.4187633987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113681&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]670326[/C][C]668237.219818376[/C][C]2088.78018162376[/C][/ROW]
[ROW][C]14[/C][C]678423[/C][C]676144.043939775[/C][C]2278.95606022526[/C][/ROW]
[ROW][C]15[/C][C]641502[/C][C]641317.479892395[/C][C]184.520107605262[/C][/ROW]
[ROW][C]16[/C][C]625311[/C][C]625905.5453581[/C][C]-594.545358099393[/C][/ROW]
[ROW][C]17[/C][C]628177[/C][C]628846.98828057[/C][C]-669.988280570717[/C][/ROW]
[ROW][C]18[/C][C]589767[/C][C]591452.903591505[/C][C]-1685.90359150525[/C][/ROW]
[ROW][C]19[/C][C]582471[/C][C]562903.359910489[/C][C]19567.6400895109[/C][/ROW]
[ROW][C]20[/C][C]636248[/C][C]640338.851852142[/C][C]-4090.85185214237[/C][/ROW]
[ROW][C]21[/C][C]599885[/C][C]637432.82037809[/C][C]-37547.8203780904[/C][/ROW]
[ROW][C]22[/C][C]621694[/C][C]597915.7346686[/C][C]23778.2653313997[/C][/ROW]
[ROW][C]23[/C][C]637406[/C][C]657393.031473608[/C][C]-19987.0314736081[/C][/ROW]
[ROW][C]24[/C][C]595994[/C][C]595061.516318865[/C][C]932.48368113453[/C][/ROW]
[ROW][C]25[/C][C]696308[/C][C]667074.9658235[/C][C]29233.0341765003[/C][/ROW]
[ROW][C]26[/C][C]674201[/C][C]685215.38115173[/C][C]-11014.3811517294[/C][/ROW]
[ROW][C]27[/C][C]648861[/C][C]644121.53516968[/C][C]4739.46483031951[/C][/ROW]
[ROW][C]28[/C][C]649605[/C][C]629918.05184364[/C][C]19686.9481563602[/C][/ROW]
[ROW][C]29[/C][C]672392[/C][C]640369.292435601[/C][C]32022.7075643989[/C][/ROW]
[ROW][C]30[/C][C]598396[/C][C]614519.528423495[/C][C]-16123.5284234949[/C][/ROW]
[ROW][C]31[/C][C]613177[/C][C]593924.567599103[/C][C]19252.4324008974[/C][/ROW]
[ROW][C]32[/C][C]638104[/C][C]656399.557486453[/C][C]-18295.5574864526[/C][/ROW]
[ROW][C]33[/C][C]615632[/C][C]627210.183362094[/C][C]-11578.1833620943[/C][/ROW]
[ROW][C]34[/C][C]634465[/C][C]635844.94318856[/C][C]-1379.94318856043[/C][/ROW]
[ROW][C]35[/C][C]638686[/C][C]658490.169206887[/C][C]-19804.1692068871[/C][/ROW]
[ROW][C]36[/C][C]604243[/C][C]609351.44167522[/C][C]-5108.44167521992[/C][/ROW]
[ROW][C]37[/C][C]706669[/C][C]696869.392651568[/C][C]9799.60734843183[/C][/ROW]
[ROW][C]38[/C][C]677185[/C][C]682517.936367155[/C][C]-5332.93636715494[/C][/ROW]
[ROW][C]39[/C][C]644328[/C][C]653424.837925338[/C][C]-9096.83792533842[/C][/ROW]
[ROW][C]40[/C][C]644825[/C][C]643443.6512916[/C][C]1381.34870839992[/C][/ROW]
[ROW][C]41[/C][C]605707[/C][C]654813.310587734[/C][C]-49106.3105877343[/C][/ROW]
[ROW][C]42[/C][C]600136[/C][C]568527.527255988[/C][C]31608.4727440118[/C][/ROW]
[ROW][C]43[/C][C]612166[/C][C]587912.537248203[/C][C]24253.4627517974[/C][/ROW]
[ROW][C]44[/C][C]599659[/C][C]628693.81652344[/C][C]-29034.8165234402[/C][/ROW]
[ROW][C]45[/C][C]634210[/C][C]599717.263990958[/C][C]34492.7360090421[/C][/ROW]
[ROW][C]46[/C][C]618234[/C][C]631916.85789054[/C][C]-13682.8578905402[/C][/ROW]
[ROW][C]47[/C][C]613576[/C][C]638418.732481697[/C][C]-24842.7324816969[/C][/ROW]
[ROW][C]48[/C][C]627200[/C][C]596622.497178211[/C][C]30577.5028217891[/C][/ROW]
[ROW][C]49[/C][C]668973[/C][C]706790.592195716[/C][C]-37817.5921957165[/C][/ROW]
[ROW][C]50[/C][C]651479[/C][C]665202.416758017[/C][C]-13723.4167580174[/C][/ROW]
[ROW][C]51[/C][C]619661[/C][C]630621.497558669[/C][C]-10960.4975586688[/C][/ROW]
[ROW][C]52[/C][C]644260[/C][C]626519.776450768[/C][C]17740.2235492324[/C][/ROW]
[ROW][C]53[/C][C]579936[/C][C]612309.603114105[/C][C]-32373.6031141051[/C][/ROW]
[ROW][C]54[/C][C]601752[/C][C]582898.108231167[/C][C]18853.8917688327[/C][/ROW]
[ROW][C]55[/C][C]595376[/C][C]592916.162812658[/C][C]2459.83718734165[/C][/ROW]
[ROW][C]56[/C][C]588902[/C][C]592144.451494083[/C][C]-3242.45149408269[/C][/ROW]
[ROW][C]57[/C][C]634341[/C][C]612634.864485779[/C][C]21706.1355142212[/C][/ROW]
[ROW][C]58[/C][C]594305[/C][C]609845.231212133[/C][C]-15540.2312121327[/C][/ROW]
[ROW][C]59[/C][C]606200[/C][C]608653.455634225[/C][C]-2453.45563422504[/C][/ROW]
[ROW][C]60[/C][C]610926[/C][C]609969.721233806[/C][C]956.278766193544[/C][/ROW]
[ROW][C]61[/C][C]633685[/C][C]666190.334254506[/C][C]-32505.3342545058[/C][/ROW]
[ROW][C]62[/C][C]639696[/C][C]641697.964758653[/C][C]-2001.96475865284[/C][/ROW]
[ROW][C]63[/C][C]659451[/C][C]613218.022371085[/C][C]46232.9776289148[/C][/ROW]
[ROW][C]64[/C][C]593248[/C][C]648433.766962864[/C][C]-55185.7669628644[/C][/ROW]
[ROW][C]65[/C][C]606677[/C][C]575609.678958357[/C][C]31067.3210416434[/C][/ROW]
[ROW][C]66[/C][C]599434[/C][C]601976.550341887[/C][C]-2542.55034188682[/C][/ROW]
[ROW][C]67[/C][C]569578[/C][C]593736.600279411[/C][C]-24158.6002794114[/C][/ROW]
[ROW][C]68[/C][C]629873[/C][C]579468.990406653[/C][C]50404.009593347[/C][/ROW]
[ROW][C]69[/C][C]613438[/C][C]635601.165189725[/C][C]-22163.1651897246[/C][/ROW]
[ROW][C]70[/C][C]604172[/C][C]593097.379931351[/C][C]11074.6200686492[/C][/ROW]
[ROW][C]71[/C][C]658328[/C][C]610033.104466228[/C][C]48294.8955337722[/C][/ROW]
[ROW][C]72[/C][C]612633[/C][C]632398.045305151[/C][C]-19765.0453051509[/C][/ROW]
[ROW][C]73[/C][C]707372[/C][C]659904.230972865[/C][C]47467.7690271351[/C][/ROW]
[ROW][C]74[/C][C]739770[/C][C]684348.25177381[/C][C]55421.7482261892[/C][/ROW]
[ROW][C]75[/C][C]777535[/C][C]707527.098772627[/C][C]70007.9012273734[/C][/ROW]
[ROW][C]76[/C][C]685030[/C][C]687972.772886987[/C][C]-2942.77288698684[/C][/ROW]
[ROW][C]77[/C][C]730234[/C][C]688729.200773638[/C][C]41504.7992263619[/C][/ROW]
[ROW][C]78[/C][C]714154[/C][C]697898.775669105[/C][C]16255.2243308946[/C][/ROW]
[ROW][C]79[/C][C]630872[/C][C]683101.45524303[/C][C]-52229.4552430304[/C][/ROW]
[ROW][C]80[/C][C]719492[/C][C]705153.985607069[/C][C]14338.0143929311[/C][/ROW]
[ROW][C]81[/C][C]677023[/C][C]702319.766347463[/C][C]-25296.7663474628[/C][/ROW]
[ROW][C]82[/C][C]679272[/C][C]679501.348109869[/C][C]-229.348109868704[/C][/ROW]
[ROW][C]83[/C][C]718317[/C][C]715576.628365014[/C][C]2740.37163498602[/C][/ROW]
[ROW][C]84[/C][C]645672[/C][C]678267.418763399[/C][C]-32595.4187633987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113681&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113681&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
13670326668237.2198183762088.78018162376
14678423676144.0439397752278.95606022526
15641502641317.479892395184.520107605262
16625311625905.5453581-594.545358099393
17628177628846.98828057-669.988280570717
18589767591452.903591505-1685.90359150525
19582471562903.35991048919567.6400895109
20636248640338.851852142-4090.85185214237
21599885637432.82037809-37547.8203780904
22621694597915.734668623778.2653313997
23637406657393.031473608-19987.0314736081
24595994595061.516318865932.48368113453
25696308667074.965823529233.0341765003
26674201685215.38115173-11014.3811517294
27648861644121.535169684739.46483031951
28649605629918.0518436419686.9481563602
29672392640369.29243560132022.7075643989
30598396614519.528423495-16123.5284234949
31613177593924.56759910319252.4324008974
32638104656399.557486453-18295.5574864526
33615632627210.183362094-11578.1833620943
34634465635844.94318856-1379.94318856043
35638686658490.169206887-19804.1692068871
36604243609351.44167522-5108.44167521992
37706669696869.3926515689799.60734843183
38677185682517.936367155-5332.93636715494
39644328653424.837925338-9096.83792533842
40644825643443.65129161381.34870839992
41605707654813.310587734-49106.3105877343
42600136568527.52725598831608.4727440118
43612166587912.53724820324253.4627517974
44599659628693.81652344-29034.8165234402
45634210599717.26399095834492.7360090421
46618234631916.85789054-13682.8578905402
47613576638418.732481697-24842.7324816969
48627200596622.49717821130577.5028217891
49668973706790.592195716-37817.5921957165
50651479665202.416758017-13723.4167580174
51619661630621.497558669-10960.4975586688
52644260626519.77645076817740.2235492324
53579936612309.603114105-32373.6031141051
54601752582898.10823116718853.8917688327
55595376592916.1628126582459.83718734165
56588902592144.451494083-3242.45149408269
57634341612634.86448577921706.1355142212
58594305609845.231212133-15540.2312121327
59606200608653.455634225-2453.45563422504
60610926609969.721233806956.278766193544
61633685666190.334254506-32505.3342545058
62639696641697.964758653-2001.96475865284
63659451613218.02237108546232.9776289148
64593248648433.766962864-55185.7669628644
65606677575609.67895835731067.3210416434
66599434601976.550341887-2542.55034188682
67569578593736.600279411-24158.6002794114
68629873579468.99040665350404.009593347
69613438635601.165189725-22163.1651897246
70604172593097.37993135111074.6200686492
71658328610033.10446622848294.8955337722
72612633632398.045305151-19765.0453051509
73707372659904.23097286547467.7690271351
74739770684348.2517738155421.7482261892
75777535707527.09877262770007.9012273734
76685030687972.772886987-2942.77288698684
77730234688729.20077363841504.7992263619
78714154697898.77566910516255.2243308946
79630872683101.45524303-52229.4552430304
80719492705153.98560706914338.0143929311
81677023702319.766347463-25296.7663474628
82679272679501.348109869-229.348109868704
83718317715576.6283650142740.37163498602
84645672678267.418763399-32595.4187633987







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85743173.90718524691554.613566771794793.200803709
86754921.093855583699834.82349248810007.364218685
87766600.303599613708252.699609698824947.907589527
88675191.816349674613755.763414846736627.869284503
89704930.626446057640554.122121435769307.130770679
90682793.733366484615605.341378692749982.125354277
91618973.059742036549085.82394928688860.295534792
92702250.542260668629764.878605022774736.205916314
93669207.423190179594213.309124831744201.537255528
94671541.881068287594120.547746691748963.214389882
95709565.785471356629791.049106133789340.521836578
96649066.232517482567005.558190568731126.906844396

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 743173.90718524 & 691554.613566771 & 794793.200803709 \tabularnewline
86 & 754921.093855583 & 699834.82349248 & 810007.364218685 \tabularnewline
87 & 766600.303599613 & 708252.699609698 & 824947.907589527 \tabularnewline
88 & 675191.816349674 & 613755.763414846 & 736627.869284503 \tabularnewline
89 & 704930.626446057 & 640554.122121435 & 769307.130770679 \tabularnewline
90 & 682793.733366484 & 615605.341378692 & 749982.125354277 \tabularnewline
91 & 618973.059742036 & 549085.82394928 & 688860.295534792 \tabularnewline
92 & 702250.542260668 & 629764.878605022 & 774736.205916314 \tabularnewline
93 & 669207.423190179 & 594213.309124831 & 744201.537255528 \tabularnewline
94 & 671541.881068287 & 594120.547746691 & 748963.214389882 \tabularnewline
95 & 709565.785471356 & 629791.049106133 & 789340.521836578 \tabularnewline
96 & 649066.232517482 & 567005.558190568 & 731126.906844396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113681&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]85[/C][C]743173.90718524[/C][C]691554.613566771[/C][C]794793.200803709[/C][/ROW]
[ROW][C]86[/C][C]754921.093855583[/C][C]699834.82349248[/C][C]810007.364218685[/C][/ROW]
[ROW][C]87[/C][C]766600.303599613[/C][C]708252.699609698[/C][C]824947.907589527[/C][/ROW]
[ROW][C]88[/C][C]675191.816349674[/C][C]613755.763414846[/C][C]736627.869284503[/C][/ROW]
[ROW][C]89[/C][C]704930.626446057[/C][C]640554.122121435[/C][C]769307.130770679[/C][/ROW]
[ROW][C]90[/C][C]682793.733366484[/C][C]615605.341378692[/C][C]749982.125354277[/C][/ROW]
[ROW][C]91[/C][C]618973.059742036[/C][C]549085.82394928[/C][C]688860.295534792[/C][/ROW]
[ROW][C]92[/C][C]702250.542260668[/C][C]629764.878605022[/C][C]774736.205916314[/C][/ROW]
[ROW][C]93[/C][C]669207.423190179[/C][C]594213.309124831[/C][C]744201.537255528[/C][/ROW]
[ROW][C]94[/C][C]671541.881068287[/C][C]594120.547746691[/C][C]748963.214389882[/C][/ROW]
[ROW][C]95[/C][C]709565.785471356[/C][C]629791.049106133[/C][C]789340.521836578[/C][/ROW]
[ROW][C]96[/C][C]649066.232517482[/C][C]567005.558190568[/C][C]731126.906844396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113681&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113681&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
85743173.90718524691554.613566771794793.200803709
86754921.093855583699834.82349248810007.364218685
87766600.303599613708252.699609698824947.907589527
88675191.816349674613755.763414846736627.869284503
89704930.626446057640554.122121435769307.130770679
90682793.733366484615605.341378692749982.125354277
91618973.059742036549085.82394928688860.295534792
92702250.542260668629764.878605022774736.205916314
93669207.423190179594213.309124831744201.537255528
94671541.881068287594120.547746691748963.214389882
95709565.785471356629791.049106133789340.521836578
96649066.232517482567005.558190568731126.906844396



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')