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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 computationWed, 30 Nov 2011 08:48:45 -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/30/t1322660941dcfstu2y2scfv0j.htm/, Retrieved Fri, 29 Mar 2024 08:02:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148964, Retrieved Fri, 29 Mar 2024 08:02:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP           [Exponential Smoothing] [Exponential Smoot...] [2011-11-30 13:48:45] [76fd4dc79b6db5fbcdab5e105f7c78f7] [Current]
- RM              [Exponential Smoothing] [Paper deel 2d] [2011-12-19 22:08:13] [3346191a817a30d0b56421a47a7031a4]
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Dataseries X:
9700
9081
9084
9743
8587
9731
9563
9998
9437
10038
9918
9252
9737
9035
9133
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148964&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148964&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148964&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.11479686325585
beta0.182276928636091
gamma0.552028525015516

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.11479686325585 \tabularnewline
beta & 0.182276928636091 \tabularnewline
gamma & 0.552028525015516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148964&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]0.11479686325585[/C][/ROW]
[ROW][C]beta[/C][C]0.182276928636091[/C][/ROW]
[ROW][C]gamma[/C][C]0.552028525015516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148964&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148964&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
alpha0.11479686325585
beta0.182276928636091
gamma0.552028525015516







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397379769.78069418617-32.7806941861727
1490359093.31591227235-58.3159122723482
1591339215.67915722477-82.6791572247748
1694879566.4756962004-79.475696200403
1787008753.67194272757-53.6719427275657
1896279659.47888224219-32.4788822421888
1989479350.82964679519-403.829646795191
2092839688.29629330246-405.296293302461
2188299055.06877606413-226.068776064132
2299479559.30462733899387.695372661006
2396289450.02965532102177.970344678983
2493188795.73144049256522.268559507442
2596059305.11634733775299.883652662253
2686408683.02673791596-43.0267379159613
2792148790.39426326323423.605736736774
2895679199.17940140452367.820598595485
2985478492.3955164358454.6044835641605
3091859421.14866180949-236.14866180949
3194708937.60742360967532.392576390328
3291239416.30780748961-293.307807489606
3392788926.70135317381351.29864682619
34101709858.85165227366311.148347726339
3594349690.76166407156-256.761664071561
3696559191.43644336361463.563556636391
3794299633.91207261327-204.91207261327
3887398805.93614542596-66.9361454259579
3995529174.25034323883377.749656761171
4096879587.135014051399.8649859486995
4190198702.36240765303316.637592346971
4296729569.24247373369102.757526266312
4392069533.565340431-327.565340431001
4490699529.10504364352-460.105043643516
4597889346.48317982708441.516820172916
461031210312.1941514859-0.19415148594635
47101059829.08633616261275.913663837389
4898639759.7848112513103.215188748703
4996569850.2062507638-194.206250763798
5092959079.6275415155215.372458484502
5199469740.26702875184205.732971248157
52970110023.4477784244-322.447778424379
5390499175.04657773491-126.046577734909
54101909906.03808865092283.961911349083
5597069673.3246606463332.6753393536746
5697659651.81359392721113.186406072788
57989310009.7694134686-116.769413468601
58999410733.3832933416-739.383293341622
591043310283.3685553516149.631444648445
601007310101.6100230068-28.6100230068132
611011210018.946343813793.0536561862737
6292669460.26384711883-194.263847118831
63982010070.9014034058-250.901403405782
641009710019.923130731777.0768692682614
6591159285.06041473299-170.060414732989
661041110212.2471979522198.75280204782
6796789823.76969799112-145.769697991118
68104089800.50024362214607.499756377858
691015310095.607330046157.3926699539279
701036810531.7503165482-163.750316548214
711058110587.944643106-6.94464310599506
721059710296.1614075979300.838592402088
731068010317.9752465686362.024753431351
7497389641.7787903481796.2212096518288
75955610297.302030776-741.302030776027

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9737 & 9769.78069418617 & -32.7806941861727 \tabularnewline
14 & 9035 & 9093.31591227235 & -58.3159122723482 \tabularnewline
15 & 9133 & 9215.67915722477 & -82.6791572247748 \tabularnewline
16 & 9487 & 9566.4756962004 & -79.475696200403 \tabularnewline
17 & 8700 & 8753.67194272757 & -53.6719427275657 \tabularnewline
18 & 9627 & 9659.47888224219 & -32.4788822421888 \tabularnewline
19 & 8947 & 9350.82964679519 & -403.829646795191 \tabularnewline
20 & 9283 & 9688.29629330246 & -405.296293302461 \tabularnewline
21 & 8829 & 9055.06877606413 & -226.068776064132 \tabularnewline
22 & 9947 & 9559.30462733899 & 387.695372661006 \tabularnewline
23 & 9628 & 9450.02965532102 & 177.970344678983 \tabularnewline
24 & 9318 & 8795.73144049256 & 522.268559507442 \tabularnewline
25 & 9605 & 9305.11634733775 & 299.883652662253 \tabularnewline
26 & 8640 & 8683.02673791596 & -43.0267379159613 \tabularnewline
27 & 9214 & 8790.39426326323 & 423.605736736774 \tabularnewline
28 & 9567 & 9199.17940140452 & 367.820598595485 \tabularnewline
29 & 8547 & 8492.39551643584 & 54.6044835641605 \tabularnewline
30 & 9185 & 9421.14866180949 & -236.14866180949 \tabularnewline
31 & 9470 & 8937.60742360967 & 532.392576390328 \tabularnewline
32 & 9123 & 9416.30780748961 & -293.307807489606 \tabularnewline
33 & 9278 & 8926.70135317381 & 351.29864682619 \tabularnewline
34 & 10170 & 9858.85165227366 & 311.148347726339 \tabularnewline
35 & 9434 & 9690.76166407156 & -256.761664071561 \tabularnewline
36 & 9655 & 9191.43644336361 & 463.563556636391 \tabularnewline
37 & 9429 & 9633.91207261327 & -204.91207261327 \tabularnewline
38 & 8739 & 8805.93614542596 & -66.9361454259579 \tabularnewline
39 & 9552 & 9174.25034323883 & 377.749656761171 \tabularnewline
40 & 9687 & 9587.1350140513 & 99.8649859486995 \tabularnewline
41 & 9019 & 8702.36240765303 & 316.637592346971 \tabularnewline
42 & 9672 & 9569.24247373369 & 102.757526266312 \tabularnewline
43 & 9206 & 9533.565340431 & -327.565340431001 \tabularnewline
44 & 9069 & 9529.10504364352 & -460.105043643516 \tabularnewline
45 & 9788 & 9346.48317982708 & 441.516820172916 \tabularnewline
46 & 10312 & 10312.1941514859 & -0.19415148594635 \tabularnewline
47 & 10105 & 9829.08633616261 & 275.913663837389 \tabularnewline
48 & 9863 & 9759.7848112513 & 103.215188748703 \tabularnewline
49 & 9656 & 9850.2062507638 & -194.206250763798 \tabularnewline
50 & 9295 & 9079.6275415155 & 215.372458484502 \tabularnewline
51 & 9946 & 9740.26702875184 & 205.732971248157 \tabularnewline
52 & 9701 & 10023.4477784244 & -322.447778424379 \tabularnewline
53 & 9049 & 9175.04657773491 & -126.046577734909 \tabularnewline
54 & 10190 & 9906.03808865092 & 283.961911349083 \tabularnewline
55 & 9706 & 9673.32466064633 & 32.6753393536746 \tabularnewline
56 & 9765 & 9651.81359392721 & 113.186406072788 \tabularnewline
57 & 9893 & 10009.7694134686 & -116.769413468601 \tabularnewline
58 & 9994 & 10733.3832933416 & -739.383293341622 \tabularnewline
59 & 10433 & 10283.3685553516 & 149.631444648445 \tabularnewline
60 & 10073 & 10101.6100230068 & -28.6100230068132 \tabularnewline
61 & 10112 & 10018.9463438137 & 93.0536561862737 \tabularnewline
62 & 9266 & 9460.26384711883 & -194.263847118831 \tabularnewline
63 & 9820 & 10070.9014034058 & -250.901403405782 \tabularnewline
64 & 10097 & 10019.9231307317 & 77.0768692682614 \tabularnewline
65 & 9115 & 9285.06041473299 & -170.060414732989 \tabularnewline
66 & 10411 & 10212.2471979522 & 198.75280204782 \tabularnewline
67 & 9678 & 9823.76969799112 & -145.769697991118 \tabularnewline
68 & 10408 & 9800.50024362214 & 607.499756377858 \tabularnewline
69 & 10153 & 10095.6073300461 & 57.3926699539279 \tabularnewline
70 & 10368 & 10531.7503165482 & -163.750316548214 \tabularnewline
71 & 10581 & 10587.944643106 & -6.94464310599506 \tabularnewline
72 & 10597 & 10296.1614075979 & 300.838592402088 \tabularnewline
73 & 10680 & 10317.9752465686 & 362.024753431351 \tabularnewline
74 & 9738 & 9641.77879034817 & 96.2212096518288 \tabularnewline
75 & 9556 & 10297.302030776 & -741.302030776027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148964&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]9737[/C][C]9769.78069418617[/C][C]-32.7806941861727[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9093.31591227235[/C][C]-58.3159122723482[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9215.67915722477[/C][C]-82.6791572247748[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9566.4756962004[/C][C]-79.475696200403[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]8753.67194272757[/C][C]-53.6719427275657[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]9659.47888224219[/C][C]-32.4788822421888[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9350.82964679519[/C][C]-403.829646795191[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9688.29629330246[/C][C]-405.296293302461[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9055.06877606413[/C][C]-226.068776064132[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]9559.30462733899[/C][C]387.695372661006[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9450.02965532102[/C][C]177.970344678983[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]8795.73144049256[/C][C]522.268559507442[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9305.11634733775[/C][C]299.883652662253[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]8683.02673791596[/C][C]-43.0267379159613[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]8790.39426326323[/C][C]423.605736736774[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9199.17940140452[/C][C]367.820598595485[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]8492.39551643584[/C][C]54.6044835641605[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]9421.14866180949[/C][C]-236.14866180949[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]8937.60742360967[/C][C]532.392576390328[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9416.30780748961[/C][C]-293.307807489606[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]8926.70135317381[/C][C]351.29864682619[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9858.85165227366[/C][C]311.148347726339[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9690.76166407156[/C][C]-256.761664071561[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9191.43644336361[/C][C]463.563556636391[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9633.91207261327[/C][C]-204.91207261327[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]8805.93614542596[/C][C]-66.9361454259579[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9174.25034323883[/C][C]377.749656761171[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9587.1350140513[/C][C]99.8649859486995[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]8702.36240765303[/C][C]316.637592346971[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9569.24247373369[/C][C]102.757526266312[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9533.565340431[/C][C]-327.565340431001[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9529.10504364352[/C][C]-460.105043643516[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9346.48317982708[/C][C]441.516820172916[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]10312.1941514859[/C][C]-0.19415148594635[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]9829.08633616261[/C][C]275.913663837389[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]9759.7848112513[/C][C]103.215188748703[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]9850.2062507638[/C][C]-194.206250763798[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9079.6275415155[/C][C]215.372458484502[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9740.26702875184[/C][C]205.732971248157[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]10023.4477784244[/C][C]-322.447778424379[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9175.04657773491[/C][C]-126.046577734909[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9906.03808865092[/C][C]283.961911349083[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9673.32466064633[/C][C]32.6753393536746[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9651.81359392721[/C][C]113.186406072788[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]10009.7694134686[/C][C]-116.769413468601[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]10733.3832933416[/C][C]-739.383293341622[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]10283.3685553516[/C][C]149.631444648445[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]10101.6100230068[/C][C]-28.6100230068132[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]10018.9463438137[/C][C]93.0536561862737[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]9460.26384711883[/C][C]-194.263847118831[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]10070.9014034058[/C][C]-250.901403405782[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]10019.9231307317[/C][C]77.0768692682614[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9285.06041473299[/C][C]-170.060414732989[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]10212.2471979522[/C][C]198.75280204782[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9823.76969799112[/C][C]-145.769697991118[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]9800.50024362214[/C][C]607.499756377858[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]10095.6073300461[/C][C]57.3926699539279[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10531.7503165482[/C][C]-163.750316548214[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10587.944643106[/C][C]-6.94464310599506[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10296.1614075979[/C][C]300.838592402088[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10317.9752465686[/C][C]362.024753431351[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]9641.77879034817[/C][C]96.2212096518288[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10297.302030776[/C][C]-741.302030776027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148964&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148964&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
1397379769.78069418617-32.7806941861727
1490359093.31591227235-58.3159122723482
1591339215.67915722477-82.6791572247748
1694879566.4756962004-79.475696200403
1787008753.67194272757-53.6719427275657
1896279659.47888224219-32.4788822421888
1989479350.82964679519-403.829646795191
2092839688.29629330246-405.296293302461
2188299055.06877606413-226.068776064132
2299479559.30462733899387.695372661006
2396289450.02965532102177.970344678983
2493188795.73144049256522.268559507442
2596059305.11634733775299.883652662253
2686408683.02673791596-43.0267379159613
2792148790.39426326323423.605736736774
2895679199.17940140452367.820598595485
2985478492.3955164358454.6044835641605
3091859421.14866180949-236.14866180949
3194708937.60742360967532.392576390328
3291239416.30780748961-293.307807489606
3392788926.70135317381351.29864682619
34101709858.85165227366311.148347726339
3594349690.76166407156-256.761664071561
3696559191.43644336361463.563556636391
3794299633.91207261327-204.91207261327
3887398805.93614542596-66.9361454259579
3995529174.25034323883377.749656761171
4096879587.135014051399.8649859486995
4190198702.36240765303316.637592346971
4296729569.24247373369102.757526266312
4392069533.565340431-327.565340431001
4490699529.10504364352-460.105043643516
4597889346.48317982708441.516820172916
461031210312.1941514859-0.19415148594635
47101059829.08633616261275.913663837389
4898639759.7848112513103.215188748703
4996569850.2062507638-194.206250763798
5092959079.6275415155215.372458484502
5199469740.26702875184205.732971248157
52970110023.4477784244-322.447778424379
5390499175.04657773491-126.046577734909
54101909906.03808865092283.961911349083
5597069673.3246606463332.6753393536746
5697659651.81359392721113.186406072788
57989310009.7694134686-116.769413468601
58999410733.3832933416-739.383293341622
591043310283.3685553516149.631444648445
601007310101.6100230068-28.6100230068132
611011210018.946343813793.0536561862737
6292669460.26384711883-194.263847118831
63982010070.9014034058-250.901403405782
641009710019.923130731777.0768692682614
6591159285.06041473299-170.060414732989
661041110212.2471979522198.75280204782
6796789823.76969799112-145.769697991118
68104089800.50024362214607.499756377858
691015310095.607330046157.3926699539279
701036810531.7503165482-163.750316548214
711058110587.944643106-6.94464310599506
721059710296.1614075979300.838592402088
731068010317.9752465686362.024753431351
7497389641.7787903481796.2212096518288
75955610297.302030776-741.302030776027







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7610363.853384048510016.406534828610711.3002332684
779480.821328219089126.125878359179835.516778079
7810656.234050279210286.189003963811026.2790965946
7910065.60119551279684.8360492544610446.3663417709
8010448.027722160310047.237088711210848.8183556094
8110400.77751793059980.7507613897710820.8042744712
8210726.795950062310279.026802961611174.565097163
8310882.225555046710405.527708567111358.9234015263
8410736.866235886110235.128184853211238.6042869191
8510746.975279558510214.563685046111279.3868740709
869869.056694205639332.3479543543110405.7654340569
8710089.7332207639629.7716139714110549.6948275547

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 10363.8533840485 & 10016.4065348286 & 10711.3002332684 \tabularnewline
77 & 9480.82132821908 & 9126.12587835917 & 9835.516778079 \tabularnewline
78 & 10656.2340502792 & 10286.1890039638 & 11026.2790965946 \tabularnewline
79 & 10065.6011955127 & 9684.83604925446 & 10446.3663417709 \tabularnewline
80 & 10448.0277221603 & 10047.2370887112 & 10848.8183556094 \tabularnewline
81 & 10400.7775179305 & 9980.75076138977 & 10820.8042744712 \tabularnewline
82 & 10726.7959500623 & 10279.0268029616 & 11174.565097163 \tabularnewline
83 & 10882.2255550467 & 10405.5277085671 & 11358.9234015263 \tabularnewline
84 & 10736.8662358861 & 10235.1281848532 & 11238.6042869191 \tabularnewline
85 & 10746.9752795585 & 10214.5636850461 & 11279.3868740709 \tabularnewline
86 & 9869.05669420563 & 9332.34795435431 & 10405.7654340569 \tabularnewline
87 & 10089.733220763 & 9629.77161397141 & 10549.6948275547 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148964&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]76[/C][C]10363.8533840485[/C][C]10016.4065348286[/C][C]10711.3002332684[/C][/ROW]
[ROW][C]77[/C][C]9480.82132821908[/C][C]9126.12587835917[/C][C]9835.516778079[/C][/ROW]
[ROW][C]78[/C][C]10656.2340502792[/C][C]10286.1890039638[/C][C]11026.2790965946[/C][/ROW]
[ROW][C]79[/C][C]10065.6011955127[/C][C]9684.83604925446[/C][C]10446.3663417709[/C][/ROW]
[ROW][C]80[/C][C]10448.0277221603[/C][C]10047.2370887112[/C][C]10848.8183556094[/C][/ROW]
[ROW][C]81[/C][C]10400.7775179305[/C][C]9980.75076138977[/C][C]10820.8042744712[/C][/ROW]
[ROW][C]82[/C][C]10726.7959500623[/C][C]10279.0268029616[/C][C]11174.565097163[/C][/ROW]
[ROW][C]83[/C][C]10882.2255550467[/C][C]10405.5277085671[/C][C]11358.9234015263[/C][/ROW]
[ROW][C]84[/C][C]10736.8662358861[/C][C]10235.1281848532[/C][C]11238.6042869191[/C][/ROW]
[ROW][C]85[/C][C]10746.9752795585[/C][C]10214.5636850461[/C][C]11279.3868740709[/C][/ROW]
[ROW][C]86[/C][C]9869.05669420563[/C][C]9332.34795435431[/C][C]10405.7654340569[/C][/ROW]
[ROW][C]87[/C][C]10089.733220763[/C][C]9629.77161397141[/C][C]10549.6948275547[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148964&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148964&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
7610363.853384048510016.406534828610711.3002332684
779480.821328219089126.125878359179835.516778079
7810656.234050279210286.189003963811026.2790965946
7910065.60119551279684.8360492544610446.3663417709
8010448.027722160310047.237088711210848.8183556094
8110400.77751793059980.7507613897710820.8042744712
8210726.795950062310279.026802961611174.565097163
8310882.225555046710405.527708567111358.9234015263
8410736.866235886110235.128184853211238.6042869191
8510746.975279558510214.563685046111279.3868740709
869869.056694205639332.3479543543110405.7654340569
8710089.7332207639629.7716139714110549.6948275547



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