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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 computationThu, 09 Dec 2010 16:33:47 +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/09/t1291912459sjh3y2xuefxyyvp.htm/, Retrieved Sun, 28 Apr 2024 22:21:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107260, Retrieved Sun, 28 Apr 2024 22:21:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145
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   [Decomposition by Loess] [] [2010-12-07 11:51:00] [9315c5fa5df29386545a575306c6a452]
- RMPD      [Exponential Smoothing] [ES triple additive] [2010-12-09 16:33:47] [be9b1effb945c5b0652fb49bcca5faef] [Current]
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Dataseries X:
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107260&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]3 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=107260&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107260&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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.352911347621157
beta0
gamma0.797570196930633

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.352911347621157 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.797570196930633 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107260&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]0.352911347621157[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.797570196930633[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107260&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107260&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
alpha0.352911347621157
beta0
gamma0.797570196930633







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132802926890.14449786331138.85550213675
142938328873.9145686606509.08543133935
153643836198.8066350815239.193364918538
163203432052.0340619628-18.0340619627750
172267922785.8580109783-106.858010978282
182431924450.2933137790-131.293313779031
191800422477.4384542722-4473.43845427217
201753717382.2329683339154.767031666121
212036619775.4987175057590.5012824943
222278224048.8316950087-1266.83169500866
231916915781.60745510653387.39254489350
241380714840.1200971726-1033.12009717260
252974327729.30375636852013.69624363149
262559129696.7915852829-4105.79158528287
272909635253.7502605778-6157.75026057778
282648228716.6689708834-2234.66897088342
292240518622.37538915053782.62461084946
302704421646.84221941935397.15778058068
311797019384.0653540573-1414.06535405733
321873017757.1578342543972.842165745667
331968420664.0134286921-980.013428692135
341978523424.5269491807-3639.52694918066
351847916721.99035521351757.00964478651
361069812923.7018793200-2225.70187932005
373195626964.46761542344991.53238457656
382950626824.60836230092681.39163769914
393450633717.8279667315788.172033268536
402716531656.7383293261-4491.73832932611
412673623871.41629582182864.58370417816
422369127405.1544197002-3714.15441970022
431815718411.6292002137-254.629200213651
441732818425.7795423136-1097.77954231358
451820519594.0231543635-1389.02315436350
462099520837.6212331827157.37876681731
471738218260.2008622619-878.20086226186
48936711476.4447580411-2109.44475804115
493112429283.04362351421840.95637648576
502655126839.0498850930-288.049885093045
513065131707.2318474280-1056.23184742796
522585926270.2766784284-411.276678428389
532510023721.58354358461378.41645641538
542577823335.55868847092442.44131152914
552041818300.22217040792117.77782959211
561868818716.473143196-28.4731431959917
572042420111.7766901771312.22330982293
582477622753.85985484022022.14014515975
591981420300.0737134258-486.073713425802
601273813019.2604494312-281.260449431165
613156633509.842892375-1943.84289237502
623011128631.37334160931479.62665839066
633001933726.9307613903-3707.93076139034
643193427687.02143038274246.97856961734
652582627705.9375968030-1879.93759680296
662683526719.1443852706115.855614729368
672020520695.1709973326-490.170997332618
681778919083.3700614636-1294.37006146361
692052020207.7571916433312.242808356743
702251823732.3329632771-1214.33296327708
711557218841.8730147381-3269.87301473814
721150910684.3292315165824.670768483455
732544730707.1508400117-5260.15084001175
742409026425.1665064646-2335.16650646464
752778627497.1488837408288.851116259248
762619526973.2669903791-778.266990379092
772051622056.6239717962-1540.62397179622
782275922219.6045190107539.39548098926
791902816032.33365550812995.66634449186
801697115235.67824318341735.32175681665
812003618258.44868709851777.55131290155
822248521512.2848027183972.71519728168
831873016332.79757588492397.20242411511
841453812288.41743491712249.5825650829

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 28029 & 26890.1444978633 & 1138.85550213675 \tabularnewline
14 & 29383 & 28873.9145686606 & 509.08543133935 \tabularnewline
15 & 36438 & 36198.8066350815 & 239.193364918538 \tabularnewline
16 & 32034 & 32052.0340619628 & -18.0340619627750 \tabularnewline
17 & 22679 & 22785.8580109783 & -106.858010978282 \tabularnewline
18 & 24319 & 24450.2933137790 & -131.293313779031 \tabularnewline
19 & 18004 & 22477.4384542722 & -4473.43845427217 \tabularnewline
20 & 17537 & 17382.2329683339 & 154.767031666121 \tabularnewline
21 & 20366 & 19775.4987175057 & 590.5012824943 \tabularnewline
22 & 22782 & 24048.8316950087 & -1266.83169500866 \tabularnewline
23 & 19169 & 15781.6074551065 & 3387.39254489350 \tabularnewline
24 & 13807 & 14840.1200971726 & -1033.12009717260 \tabularnewline
25 & 29743 & 27729.3037563685 & 2013.69624363149 \tabularnewline
26 & 25591 & 29696.7915852829 & -4105.79158528287 \tabularnewline
27 & 29096 & 35253.7502605778 & -6157.75026057778 \tabularnewline
28 & 26482 & 28716.6689708834 & -2234.66897088342 \tabularnewline
29 & 22405 & 18622.3753891505 & 3782.62461084946 \tabularnewline
30 & 27044 & 21646.8422194193 & 5397.15778058068 \tabularnewline
31 & 17970 & 19384.0653540573 & -1414.06535405733 \tabularnewline
32 & 18730 & 17757.1578342543 & 972.842165745667 \tabularnewline
33 & 19684 & 20664.0134286921 & -980.013428692135 \tabularnewline
34 & 19785 & 23424.5269491807 & -3639.52694918066 \tabularnewline
35 & 18479 & 16721.9903552135 & 1757.00964478651 \tabularnewline
36 & 10698 & 12923.7018793200 & -2225.70187932005 \tabularnewline
37 & 31956 & 26964.4676154234 & 4991.53238457656 \tabularnewline
38 & 29506 & 26824.6083623009 & 2681.39163769914 \tabularnewline
39 & 34506 & 33717.8279667315 & 788.172033268536 \tabularnewline
40 & 27165 & 31656.7383293261 & -4491.73832932611 \tabularnewline
41 & 26736 & 23871.4162958218 & 2864.58370417816 \tabularnewline
42 & 23691 & 27405.1544197002 & -3714.15441970022 \tabularnewline
43 & 18157 & 18411.6292002137 & -254.629200213651 \tabularnewline
44 & 17328 & 18425.7795423136 & -1097.77954231358 \tabularnewline
45 & 18205 & 19594.0231543635 & -1389.02315436350 \tabularnewline
46 & 20995 & 20837.6212331827 & 157.37876681731 \tabularnewline
47 & 17382 & 18260.2008622619 & -878.20086226186 \tabularnewline
48 & 9367 & 11476.4447580411 & -2109.44475804115 \tabularnewline
49 & 31124 & 29283.0436235142 & 1840.95637648576 \tabularnewline
50 & 26551 & 26839.0498850930 & -288.049885093045 \tabularnewline
51 & 30651 & 31707.2318474280 & -1056.23184742796 \tabularnewline
52 & 25859 & 26270.2766784284 & -411.276678428389 \tabularnewline
53 & 25100 & 23721.5835435846 & 1378.41645641538 \tabularnewline
54 & 25778 & 23335.5586884709 & 2442.44131152914 \tabularnewline
55 & 20418 & 18300.2221704079 & 2117.77782959211 \tabularnewline
56 & 18688 & 18716.473143196 & -28.4731431959917 \tabularnewline
57 & 20424 & 20111.7766901771 & 312.22330982293 \tabularnewline
58 & 24776 & 22753.8598548402 & 2022.14014515975 \tabularnewline
59 & 19814 & 20300.0737134258 & -486.073713425802 \tabularnewline
60 & 12738 & 13019.2604494312 & -281.260449431165 \tabularnewline
61 & 31566 & 33509.842892375 & -1943.84289237502 \tabularnewline
62 & 30111 & 28631.3733416093 & 1479.62665839066 \tabularnewline
63 & 30019 & 33726.9307613903 & -3707.93076139034 \tabularnewline
64 & 31934 & 27687.0214303827 & 4246.97856961734 \tabularnewline
65 & 25826 & 27705.9375968030 & -1879.93759680296 \tabularnewline
66 & 26835 & 26719.1443852706 & 115.855614729368 \tabularnewline
67 & 20205 & 20695.1709973326 & -490.170997332618 \tabularnewline
68 & 17789 & 19083.3700614636 & -1294.37006146361 \tabularnewline
69 & 20520 & 20207.7571916433 & 312.242808356743 \tabularnewline
70 & 22518 & 23732.3329632771 & -1214.33296327708 \tabularnewline
71 & 15572 & 18841.8730147381 & -3269.87301473814 \tabularnewline
72 & 11509 & 10684.3292315165 & 824.670768483455 \tabularnewline
73 & 25447 & 30707.1508400117 & -5260.15084001175 \tabularnewline
74 & 24090 & 26425.1665064646 & -2335.16650646464 \tabularnewline
75 & 27786 & 27497.1488837408 & 288.851116259248 \tabularnewline
76 & 26195 & 26973.2669903791 & -778.266990379092 \tabularnewline
77 & 20516 & 22056.6239717962 & -1540.62397179622 \tabularnewline
78 & 22759 & 22219.6045190107 & 539.39548098926 \tabularnewline
79 & 19028 & 16032.3336555081 & 2995.66634449186 \tabularnewline
80 & 16971 & 15235.6782431834 & 1735.32175681665 \tabularnewline
81 & 20036 & 18258.4486870985 & 1777.55131290155 \tabularnewline
82 & 22485 & 21512.2848027183 & 972.71519728168 \tabularnewline
83 & 18730 & 16332.7975758849 & 2397.20242411511 \tabularnewline
84 & 14538 & 12288.4174349171 & 2249.5825650829 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107260&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]28029[/C][C]26890.1444978633[/C][C]1138.85550213675[/C][/ROW]
[ROW][C]14[/C][C]29383[/C][C]28873.9145686606[/C][C]509.08543133935[/C][/ROW]
[ROW][C]15[/C][C]36438[/C][C]36198.8066350815[/C][C]239.193364918538[/C][/ROW]
[ROW][C]16[/C][C]32034[/C][C]32052.0340619628[/C][C]-18.0340619627750[/C][/ROW]
[ROW][C]17[/C][C]22679[/C][C]22785.8580109783[/C][C]-106.858010978282[/C][/ROW]
[ROW][C]18[/C][C]24319[/C][C]24450.2933137790[/C][C]-131.293313779031[/C][/ROW]
[ROW][C]19[/C][C]18004[/C][C]22477.4384542722[/C][C]-4473.43845427217[/C][/ROW]
[ROW][C]20[/C][C]17537[/C][C]17382.2329683339[/C][C]154.767031666121[/C][/ROW]
[ROW][C]21[/C][C]20366[/C][C]19775.4987175057[/C][C]590.5012824943[/C][/ROW]
[ROW][C]22[/C][C]22782[/C][C]24048.8316950087[/C][C]-1266.83169500866[/C][/ROW]
[ROW][C]23[/C][C]19169[/C][C]15781.6074551065[/C][C]3387.39254489350[/C][/ROW]
[ROW][C]24[/C][C]13807[/C][C]14840.1200971726[/C][C]-1033.12009717260[/C][/ROW]
[ROW][C]25[/C][C]29743[/C][C]27729.3037563685[/C][C]2013.69624363149[/C][/ROW]
[ROW][C]26[/C][C]25591[/C][C]29696.7915852829[/C][C]-4105.79158528287[/C][/ROW]
[ROW][C]27[/C][C]29096[/C][C]35253.7502605778[/C][C]-6157.75026057778[/C][/ROW]
[ROW][C]28[/C][C]26482[/C][C]28716.6689708834[/C][C]-2234.66897088342[/C][/ROW]
[ROW][C]29[/C][C]22405[/C][C]18622.3753891505[/C][C]3782.62461084946[/C][/ROW]
[ROW][C]30[/C][C]27044[/C][C]21646.8422194193[/C][C]5397.15778058068[/C][/ROW]
[ROW][C]31[/C][C]17970[/C][C]19384.0653540573[/C][C]-1414.06535405733[/C][/ROW]
[ROW][C]32[/C][C]18730[/C][C]17757.1578342543[/C][C]972.842165745667[/C][/ROW]
[ROW][C]33[/C][C]19684[/C][C]20664.0134286921[/C][C]-980.013428692135[/C][/ROW]
[ROW][C]34[/C][C]19785[/C][C]23424.5269491807[/C][C]-3639.52694918066[/C][/ROW]
[ROW][C]35[/C][C]18479[/C][C]16721.9903552135[/C][C]1757.00964478651[/C][/ROW]
[ROW][C]36[/C][C]10698[/C][C]12923.7018793200[/C][C]-2225.70187932005[/C][/ROW]
[ROW][C]37[/C][C]31956[/C][C]26964.4676154234[/C][C]4991.53238457656[/C][/ROW]
[ROW][C]38[/C][C]29506[/C][C]26824.6083623009[/C][C]2681.39163769914[/C][/ROW]
[ROW][C]39[/C][C]34506[/C][C]33717.8279667315[/C][C]788.172033268536[/C][/ROW]
[ROW][C]40[/C][C]27165[/C][C]31656.7383293261[/C][C]-4491.73832932611[/C][/ROW]
[ROW][C]41[/C][C]26736[/C][C]23871.4162958218[/C][C]2864.58370417816[/C][/ROW]
[ROW][C]42[/C][C]23691[/C][C]27405.1544197002[/C][C]-3714.15441970022[/C][/ROW]
[ROW][C]43[/C][C]18157[/C][C]18411.6292002137[/C][C]-254.629200213651[/C][/ROW]
[ROW][C]44[/C][C]17328[/C][C]18425.7795423136[/C][C]-1097.77954231358[/C][/ROW]
[ROW][C]45[/C][C]18205[/C][C]19594.0231543635[/C][C]-1389.02315436350[/C][/ROW]
[ROW][C]46[/C][C]20995[/C][C]20837.6212331827[/C][C]157.37876681731[/C][/ROW]
[ROW][C]47[/C][C]17382[/C][C]18260.2008622619[/C][C]-878.20086226186[/C][/ROW]
[ROW][C]48[/C][C]9367[/C][C]11476.4447580411[/C][C]-2109.44475804115[/C][/ROW]
[ROW][C]49[/C][C]31124[/C][C]29283.0436235142[/C][C]1840.95637648576[/C][/ROW]
[ROW][C]50[/C][C]26551[/C][C]26839.0498850930[/C][C]-288.049885093045[/C][/ROW]
[ROW][C]51[/C][C]30651[/C][C]31707.2318474280[/C][C]-1056.23184742796[/C][/ROW]
[ROW][C]52[/C][C]25859[/C][C]26270.2766784284[/C][C]-411.276678428389[/C][/ROW]
[ROW][C]53[/C][C]25100[/C][C]23721.5835435846[/C][C]1378.41645641538[/C][/ROW]
[ROW][C]54[/C][C]25778[/C][C]23335.5586884709[/C][C]2442.44131152914[/C][/ROW]
[ROW][C]55[/C][C]20418[/C][C]18300.2221704079[/C][C]2117.77782959211[/C][/ROW]
[ROW][C]56[/C][C]18688[/C][C]18716.473143196[/C][C]-28.4731431959917[/C][/ROW]
[ROW][C]57[/C][C]20424[/C][C]20111.7766901771[/C][C]312.22330982293[/C][/ROW]
[ROW][C]58[/C][C]24776[/C][C]22753.8598548402[/C][C]2022.14014515975[/C][/ROW]
[ROW][C]59[/C][C]19814[/C][C]20300.0737134258[/C][C]-486.073713425802[/C][/ROW]
[ROW][C]60[/C][C]12738[/C][C]13019.2604494312[/C][C]-281.260449431165[/C][/ROW]
[ROW][C]61[/C][C]31566[/C][C]33509.842892375[/C][C]-1943.84289237502[/C][/ROW]
[ROW][C]62[/C][C]30111[/C][C]28631.3733416093[/C][C]1479.62665839066[/C][/ROW]
[ROW][C]63[/C][C]30019[/C][C]33726.9307613903[/C][C]-3707.93076139034[/C][/ROW]
[ROW][C]64[/C][C]31934[/C][C]27687.0214303827[/C][C]4246.97856961734[/C][/ROW]
[ROW][C]65[/C][C]25826[/C][C]27705.9375968030[/C][C]-1879.93759680296[/C][/ROW]
[ROW][C]66[/C][C]26835[/C][C]26719.1443852706[/C][C]115.855614729368[/C][/ROW]
[ROW][C]67[/C][C]20205[/C][C]20695.1709973326[/C][C]-490.170997332618[/C][/ROW]
[ROW][C]68[/C][C]17789[/C][C]19083.3700614636[/C][C]-1294.37006146361[/C][/ROW]
[ROW][C]69[/C][C]20520[/C][C]20207.7571916433[/C][C]312.242808356743[/C][/ROW]
[ROW][C]70[/C][C]22518[/C][C]23732.3329632771[/C][C]-1214.33296327708[/C][/ROW]
[ROW][C]71[/C][C]15572[/C][C]18841.8730147381[/C][C]-3269.87301473814[/C][/ROW]
[ROW][C]72[/C][C]11509[/C][C]10684.3292315165[/C][C]824.670768483455[/C][/ROW]
[ROW][C]73[/C][C]25447[/C][C]30707.1508400117[/C][C]-5260.15084001175[/C][/ROW]
[ROW][C]74[/C][C]24090[/C][C]26425.1665064646[/C][C]-2335.16650646464[/C][/ROW]
[ROW][C]75[/C][C]27786[/C][C]27497.1488837408[/C][C]288.851116259248[/C][/ROW]
[ROW][C]76[/C][C]26195[/C][C]26973.2669903791[/C][C]-778.266990379092[/C][/ROW]
[ROW][C]77[/C][C]20516[/C][C]22056.6239717962[/C][C]-1540.62397179622[/C][/ROW]
[ROW][C]78[/C][C]22759[/C][C]22219.6045190107[/C][C]539.39548098926[/C][/ROW]
[ROW][C]79[/C][C]19028[/C][C]16032.3336555081[/C][C]2995.66634449186[/C][/ROW]
[ROW][C]80[/C][C]16971[/C][C]15235.6782431834[/C][C]1735.32175681665[/C][/ROW]
[ROW][C]81[/C][C]20036[/C][C]18258.4486870985[/C][C]1777.55131290155[/C][/ROW]
[ROW][C]82[/C][C]22485[/C][C]21512.2848027183[/C][C]972.71519728168[/C][/ROW]
[ROW][C]83[/C][C]18730[/C][C]16332.7975758849[/C][C]2397.20242411511[/C][/ROW]
[ROW][C]84[/C][C]14538[/C][C]12288.4174349171[/C][C]2249.5825650829[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107260&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107260&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
132802926890.14449786331138.85550213675
142938328873.9145686606509.08543133935
153643836198.8066350815239.193364918538
163203432052.0340619628-18.0340619627750
172267922785.8580109783-106.858010978282
182431924450.2933137790-131.293313779031
191800422477.4384542722-4473.43845427217
201753717382.2329683339154.767031666121
212036619775.4987175057590.5012824943
222278224048.8316950087-1266.83169500866
231916915781.60745510653387.39254489350
241380714840.1200971726-1033.12009717260
252974327729.30375636852013.69624363149
262559129696.7915852829-4105.79158528287
272909635253.7502605778-6157.75026057778
282648228716.6689708834-2234.66897088342
292240518622.37538915053782.62461084946
302704421646.84221941935397.15778058068
311797019384.0653540573-1414.06535405733
321873017757.1578342543972.842165745667
331968420664.0134286921-980.013428692135
341978523424.5269491807-3639.52694918066
351847916721.99035521351757.00964478651
361069812923.7018793200-2225.70187932005
373195626964.46761542344991.53238457656
382950626824.60836230092681.39163769914
393450633717.8279667315788.172033268536
402716531656.7383293261-4491.73832932611
412673623871.41629582182864.58370417816
422369127405.1544197002-3714.15441970022
431815718411.6292002137-254.629200213651
441732818425.7795423136-1097.77954231358
451820519594.0231543635-1389.02315436350
462099520837.6212331827157.37876681731
471738218260.2008622619-878.20086226186
48936711476.4447580411-2109.44475804115
493112429283.04362351421840.95637648576
502655126839.0498850930-288.049885093045
513065131707.2318474280-1056.23184742796
522585926270.2766784284-411.276678428389
532510023721.58354358461378.41645641538
542577823335.55868847092442.44131152914
552041818300.22217040792117.77782959211
561868818716.473143196-28.4731431959917
572042420111.7766901771312.22330982293
582477622753.85985484022022.14014515975
591981420300.0737134258-486.073713425802
601273813019.2604494312-281.260449431165
613156633509.842892375-1943.84289237502
623011128631.37334160931479.62665839066
633001933726.9307613903-3707.93076139034
643193427687.02143038274246.97856961734
652582627705.9375968030-1879.93759680296
662683526719.1443852706115.855614729368
672020520695.1709973326-490.170997332618
681778919083.3700614636-1294.37006146361
692052020207.7571916433312.242808356743
702251823732.3329632771-1214.33296327708
711557218841.8730147381-3269.87301473814
721150910684.3292315165824.670768483455
732544730707.1508400117-5260.15084001175
742409026425.1665064646-2335.16650646464
752778627497.1488837408288.851116259248
762619526973.2669903791-778.266990379092
772051622056.6239717962-1540.62397179622
782275922219.6045190107539.39548098926
791902816032.33365550812995.66634449186
801697115235.67824318341735.32175681665
812003618258.44868709851777.55131290155
822248521512.2848027183972.71519728168
831873016332.79757588492397.20242411511
841453812288.41743491712249.5825650829







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8529673.738526913125065.267938322434282.2091155038
8628757.701504505223870.665780901533644.737228109
8732008.042524699326857.485742986137158.5993064126
8830831.483608251925430.247438676936232.719777827
8925796.048453015720155.262234996231436.8346710352
9027576.227859581621705.658368018433446.7973511448
9122466.276222584716374.584901354928557.9675438144
9219961.954056251113656.890999388126267.0171131142
9322394.104376195515882.657751297728905.5510010932
9424605.247650769517893.760919294431316.7343822446
9519817.654090357012911.919433954526723.3887467596
9614851.08760526587756.4214297144621945.7537808172

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 29673.7385269131 & 25065.2679383224 & 34282.2091155038 \tabularnewline
86 & 28757.7015045052 & 23870.6657809015 & 33644.737228109 \tabularnewline
87 & 32008.0425246993 & 26857.4857429861 & 37158.5993064126 \tabularnewline
88 & 30831.4836082519 & 25430.2474386769 & 36232.719777827 \tabularnewline
89 & 25796.0484530157 & 20155.2622349962 & 31436.8346710352 \tabularnewline
90 & 27576.2278595816 & 21705.6583680184 & 33446.7973511448 \tabularnewline
91 & 22466.2762225847 & 16374.5849013549 & 28557.9675438144 \tabularnewline
92 & 19961.9540562511 & 13656.8909993881 & 26267.0171131142 \tabularnewline
93 & 22394.1043761955 & 15882.6577512977 & 28905.5510010932 \tabularnewline
94 & 24605.2476507695 & 17893.7609192944 & 31316.7343822446 \tabularnewline
95 & 19817.6540903570 & 12911.9194339545 & 26723.3887467596 \tabularnewline
96 & 14851.0876052658 & 7756.42142971446 & 21945.7537808172 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107260&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]29673.7385269131[/C][C]25065.2679383224[/C][C]34282.2091155038[/C][/ROW]
[ROW][C]86[/C][C]28757.7015045052[/C][C]23870.6657809015[/C][C]33644.737228109[/C][/ROW]
[ROW][C]87[/C][C]32008.0425246993[/C][C]26857.4857429861[/C][C]37158.5993064126[/C][/ROW]
[ROW][C]88[/C][C]30831.4836082519[/C][C]25430.2474386769[/C][C]36232.719777827[/C][/ROW]
[ROW][C]89[/C][C]25796.0484530157[/C][C]20155.2622349962[/C][C]31436.8346710352[/C][/ROW]
[ROW][C]90[/C][C]27576.2278595816[/C][C]21705.6583680184[/C][C]33446.7973511448[/C][/ROW]
[ROW][C]91[/C][C]22466.2762225847[/C][C]16374.5849013549[/C][C]28557.9675438144[/C][/ROW]
[ROW][C]92[/C][C]19961.9540562511[/C][C]13656.8909993881[/C][C]26267.0171131142[/C][/ROW]
[ROW][C]93[/C][C]22394.1043761955[/C][C]15882.6577512977[/C][C]28905.5510010932[/C][/ROW]
[ROW][C]94[/C][C]24605.2476507695[/C][C]17893.7609192944[/C][C]31316.7343822446[/C][/ROW]
[ROW][C]95[/C][C]19817.6540903570[/C][C]12911.9194339545[/C][C]26723.3887467596[/C][/ROW]
[ROW][C]96[/C][C]14851.0876052658[/C][C]7756.42142971446[/C][C]21945.7537808172[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107260&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107260&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
8529673.738526913125065.267938322434282.2091155038
8628757.701504505223870.665780901533644.737228109
8732008.042524699326857.485742986137158.5993064126
8830831.483608251925430.247438676936232.719777827
8925796.048453015720155.262234996231436.8346710352
9027576.227859581621705.658368018433446.7973511448
9122466.276222584716374.584901354928557.9675438144
9219961.954056251113656.890999388126267.0171131142
9322394.104376195515882.657751297728905.5510010932
9424605.247650769517893.760919294431316.7343822446
9519817.654090357012911.919433954526723.3887467596
9614851.08760526587756.4214297144621945.7537808172



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')