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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 09 Jan 2013 13:14:43 -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/2013/Jan/09/t1357755378ihkyb1jykcz1yag.htm/, Retrieved Mon, 29 Apr 2024 12:43:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205119, Retrieved Mon, 29 Apr 2024 12:43:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bootstrap Plot - Central Tendency] [maximumprijzen st...] [2013-01-09 11:37:25] [251e6916fe5b161c77205c1c19032f50]
- R P   [Bootstrap Plot - Central Tendency] [maximumprijzen st...] [2013-01-09 11:42:15] [251e6916fe5b161c77205c1c19032f50]
-   P     [Bootstrap Plot - Central Tendency] [maximumprijzen st...] [2013-01-09 11:45:46] [251e6916fe5b161c77205c1c19032f50]
- RMPD      [Blocked Bootstrap Plot - Central Tendency] [niet werkende wer...] [2013-01-09 16:05:30] [251e6916fe5b161c77205c1c19032f50]
- RMP           [Exponential Smoothing] [niet werkende wer...] [2013-01-09 18:14:43] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
125326
122716
116615
113719
110737
112093
143565
149946
149147
134339
122683
115614
116566
111272
104609
101802
94542
93051
124129
130374
123946
114971
105531
104919
104782
101281
94545
93248
84031
87486
115867
120327
117008
108811
104519
106758
109337
109078
108293
106534
99197
103493
130676
137448
134704
123725
118277
121225
120528
118240
112514
107304
100001
102082
130455
135574
132540
119920
112454
109415
109843
106365
102304
97968
92462
92286
120092
126656
124144
114045
108120
105698
111203




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205119&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205119&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205119&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.845185256134635
beta0.0537363877757178
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.845185256134635 \tabularnewline
beta & 0.0537363877757178 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205119&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]0.845185256134635[/C][/ROW]
[ROW][C]beta[/C][C]0.0537363877757178[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205119&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205119&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
alpha0.845185256134635
beta0.0537363877757178
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13116566124441.288382663-7875.28838266317
14111272112280.983690109-1008.98369010871
15104609104768.742911635-159.742911634661
16101802101822.070909056-20.0709090562304
179454294257.0435184636284.956481536399
189305192430.5383011475620.461698852509
19124129124177.399370929-48.3993709289789
20130374128350.5304149232023.46958507688
21123946128296.774481308-4350.77448130763
22114971111078.9750063983892.02499360248
23105531103696.7172626741834.28273732608
2410491998799.78030644646119.21969355359
25104782103813.2864046968.713595400302
26101281100925.800844964355.199155036069
279454595631.5049571612-1086.50495716117
289324892478.068050529769.931949470963
298403186589.4162256262-2558.41622562622
308748682786.51946440994699.48053559006
31115867116326.338525024-459.338525024359
32120327120736.874772805-409.874772805284
33117008118269.894731633-1261.89473163313
34108811106151.8299764962659.17002350358
3510451998501.94466794016017.05533205991
3610675898562.69533431678195.3046656833
37109337105357.4259560083979.57404399214
38109078105760.2040600353317.79593996522
39108293103433.4251875094859.57481249084
40106534106774.073454387-240.073454386991
419919799812.717467086-615.717467085968
42103493100121.6055849283371.39441507222
43130676138678.946345694-8002.94634569396
44137448138919.849401794-1471.84940179368
45134704136582.69080579-1878.69080579036
46123725124301.460754133-576.460754133397
47118277114182.4182145494094.58178545053
48121225113189.4243500338035.5756499672
49120528119931.894920116596.105079883899
50118240117699.584728776540.415271224279
51112514113310.942454012-796.942454012169
52107304111226.493159178-3922.4931591783
53100001101045.55253933-1044.55253932974
54102082101629.494350386452.505649613508
55130455135264.7899828-4809.78998279985
56135574139238.39200175-3664.39200175041
57132540134884.028550864-2344.02855086356
58119920122429.095776971-2509.09577697136
59112454111428.3483817341025.65161826572
60109415108253.5970597771161.40294022311
61109843107551.0983810332291.90161896718
62106365106483.512106663-118.512106662674
63102304101325.299820337978.700179663312
649796899986.8885850428-2018.88858504283
659246292060.8309817527401.169018247252
669228693687.6407414528-1401.64074145276
67120092121398.341395226-1306.34139522586
68126656127498.508282391-842.508282391485
69124144125556.73233775-1412.73233774953
70114045114316.662566801-271.662566800558
71108120106076.7647251322043.23527486816
72105698103918.658623131779.34137687003
73111203103965.1832001147237.81679988586

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 116566 & 124441.288382663 & -7875.28838266317 \tabularnewline
14 & 111272 & 112280.983690109 & -1008.98369010871 \tabularnewline
15 & 104609 & 104768.742911635 & -159.742911634661 \tabularnewline
16 & 101802 & 101822.070909056 & -20.0709090562304 \tabularnewline
17 & 94542 & 94257.0435184636 & 284.956481536399 \tabularnewline
18 & 93051 & 92430.5383011475 & 620.461698852509 \tabularnewline
19 & 124129 & 124177.399370929 & -48.3993709289789 \tabularnewline
20 & 130374 & 128350.530414923 & 2023.46958507688 \tabularnewline
21 & 123946 & 128296.774481308 & -4350.77448130763 \tabularnewline
22 & 114971 & 111078.975006398 & 3892.02499360248 \tabularnewline
23 & 105531 & 103696.717262674 & 1834.28273732608 \tabularnewline
24 & 104919 & 98799.7803064464 & 6119.21969355359 \tabularnewline
25 & 104782 & 103813.2864046 & 968.713595400302 \tabularnewline
26 & 101281 & 100925.800844964 & 355.199155036069 \tabularnewline
27 & 94545 & 95631.5049571612 & -1086.50495716117 \tabularnewline
28 & 93248 & 92478.068050529 & 769.931949470963 \tabularnewline
29 & 84031 & 86589.4162256262 & -2558.41622562622 \tabularnewline
30 & 87486 & 82786.5194644099 & 4699.48053559006 \tabularnewline
31 & 115867 & 116326.338525024 & -459.338525024359 \tabularnewline
32 & 120327 & 120736.874772805 & -409.874772805284 \tabularnewline
33 & 117008 & 118269.894731633 & -1261.89473163313 \tabularnewline
34 & 108811 & 106151.829976496 & 2659.17002350358 \tabularnewline
35 & 104519 & 98501.9446679401 & 6017.05533205991 \tabularnewline
36 & 106758 & 98562.6953343167 & 8195.3046656833 \tabularnewline
37 & 109337 & 105357.425956008 & 3979.57404399214 \tabularnewline
38 & 109078 & 105760.204060035 & 3317.79593996522 \tabularnewline
39 & 108293 & 103433.425187509 & 4859.57481249084 \tabularnewline
40 & 106534 & 106774.073454387 & -240.073454386991 \tabularnewline
41 & 99197 & 99812.717467086 & -615.717467085968 \tabularnewline
42 & 103493 & 100121.605584928 & 3371.39441507222 \tabularnewline
43 & 130676 & 138678.946345694 & -8002.94634569396 \tabularnewline
44 & 137448 & 138919.849401794 & -1471.84940179368 \tabularnewline
45 & 134704 & 136582.69080579 & -1878.69080579036 \tabularnewline
46 & 123725 & 124301.460754133 & -576.460754133397 \tabularnewline
47 & 118277 & 114182.418214549 & 4094.58178545053 \tabularnewline
48 & 121225 & 113189.424350033 & 8035.5756499672 \tabularnewline
49 & 120528 & 119931.894920116 & 596.105079883899 \tabularnewline
50 & 118240 & 117699.584728776 & 540.415271224279 \tabularnewline
51 & 112514 & 113310.942454012 & -796.942454012169 \tabularnewline
52 & 107304 & 111226.493159178 & -3922.4931591783 \tabularnewline
53 & 100001 & 101045.55253933 & -1044.55253932974 \tabularnewline
54 & 102082 & 101629.494350386 & 452.505649613508 \tabularnewline
55 & 130455 & 135264.7899828 & -4809.78998279985 \tabularnewline
56 & 135574 & 139238.39200175 & -3664.39200175041 \tabularnewline
57 & 132540 & 134884.028550864 & -2344.02855086356 \tabularnewline
58 & 119920 & 122429.095776971 & -2509.09577697136 \tabularnewline
59 & 112454 & 111428.348381734 & 1025.65161826572 \tabularnewline
60 & 109415 & 108253.597059777 & 1161.40294022311 \tabularnewline
61 & 109843 & 107551.098381033 & 2291.90161896718 \tabularnewline
62 & 106365 & 106483.512106663 & -118.512106662674 \tabularnewline
63 & 102304 & 101325.299820337 & 978.700179663312 \tabularnewline
64 & 97968 & 99986.8885850428 & -2018.88858504283 \tabularnewline
65 & 92462 & 92060.8309817527 & 401.169018247252 \tabularnewline
66 & 92286 & 93687.6407414528 & -1401.64074145276 \tabularnewline
67 & 120092 & 121398.341395226 & -1306.34139522586 \tabularnewline
68 & 126656 & 127498.508282391 & -842.508282391485 \tabularnewline
69 & 124144 & 125556.73233775 & -1412.73233774953 \tabularnewline
70 & 114045 & 114316.662566801 & -271.662566800558 \tabularnewline
71 & 108120 & 106076.764725132 & 2043.23527486816 \tabularnewline
72 & 105698 & 103918.65862313 & 1779.34137687003 \tabularnewline
73 & 111203 & 103965.183200114 & 7237.81679988586 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205119&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]116566[/C][C]124441.288382663[/C][C]-7875.28838266317[/C][/ROW]
[ROW][C]14[/C][C]111272[/C][C]112280.983690109[/C][C]-1008.98369010871[/C][/ROW]
[ROW][C]15[/C][C]104609[/C][C]104768.742911635[/C][C]-159.742911634661[/C][/ROW]
[ROW][C]16[/C][C]101802[/C][C]101822.070909056[/C][C]-20.0709090562304[/C][/ROW]
[ROW][C]17[/C][C]94542[/C][C]94257.0435184636[/C][C]284.956481536399[/C][/ROW]
[ROW][C]18[/C][C]93051[/C][C]92430.5383011475[/C][C]620.461698852509[/C][/ROW]
[ROW][C]19[/C][C]124129[/C][C]124177.399370929[/C][C]-48.3993709289789[/C][/ROW]
[ROW][C]20[/C][C]130374[/C][C]128350.530414923[/C][C]2023.46958507688[/C][/ROW]
[ROW][C]21[/C][C]123946[/C][C]128296.774481308[/C][C]-4350.77448130763[/C][/ROW]
[ROW][C]22[/C][C]114971[/C][C]111078.975006398[/C][C]3892.02499360248[/C][/ROW]
[ROW][C]23[/C][C]105531[/C][C]103696.717262674[/C][C]1834.28273732608[/C][/ROW]
[ROW][C]24[/C][C]104919[/C][C]98799.7803064464[/C][C]6119.21969355359[/C][/ROW]
[ROW][C]25[/C][C]104782[/C][C]103813.2864046[/C][C]968.713595400302[/C][/ROW]
[ROW][C]26[/C][C]101281[/C][C]100925.800844964[/C][C]355.199155036069[/C][/ROW]
[ROW][C]27[/C][C]94545[/C][C]95631.5049571612[/C][C]-1086.50495716117[/C][/ROW]
[ROW][C]28[/C][C]93248[/C][C]92478.068050529[/C][C]769.931949470963[/C][/ROW]
[ROW][C]29[/C][C]84031[/C][C]86589.4162256262[/C][C]-2558.41622562622[/C][/ROW]
[ROW][C]30[/C][C]87486[/C][C]82786.5194644099[/C][C]4699.48053559006[/C][/ROW]
[ROW][C]31[/C][C]115867[/C][C]116326.338525024[/C][C]-459.338525024359[/C][/ROW]
[ROW][C]32[/C][C]120327[/C][C]120736.874772805[/C][C]-409.874772805284[/C][/ROW]
[ROW][C]33[/C][C]117008[/C][C]118269.894731633[/C][C]-1261.89473163313[/C][/ROW]
[ROW][C]34[/C][C]108811[/C][C]106151.829976496[/C][C]2659.17002350358[/C][/ROW]
[ROW][C]35[/C][C]104519[/C][C]98501.9446679401[/C][C]6017.05533205991[/C][/ROW]
[ROW][C]36[/C][C]106758[/C][C]98562.6953343167[/C][C]8195.3046656833[/C][/ROW]
[ROW][C]37[/C][C]109337[/C][C]105357.425956008[/C][C]3979.57404399214[/C][/ROW]
[ROW][C]38[/C][C]109078[/C][C]105760.204060035[/C][C]3317.79593996522[/C][/ROW]
[ROW][C]39[/C][C]108293[/C][C]103433.425187509[/C][C]4859.57481249084[/C][/ROW]
[ROW][C]40[/C][C]106534[/C][C]106774.073454387[/C][C]-240.073454386991[/C][/ROW]
[ROW][C]41[/C][C]99197[/C][C]99812.717467086[/C][C]-615.717467085968[/C][/ROW]
[ROW][C]42[/C][C]103493[/C][C]100121.605584928[/C][C]3371.39441507222[/C][/ROW]
[ROW][C]43[/C][C]130676[/C][C]138678.946345694[/C][C]-8002.94634569396[/C][/ROW]
[ROW][C]44[/C][C]137448[/C][C]138919.849401794[/C][C]-1471.84940179368[/C][/ROW]
[ROW][C]45[/C][C]134704[/C][C]136582.69080579[/C][C]-1878.69080579036[/C][/ROW]
[ROW][C]46[/C][C]123725[/C][C]124301.460754133[/C][C]-576.460754133397[/C][/ROW]
[ROW][C]47[/C][C]118277[/C][C]114182.418214549[/C][C]4094.58178545053[/C][/ROW]
[ROW][C]48[/C][C]121225[/C][C]113189.424350033[/C][C]8035.5756499672[/C][/ROW]
[ROW][C]49[/C][C]120528[/C][C]119931.894920116[/C][C]596.105079883899[/C][/ROW]
[ROW][C]50[/C][C]118240[/C][C]117699.584728776[/C][C]540.415271224279[/C][/ROW]
[ROW][C]51[/C][C]112514[/C][C]113310.942454012[/C][C]-796.942454012169[/C][/ROW]
[ROW][C]52[/C][C]107304[/C][C]111226.493159178[/C][C]-3922.4931591783[/C][/ROW]
[ROW][C]53[/C][C]100001[/C][C]101045.55253933[/C][C]-1044.55253932974[/C][/ROW]
[ROW][C]54[/C][C]102082[/C][C]101629.494350386[/C][C]452.505649613508[/C][/ROW]
[ROW][C]55[/C][C]130455[/C][C]135264.7899828[/C][C]-4809.78998279985[/C][/ROW]
[ROW][C]56[/C][C]135574[/C][C]139238.39200175[/C][C]-3664.39200175041[/C][/ROW]
[ROW][C]57[/C][C]132540[/C][C]134884.028550864[/C][C]-2344.02855086356[/C][/ROW]
[ROW][C]58[/C][C]119920[/C][C]122429.095776971[/C][C]-2509.09577697136[/C][/ROW]
[ROW][C]59[/C][C]112454[/C][C]111428.348381734[/C][C]1025.65161826572[/C][/ROW]
[ROW][C]60[/C][C]109415[/C][C]108253.597059777[/C][C]1161.40294022311[/C][/ROW]
[ROW][C]61[/C][C]109843[/C][C]107551.098381033[/C][C]2291.90161896718[/C][/ROW]
[ROW][C]62[/C][C]106365[/C][C]106483.512106663[/C][C]-118.512106662674[/C][/ROW]
[ROW][C]63[/C][C]102304[/C][C]101325.299820337[/C][C]978.700179663312[/C][/ROW]
[ROW][C]64[/C][C]97968[/C][C]99986.8885850428[/C][C]-2018.88858504283[/C][/ROW]
[ROW][C]65[/C][C]92462[/C][C]92060.8309817527[/C][C]401.169018247252[/C][/ROW]
[ROW][C]66[/C][C]92286[/C][C]93687.6407414528[/C][C]-1401.64074145276[/C][/ROW]
[ROW][C]67[/C][C]120092[/C][C]121398.341395226[/C][C]-1306.34139522586[/C][/ROW]
[ROW][C]68[/C][C]126656[/C][C]127498.508282391[/C][C]-842.508282391485[/C][/ROW]
[ROW][C]69[/C][C]124144[/C][C]125556.73233775[/C][C]-1412.73233774953[/C][/ROW]
[ROW][C]70[/C][C]114045[/C][C]114316.662566801[/C][C]-271.662566800558[/C][/ROW]
[ROW][C]71[/C][C]108120[/C][C]106076.764725132[/C][C]2043.23527486816[/C][/ROW]
[ROW][C]72[/C][C]105698[/C][C]103918.65862313[/C][C]1779.34137687003[/C][/ROW]
[ROW][C]73[/C][C]111203[/C][C]103965.183200114[/C][C]7237.81679988586[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205119&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205119&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
13116566124441.288382663-7875.28838266317
14111272112280.983690109-1008.98369010871
15104609104768.742911635-159.742911634661
16101802101822.070909056-20.0709090562304
179454294257.0435184636284.956481536399
189305192430.5383011475620.461698852509
19124129124177.399370929-48.3993709289789
20130374128350.5304149232023.46958507688
21123946128296.774481308-4350.77448130763
22114971111078.9750063983892.02499360248
23105531103696.7172626741834.28273732608
2410491998799.78030644646119.21969355359
25104782103813.2864046968.713595400302
26101281100925.800844964355.199155036069
279454595631.5049571612-1086.50495716117
289324892478.068050529769.931949470963
298403186589.4162256262-2558.41622562622
308748682786.51946440994699.48053559006
31115867116326.338525024-459.338525024359
32120327120736.874772805-409.874772805284
33117008118269.894731633-1261.89473163313
34108811106151.8299764962659.17002350358
3510451998501.94466794016017.05533205991
3610675898562.69533431678195.3046656833
37109337105357.4259560083979.57404399214
38109078105760.2040600353317.79593996522
39108293103433.4251875094859.57481249084
40106534106774.073454387-240.073454386991
419919799812.717467086-615.717467085968
42103493100121.6055849283371.39441507222
43130676138678.946345694-8002.94634569396
44137448138919.849401794-1471.84940179368
45134704136582.69080579-1878.69080579036
46123725124301.460754133-576.460754133397
47118277114182.4182145494094.58178545053
48121225113189.4243500338035.5756499672
49120528119931.894920116596.105079883899
50118240117699.584728776540.415271224279
51112514113310.942454012-796.942454012169
52107304111226.493159178-3922.4931591783
53100001101045.55253933-1044.55253932974
54102082101629.494350386452.505649613508
55130455135264.7899828-4809.78998279985
56135574139238.39200175-3664.39200175041
57132540134884.028550864-2344.02855086356
58119920122429.095776971-2509.09577697136
59112454111428.3483817341025.65161826572
60109415108253.5970597771161.40294022311
61109843107551.0983810332291.90161896718
62106365106483.512106663-118.512106662674
63102304101325.299820337978.700179663312
649796899986.8885850428-2018.88858504283
659246292060.8309817527401.169018247252
669228693687.6407414528-1401.64074145276
67120092121398.341395226-1306.34139522586
68126656127498.508282391-842.508282391485
69124144125556.73233775-1412.73233774953
70114045114316.662566801-271.662566800558
71108120106076.7647251322043.23527486816
72105698103918.658623131779.34137687003
73111203103965.1832001147237.81679988586







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74106930.668108545100558.318236729113303.01798036
75102244.3278597593874.3579369752110614.297782526
7699789.594104946889676.2857318933109902.902478
7794095.348055690382707.6904385079105483.005672873
7895363.175978550282161.3178772837108565.034079817
79125648.604666046106908.822780841144388.386551252
80133772.140945605112264.717970139155279.563921072
81132931.259225747109966.68648673155895.831964763
82122945.592516372100107.325339894145783.85969285
83115253.21546693292273.2964869415138233.134446922
84111505.94395550287727.8110356374135284.076875368
85111144.89429379386693.574695733135596.213891853

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 106930.668108545 & 100558.318236729 & 113303.01798036 \tabularnewline
75 & 102244.32785975 & 93874.3579369752 & 110614.297782526 \tabularnewline
76 & 99789.5941049468 & 89676.2857318933 & 109902.902478 \tabularnewline
77 & 94095.3480556903 & 82707.6904385079 & 105483.005672873 \tabularnewline
78 & 95363.1759785502 & 82161.3178772837 & 108565.034079817 \tabularnewline
79 & 125648.604666046 & 106908.822780841 & 144388.386551252 \tabularnewline
80 & 133772.140945605 & 112264.717970139 & 155279.563921072 \tabularnewline
81 & 132931.259225747 & 109966.68648673 & 155895.831964763 \tabularnewline
82 & 122945.592516372 & 100107.325339894 & 145783.85969285 \tabularnewline
83 & 115253.215466932 & 92273.2964869415 & 138233.134446922 \tabularnewline
84 & 111505.943955502 & 87727.8110356374 & 135284.076875368 \tabularnewline
85 & 111144.894293793 & 86693.574695733 & 135596.213891853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205119&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]74[/C][C]106930.668108545[/C][C]100558.318236729[/C][C]113303.01798036[/C][/ROW]
[ROW][C]75[/C][C]102244.32785975[/C][C]93874.3579369752[/C][C]110614.297782526[/C][/ROW]
[ROW][C]76[/C][C]99789.5941049468[/C][C]89676.2857318933[/C][C]109902.902478[/C][/ROW]
[ROW][C]77[/C][C]94095.3480556903[/C][C]82707.6904385079[/C][C]105483.005672873[/C][/ROW]
[ROW][C]78[/C][C]95363.1759785502[/C][C]82161.3178772837[/C][C]108565.034079817[/C][/ROW]
[ROW][C]79[/C][C]125648.604666046[/C][C]106908.822780841[/C][C]144388.386551252[/C][/ROW]
[ROW][C]80[/C][C]133772.140945605[/C][C]112264.717970139[/C][C]155279.563921072[/C][/ROW]
[ROW][C]81[/C][C]132931.259225747[/C][C]109966.68648673[/C][C]155895.831964763[/C][/ROW]
[ROW][C]82[/C][C]122945.592516372[/C][C]100107.325339894[/C][C]145783.85969285[/C][/ROW]
[ROW][C]83[/C][C]115253.215466932[/C][C]92273.2964869415[/C][C]138233.134446922[/C][/ROW]
[ROW][C]84[/C][C]111505.943955502[/C][C]87727.8110356374[/C][C]135284.076875368[/C][/ROW]
[ROW][C]85[/C][C]111144.894293793[/C][C]86693.574695733[/C][C]135596.213891853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205119&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205119&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
74106930.668108545100558.318236729113303.01798036
75102244.3278597593874.3579369752110614.297782526
7699789.594104946889676.2857318933109902.902478
7794095.348055690382707.6904385079105483.005672873
7895363.175978550282161.3178772837108565.034079817
79125648.604666046106908.822780841144388.386551252
80133772.140945605112264.717970139155279.563921072
81132931.259225747109966.68648673155895.831964763
82122945.592516372100107.325339894145783.85969285
83115253.21546693292273.2964869415138233.134446922
84111505.94395550287727.8110356374135284.076875368
85111144.89429379386693.574695733135596.213891853



Parameters (Session):
par1 = 12 ;
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')