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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 25 May 2013 08:40:15 -0400
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/May/25/t1369485652j5w3ow8z42vt8yt.htm/, Retrieved Fri, 03 May 2024 01:24:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210495, Retrieved Fri, 03 May 2024 01:24:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variability] [] [2013-04-28 12:09:59] [b6e284768173daa602d243042729bd3c]
- RMPD  [Classical Decomposition] [] [2013-05-25 12:05:24] [b6e284768173daa602d243042729bd3c]
- RMPD      [Exponential Smoothing] [] [2013-05-25 12:40:15] [7dd81915b60453c4edd7571cc080755b] [Current]
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Dataseries X:
102,42
102,46
102,76
102,4
102,47
102,27
102,17
101,84
102,13
103,34
103,43
103,59
104,21
105,42
105,95
106,28
106,49
106,49
106,49
107,38
108,69
108,76
108,84
108,67
108,79
109,96
110,86
111
111,84
112,21
112,4
113,76
114,85
115,23
115,39
115,29
115,53
116,26
116,85
117,37
118,03
118,49
119,32
119,4
122,26
122,91
123,78
123,99
124,7
125,89
127,57
128,97
130,65
130,73
130,95
131,36
132,85
133,08
133,13
133,27
133,9
134,85
135,49
136,21
136,31
136,22
136,22
135,51
137,3
138,42
138,92
138,67




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' @ yule.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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210495&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210495&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210495&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' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.108662487764098
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.108662487764098 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210495&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.108662487764098[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210495&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210495&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
alpha1
beta0.108662487764098
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3102.76102.50.260000000000019
4102.4102.828252246819-0.428252246818658
5102.47102.4217172922890.0482827077112091
6102.27102.496963811425-0.226963811424667
7102.17102.272301359043-0.102301359042841
8101.84102.161185038868-0.321185038867597
9102.13101.7962842735120.33371572648835
10103.34102.1225466545581.21745334544214
11103.43103.46483816381-0.0348381638103348
12103.59103.5510525622620.0389474377384289
13104.21103.7152846877380.494715312261732
14105.42104.3890416843041.0309583156964
15105.95105.7110681796680.238931820331729
16106.28106.2670311056720.0129688943284805
17106.49106.598440337993-0.108440337992803
18106.49106.796656941093-0.306656941092527
19106.49106.763334834983-0.273334834983288
20107.38106.7336335918210.646366408178594
21108.69107.6938693737410.996130626258761
22108.76109.112111405729-0.352111405728522
23108.84109.143850104412-0.30385010441195
24108.67109.190832996159-0.520832996159172
25108.79108.964237987087-0.174237987086883
26109.96109.0653048539470.894695146052968
27110.86110.3325246543080.527475345692409
28111111.289841437605-0.289841437604764
29111.84111.3983465459370.441653454062504
30112.21112.286337708986-0.0763377089855481
31112.4112.648042663617-0.248042663616943
32113.76112.8110897307170.948910269283289
33114.85114.2742006812420.575799318758058
34115.23115.426768467671-0.196768467671049
35115.39115.78538711646-0.395387116460398
36115.29115.902423368756-0.612423368755927
37115.53115.735875921942-0.205875921942052
38116.26115.9535049320930.306495067906909
39116.85116.7168094486590.133190551340704
40117.37117.3212822653150.0487177346853684
41118.03117.8465760555640.183423944436214
42118.49118.526507357682-0.0365073576817281
43119.32118.9825403773740.337459622625673
44119.4119.849209579489-0.449209579488752
45122.26119.8803973490542.37960265094594
46122.91122.998970892996-0.0889708929959028
47123.78123.6393030944240.140696905575638
48123.99124.524591570205-0.534591570204924
49124.7124.6765015202490.0234984797512681
50125.89125.3890549235170.500945076482807
51127.57126.6334888617610.936511138239013
52128.97128.4152524918610.554747508139172
53130.65129.8755327361760.774467263823851
54130.73131.639688275755-0.909688275755116
55130.95131.620839284622-0.670839284621735
56131.36131.767944219065-0.407944219064831
57132.85132.1336159853520.716384014647701
58133.08133.701460054578-0.621460054578307
59133.13133.863930659002-0.733930659001857
60133.27133.834179927748-0.564179927748341
61133.9133.912874733253-0.0128747332526586
62134.85134.5414757327080.308524267291887
63135.49135.525000747128-0.0350007471276399
64136.21136.1611974788710.0488025211288345
65136.31136.886500482226-0.57650048222618
66136.22136.92385650563-0.703856505630284
67136.22136.7573737067-0.537373706699555
68135.51136.698981342871-1.18898134287056
69137.3135.8597836722491.44021632775087
70138.42137.8062811613410.61371883865894
71138.92138.992969377137-0.0729693771374116
72138.67139.485040343087-0.815040343087048

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 102.76 & 102.5 & 0.260000000000019 \tabularnewline
4 & 102.4 & 102.828252246819 & -0.428252246818658 \tabularnewline
5 & 102.47 & 102.421717292289 & 0.0482827077112091 \tabularnewline
6 & 102.27 & 102.496963811425 & -0.226963811424667 \tabularnewline
7 & 102.17 & 102.272301359043 & -0.102301359042841 \tabularnewline
8 & 101.84 & 102.161185038868 & -0.321185038867597 \tabularnewline
9 & 102.13 & 101.796284273512 & 0.33371572648835 \tabularnewline
10 & 103.34 & 102.122546654558 & 1.21745334544214 \tabularnewline
11 & 103.43 & 103.46483816381 & -0.0348381638103348 \tabularnewline
12 & 103.59 & 103.551052562262 & 0.0389474377384289 \tabularnewline
13 & 104.21 & 103.715284687738 & 0.494715312261732 \tabularnewline
14 & 105.42 & 104.389041684304 & 1.0309583156964 \tabularnewline
15 & 105.95 & 105.711068179668 & 0.238931820331729 \tabularnewline
16 & 106.28 & 106.267031105672 & 0.0129688943284805 \tabularnewline
17 & 106.49 & 106.598440337993 & -0.108440337992803 \tabularnewline
18 & 106.49 & 106.796656941093 & -0.306656941092527 \tabularnewline
19 & 106.49 & 106.763334834983 & -0.273334834983288 \tabularnewline
20 & 107.38 & 106.733633591821 & 0.646366408178594 \tabularnewline
21 & 108.69 & 107.693869373741 & 0.996130626258761 \tabularnewline
22 & 108.76 & 109.112111405729 & -0.352111405728522 \tabularnewline
23 & 108.84 & 109.143850104412 & -0.30385010441195 \tabularnewline
24 & 108.67 & 109.190832996159 & -0.520832996159172 \tabularnewline
25 & 108.79 & 108.964237987087 & -0.174237987086883 \tabularnewline
26 & 109.96 & 109.065304853947 & 0.894695146052968 \tabularnewline
27 & 110.86 & 110.332524654308 & 0.527475345692409 \tabularnewline
28 & 111 & 111.289841437605 & -0.289841437604764 \tabularnewline
29 & 111.84 & 111.398346545937 & 0.441653454062504 \tabularnewline
30 & 112.21 & 112.286337708986 & -0.0763377089855481 \tabularnewline
31 & 112.4 & 112.648042663617 & -0.248042663616943 \tabularnewline
32 & 113.76 & 112.811089730717 & 0.948910269283289 \tabularnewline
33 & 114.85 & 114.274200681242 & 0.575799318758058 \tabularnewline
34 & 115.23 & 115.426768467671 & -0.196768467671049 \tabularnewline
35 & 115.39 & 115.78538711646 & -0.395387116460398 \tabularnewline
36 & 115.29 & 115.902423368756 & -0.612423368755927 \tabularnewline
37 & 115.53 & 115.735875921942 & -0.205875921942052 \tabularnewline
38 & 116.26 & 115.953504932093 & 0.306495067906909 \tabularnewline
39 & 116.85 & 116.716809448659 & 0.133190551340704 \tabularnewline
40 & 117.37 & 117.321282265315 & 0.0487177346853684 \tabularnewline
41 & 118.03 & 117.846576055564 & 0.183423944436214 \tabularnewline
42 & 118.49 & 118.526507357682 & -0.0365073576817281 \tabularnewline
43 & 119.32 & 118.982540377374 & 0.337459622625673 \tabularnewline
44 & 119.4 & 119.849209579489 & -0.449209579488752 \tabularnewline
45 & 122.26 & 119.880397349054 & 2.37960265094594 \tabularnewline
46 & 122.91 & 122.998970892996 & -0.0889708929959028 \tabularnewline
47 & 123.78 & 123.639303094424 & 0.140696905575638 \tabularnewline
48 & 123.99 & 124.524591570205 & -0.534591570204924 \tabularnewline
49 & 124.7 & 124.676501520249 & 0.0234984797512681 \tabularnewline
50 & 125.89 & 125.389054923517 & 0.500945076482807 \tabularnewline
51 & 127.57 & 126.633488861761 & 0.936511138239013 \tabularnewline
52 & 128.97 & 128.415252491861 & 0.554747508139172 \tabularnewline
53 & 130.65 & 129.875532736176 & 0.774467263823851 \tabularnewline
54 & 130.73 & 131.639688275755 & -0.909688275755116 \tabularnewline
55 & 130.95 & 131.620839284622 & -0.670839284621735 \tabularnewline
56 & 131.36 & 131.767944219065 & -0.407944219064831 \tabularnewline
57 & 132.85 & 132.133615985352 & 0.716384014647701 \tabularnewline
58 & 133.08 & 133.701460054578 & -0.621460054578307 \tabularnewline
59 & 133.13 & 133.863930659002 & -0.733930659001857 \tabularnewline
60 & 133.27 & 133.834179927748 & -0.564179927748341 \tabularnewline
61 & 133.9 & 133.912874733253 & -0.0128747332526586 \tabularnewline
62 & 134.85 & 134.541475732708 & 0.308524267291887 \tabularnewline
63 & 135.49 & 135.525000747128 & -0.0350007471276399 \tabularnewline
64 & 136.21 & 136.161197478871 & 0.0488025211288345 \tabularnewline
65 & 136.31 & 136.886500482226 & -0.57650048222618 \tabularnewline
66 & 136.22 & 136.92385650563 & -0.703856505630284 \tabularnewline
67 & 136.22 & 136.7573737067 & -0.537373706699555 \tabularnewline
68 & 135.51 & 136.698981342871 & -1.18898134287056 \tabularnewline
69 & 137.3 & 135.859783672249 & 1.44021632775087 \tabularnewline
70 & 138.42 & 137.806281161341 & 0.61371883865894 \tabularnewline
71 & 138.92 & 138.992969377137 & -0.0729693771374116 \tabularnewline
72 & 138.67 & 139.485040343087 & -0.815040343087048 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210495&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]3[/C][C]102.76[/C][C]102.5[/C][C]0.260000000000019[/C][/ROW]
[ROW][C]4[/C][C]102.4[/C][C]102.828252246819[/C][C]-0.428252246818658[/C][/ROW]
[ROW][C]5[/C][C]102.47[/C][C]102.421717292289[/C][C]0.0482827077112091[/C][/ROW]
[ROW][C]6[/C][C]102.27[/C][C]102.496963811425[/C][C]-0.226963811424667[/C][/ROW]
[ROW][C]7[/C][C]102.17[/C][C]102.272301359043[/C][C]-0.102301359042841[/C][/ROW]
[ROW][C]8[/C][C]101.84[/C][C]102.161185038868[/C][C]-0.321185038867597[/C][/ROW]
[ROW][C]9[/C][C]102.13[/C][C]101.796284273512[/C][C]0.33371572648835[/C][/ROW]
[ROW][C]10[/C][C]103.34[/C][C]102.122546654558[/C][C]1.21745334544214[/C][/ROW]
[ROW][C]11[/C][C]103.43[/C][C]103.46483816381[/C][C]-0.0348381638103348[/C][/ROW]
[ROW][C]12[/C][C]103.59[/C][C]103.551052562262[/C][C]0.0389474377384289[/C][/ROW]
[ROW][C]13[/C][C]104.21[/C][C]103.715284687738[/C][C]0.494715312261732[/C][/ROW]
[ROW][C]14[/C][C]105.42[/C][C]104.389041684304[/C][C]1.0309583156964[/C][/ROW]
[ROW][C]15[/C][C]105.95[/C][C]105.711068179668[/C][C]0.238931820331729[/C][/ROW]
[ROW][C]16[/C][C]106.28[/C][C]106.267031105672[/C][C]0.0129688943284805[/C][/ROW]
[ROW][C]17[/C][C]106.49[/C][C]106.598440337993[/C][C]-0.108440337992803[/C][/ROW]
[ROW][C]18[/C][C]106.49[/C][C]106.796656941093[/C][C]-0.306656941092527[/C][/ROW]
[ROW][C]19[/C][C]106.49[/C][C]106.763334834983[/C][C]-0.273334834983288[/C][/ROW]
[ROW][C]20[/C][C]107.38[/C][C]106.733633591821[/C][C]0.646366408178594[/C][/ROW]
[ROW][C]21[/C][C]108.69[/C][C]107.693869373741[/C][C]0.996130626258761[/C][/ROW]
[ROW][C]22[/C][C]108.76[/C][C]109.112111405729[/C][C]-0.352111405728522[/C][/ROW]
[ROW][C]23[/C][C]108.84[/C][C]109.143850104412[/C][C]-0.30385010441195[/C][/ROW]
[ROW][C]24[/C][C]108.67[/C][C]109.190832996159[/C][C]-0.520832996159172[/C][/ROW]
[ROW][C]25[/C][C]108.79[/C][C]108.964237987087[/C][C]-0.174237987086883[/C][/ROW]
[ROW][C]26[/C][C]109.96[/C][C]109.065304853947[/C][C]0.894695146052968[/C][/ROW]
[ROW][C]27[/C][C]110.86[/C][C]110.332524654308[/C][C]0.527475345692409[/C][/ROW]
[ROW][C]28[/C][C]111[/C][C]111.289841437605[/C][C]-0.289841437604764[/C][/ROW]
[ROW][C]29[/C][C]111.84[/C][C]111.398346545937[/C][C]0.441653454062504[/C][/ROW]
[ROW][C]30[/C][C]112.21[/C][C]112.286337708986[/C][C]-0.0763377089855481[/C][/ROW]
[ROW][C]31[/C][C]112.4[/C][C]112.648042663617[/C][C]-0.248042663616943[/C][/ROW]
[ROW][C]32[/C][C]113.76[/C][C]112.811089730717[/C][C]0.948910269283289[/C][/ROW]
[ROW][C]33[/C][C]114.85[/C][C]114.274200681242[/C][C]0.575799318758058[/C][/ROW]
[ROW][C]34[/C][C]115.23[/C][C]115.426768467671[/C][C]-0.196768467671049[/C][/ROW]
[ROW][C]35[/C][C]115.39[/C][C]115.78538711646[/C][C]-0.395387116460398[/C][/ROW]
[ROW][C]36[/C][C]115.29[/C][C]115.902423368756[/C][C]-0.612423368755927[/C][/ROW]
[ROW][C]37[/C][C]115.53[/C][C]115.735875921942[/C][C]-0.205875921942052[/C][/ROW]
[ROW][C]38[/C][C]116.26[/C][C]115.953504932093[/C][C]0.306495067906909[/C][/ROW]
[ROW][C]39[/C][C]116.85[/C][C]116.716809448659[/C][C]0.133190551340704[/C][/ROW]
[ROW][C]40[/C][C]117.37[/C][C]117.321282265315[/C][C]0.0487177346853684[/C][/ROW]
[ROW][C]41[/C][C]118.03[/C][C]117.846576055564[/C][C]0.183423944436214[/C][/ROW]
[ROW][C]42[/C][C]118.49[/C][C]118.526507357682[/C][C]-0.0365073576817281[/C][/ROW]
[ROW][C]43[/C][C]119.32[/C][C]118.982540377374[/C][C]0.337459622625673[/C][/ROW]
[ROW][C]44[/C][C]119.4[/C][C]119.849209579489[/C][C]-0.449209579488752[/C][/ROW]
[ROW][C]45[/C][C]122.26[/C][C]119.880397349054[/C][C]2.37960265094594[/C][/ROW]
[ROW][C]46[/C][C]122.91[/C][C]122.998970892996[/C][C]-0.0889708929959028[/C][/ROW]
[ROW][C]47[/C][C]123.78[/C][C]123.639303094424[/C][C]0.140696905575638[/C][/ROW]
[ROW][C]48[/C][C]123.99[/C][C]124.524591570205[/C][C]-0.534591570204924[/C][/ROW]
[ROW][C]49[/C][C]124.7[/C][C]124.676501520249[/C][C]0.0234984797512681[/C][/ROW]
[ROW][C]50[/C][C]125.89[/C][C]125.389054923517[/C][C]0.500945076482807[/C][/ROW]
[ROW][C]51[/C][C]127.57[/C][C]126.633488861761[/C][C]0.936511138239013[/C][/ROW]
[ROW][C]52[/C][C]128.97[/C][C]128.415252491861[/C][C]0.554747508139172[/C][/ROW]
[ROW][C]53[/C][C]130.65[/C][C]129.875532736176[/C][C]0.774467263823851[/C][/ROW]
[ROW][C]54[/C][C]130.73[/C][C]131.639688275755[/C][C]-0.909688275755116[/C][/ROW]
[ROW][C]55[/C][C]130.95[/C][C]131.620839284622[/C][C]-0.670839284621735[/C][/ROW]
[ROW][C]56[/C][C]131.36[/C][C]131.767944219065[/C][C]-0.407944219064831[/C][/ROW]
[ROW][C]57[/C][C]132.85[/C][C]132.133615985352[/C][C]0.716384014647701[/C][/ROW]
[ROW][C]58[/C][C]133.08[/C][C]133.701460054578[/C][C]-0.621460054578307[/C][/ROW]
[ROW][C]59[/C][C]133.13[/C][C]133.863930659002[/C][C]-0.733930659001857[/C][/ROW]
[ROW][C]60[/C][C]133.27[/C][C]133.834179927748[/C][C]-0.564179927748341[/C][/ROW]
[ROW][C]61[/C][C]133.9[/C][C]133.912874733253[/C][C]-0.0128747332526586[/C][/ROW]
[ROW][C]62[/C][C]134.85[/C][C]134.541475732708[/C][C]0.308524267291887[/C][/ROW]
[ROW][C]63[/C][C]135.49[/C][C]135.525000747128[/C][C]-0.0350007471276399[/C][/ROW]
[ROW][C]64[/C][C]136.21[/C][C]136.161197478871[/C][C]0.0488025211288345[/C][/ROW]
[ROW][C]65[/C][C]136.31[/C][C]136.886500482226[/C][C]-0.57650048222618[/C][/ROW]
[ROW][C]66[/C][C]136.22[/C][C]136.92385650563[/C][C]-0.703856505630284[/C][/ROW]
[ROW][C]67[/C][C]136.22[/C][C]136.7573737067[/C][C]-0.537373706699555[/C][/ROW]
[ROW][C]68[/C][C]135.51[/C][C]136.698981342871[/C][C]-1.18898134287056[/C][/ROW]
[ROW][C]69[/C][C]137.3[/C][C]135.859783672249[/C][C]1.44021632775087[/C][/ROW]
[ROW][C]70[/C][C]138.42[/C][C]137.806281161341[/C][C]0.61371883865894[/C][/ROW]
[ROW][C]71[/C][C]138.92[/C][C]138.992969377137[/C][C]-0.0729693771374116[/C][/ROW]
[ROW][C]72[/C][C]138.67[/C][C]139.485040343087[/C][C]-0.815040343087048[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210495&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210495&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
3102.76102.50.260000000000019
4102.4102.828252246819-0.428252246818658
5102.47102.4217172922890.0482827077112091
6102.27102.496963811425-0.226963811424667
7102.17102.272301359043-0.102301359042841
8101.84102.161185038868-0.321185038867597
9102.13101.7962842735120.33371572648835
10103.34102.1225466545581.21745334544214
11103.43103.46483816381-0.0348381638103348
12103.59103.5510525622620.0389474377384289
13104.21103.7152846877380.494715312261732
14105.42104.3890416843041.0309583156964
15105.95105.7110681796680.238931820331729
16106.28106.2670311056720.0129688943284805
17106.49106.598440337993-0.108440337992803
18106.49106.796656941093-0.306656941092527
19106.49106.763334834983-0.273334834983288
20107.38106.7336335918210.646366408178594
21108.69107.6938693737410.996130626258761
22108.76109.112111405729-0.352111405728522
23108.84109.143850104412-0.30385010441195
24108.67109.190832996159-0.520832996159172
25108.79108.964237987087-0.174237987086883
26109.96109.0653048539470.894695146052968
27110.86110.3325246543080.527475345692409
28111111.289841437605-0.289841437604764
29111.84111.3983465459370.441653454062504
30112.21112.286337708986-0.0763377089855481
31112.4112.648042663617-0.248042663616943
32113.76112.8110897307170.948910269283289
33114.85114.2742006812420.575799318758058
34115.23115.426768467671-0.196768467671049
35115.39115.78538711646-0.395387116460398
36115.29115.902423368756-0.612423368755927
37115.53115.735875921942-0.205875921942052
38116.26115.9535049320930.306495067906909
39116.85116.7168094486590.133190551340704
40117.37117.3212822653150.0487177346853684
41118.03117.8465760555640.183423944436214
42118.49118.526507357682-0.0365073576817281
43119.32118.9825403773740.337459622625673
44119.4119.849209579489-0.449209579488752
45122.26119.8803973490542.37960265094594
46122.91122.998970892996-0.0889708929959028
47123.78123.6393030944240.140696905575638
48123.99124.524591570205-0.534591570204924
49124.7124.6765015202490.0234984797512681
50125.89125.3890549235170.500945076482807
51127.57126.6334888617610.936511138239013
52128.97128.4152524918610.554747508139172
53130.65129.8755327361760.774467263823851
54130.73131.639688275755-0.909688275755116
55130.95131.620839284622-0.670839284621735
56131.36131.767944219065-0.407944219064831
57132.85132.1336159853520.716384014647701
58133.08133.701460054578-0.621460054578307
59133.13133.863930659002-0.733930659001857
60133.27133.834179927748-0.564179927748341
61133.9133.912874733253-0.0128747332526586
62134.85134.5414757327080.308524267291887
63135.49135.525000747128-0.0350007471276399
64136.21136.1611974788710.0488025211288345
65136.31136.886500482226-0.57650048222618
66136.22136.92385650563-0.703856505630284
67136.22136.7573737067-0.537373706699555
68135.51136.698981342871-1.18898134287056
69137.3135.8597836722491.44021632775087
70138.42137.8062811613410.61371883865894
71138.92138.992969377137-0.0729693771374116
72138.67139.485040343087-0.815040343087048







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73139.146476031779137.944415914385140.348536149173
74139.622952063558137.828242689658141.417661437459
75140.099428095337137.783780843055142.415075347619
76140.575904127116137.764713548248143.387094705985
77141.052380158896137.754378472706144.350381845085
78141.528856190675137.744888337301145.312824044048
79142.005332222454137.731960273435146.278704171473
80142.481808254233137.713074356834147.250542151631
81142.958284286012137.686673451727148.229895120297
82143.434760317791137.651767685016149.217752950566
83143.91123634957137.607720302466150.214752396674
84144.387712381349137.554123598839151.22130116386

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 139.146476031779 & 137.944415914385 & 140.348536149173 \tabularnewline
74 & 139.622952063558 & 137.828242689658 & 141.417661437459 \tabularnewline
75 & 140.099428095337 & 137.783780843055 & 142.415075347619 \tabularnewline
76 & 140.575904127116 & 137.764713548248 & 143.387094705985 \tabularnewline
77 & 141.052380158896 & 137.754378472706 & 144.350381845085 \tabularnewline
78 & 141.528856190675 & 137.744888337301 & 145.312824044048 \tabularnewline
79 & 142.005332222454 & 137.731960273435 & 146.278704171473 \tabularnewline
80 & 142.481808254233 & 137.713074356834 & 147.250542151631 \tabularnewline
81 & 142.958284286012 & 137.686673451727 & 148.229895120297 \tabularnewline
82 & 143.434760317791 & 137.651767685016 & 149.217752950566 \tabularnewline
83 & 143.91123634957 & 137.607720302466 & 150.214752396674 \tabularnewline
84 & 144.387712381349 & 137.554123598839 & 151.22130116386 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210495&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]139.146476031779[/C][C]137.944415914385[/C][C]140.348536149173[/C][/ROW]
[ROW][C]74[/C][C]139.622952063558[/C][C]137.828242689658[/C][C]141.417661437459[/C][/ROW]
[ROW][C]75[/C][C]140.099428095337[/C][C]137.783780843055[/C][C]142.415075347619[/C][/ROW]
[ROW][C]76[/C][C]140.575904127116[/C][C]137.764713548248[/C][C]143.387094705985[/C][/ROW]
[ROW][C]77[/C][C]141.052380158896[/C][C]137.754378472706[/C][C]144.350381845085[/C][/ROW]
[ROW][C]78[/C][C]141.528856190675[/C][C]137.744888337301[/C][C]145.312824044048[/C][/ROW]
[ROW][C]79[/C][C]142.005332222454[/C][C]137.731960273435[/C][C]146.278704171473[/C][/ROW]
[ROW][C]80[/C][C]142.481808254233[/C][C]137.713074356834[/C][C]147.250542151631[/C][/ROW]
[ROW][C]81[/C][C]142.958284286012[/C][C]137.686673451727[/C][C]148.229895120297[/C][/ROW]
[ROW][C]82[/C][C]143.434760317791[/C][C]137.651767685016[/C][C]149.217752950566[/C][/ROW]
[ROW][C]83[/C][C]143.91123634957[/C][C]137.607720302466[/C][C]150.214752396674[/C][/ROW]
[ROW][C]84[/C][C]144.387712381349[/C][C]137.554123598839[/C][C]151.22130116386[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210495&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210495&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
73139.146476031779137.944415914385140.348536149173
74139.622952063558137.828242689658141.417661437459
75140.099428095337137.783780843055142.415075347619
76140.575904127116137.764713548248143.387094705985
77141.052380158896137.754378472706144.350381845085
78141.528856190675137.744888337301145.312824044048
79142.005332222454137.731960273435146.278704171473
80142.481808254233137.713074356834147.250542151631
81142.958284286012137.686673451727148.229895120297
82143.434760317791137.651767685016149.217752950566
83143.91123634957137.607720302466150.214752396674
84144.387712381349137.554123598839151.22130116386



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