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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 Dec 2013 13:40:39 -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/Dec/20/t1387564919us5u0r3h6hm5hla.htm/, Retrieved Thu, 28 Mar 2024 20:35:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232481, Retrieved Thu, 28 Mar 2024 20:35:45 +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)
-       [Exponential Smoothing] [] [2013-12-20 18:40:39] [a3c700dc1d9df9ef9f271ed7f250ff74] [Current]
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Dataseries X:
100,44
100,47
100,49
100,52
100,47
100,48
100,48
100,53
100,62
100,89
100,97
101,01
101,02
100,92
100,93
100,98
101,07
101,1
101,11
101,19
101,31
101,52
101,61
101,65
101,66
101,56
101,75
101,83
101,98
102,06
102,07
102,1
102,42
102,91
103,14
103,23
103,23
102,91
103,11
103,14
103,26
103,3
103,32
103,44
103,54
103,98
104,24
104,29
104,29
103,98
103,98
103,89
103,86
103,88
103,88
104,31
104,41
104,8
104,89
104,9
104,9
104,54
104,67
104,87
105,04
105,09
105,1
105,46
105,83
106,27
106,46
106,52
106,53
105,96
106
106,15
106,32
106,41
106,41
106,81
106,99
107,35
107,53
107,56




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232481&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232481&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232481&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.899894829794702
beta0.0367668330068828
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.899894829794702 \tabularnewline
beta & 0.0367668330068828 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232481&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]0.899894829794702[/C][/ROW]
[ROW][C]beta[/C][C]0.0367668330068828[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232481&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232481&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
alpha0.899894829794702
beta0.0367668330068828
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13101.02100.7488095891150.271190410884529
14100.92100.8974290820510.0225709179485989
15100.93100.930523322077-0.000523322077455646
16100.98100.984065600126-0.00406560012635282
17101.07101.076369548473-0.00636954847259119
18101.1101.105971457559-0.00597145755864403
19101.11101.0739690950010.0360309049988103
20101.19101.1731633637770.0168366362230614
21101.31101.3017808117950.00821918820517453
22101.52101.603797585223-0.0837975852225412
23101.61101.622199803509-0.012199803508679
24101.65101.657654661848-0.00765466184797958
25101.66101.692822685321-0.0328226853214488
26101.56101.5395389403550.0204610596447452
27101.75101.565749613520.184250386480002
28101.83101.788918931940.0410810680596683
29101.98101.9271709364420.0528290635583204
30102.06102.0170765793670.0429234206327891
31102.07102.0413243196740.0286756803261312
32102.1102.140595139757-0.0405951397574711
33102.42102.2238115197060.196188480294452
34102.91102.7011014002110.208898599789322
35103.14103.0132604859460.126739514054023
36103.23103.2012499667460.0287500332541981
37103.23103.294790340069-0.0647903400693224
38102.91103.142669476174-0.232669476174379
39103.11102.9759362221710.134063777828885
40103.14103.156603778684-0.016603778684356
41103.26103.2599652051523.47948476502324e-05
42103.3103.314663268191-0.0146632681908869
43103.32103.2963394360130.0236605639871499
44103.44103.39566252270.0443374772997629
45103.54103.594321978194-0.0543219781939115
46103.98103.8559889321360.124011067863805
47104.24104.0871408599790.152859140020695
48104.29104.292729172898-0.00272917289824193
49104.29104.351371211177-0.0613712111765068
50103.98104.186655542399-0.206655542399147
51103.98104.084111559321-0.104111559321225
52103.89104.03122802091-0.141228020909637
53103.86104.016443630516-0.156443630515682
54103.88103.915562747973-0.0355627479728184
55103.88103.8679969570450.0120030429547455
56104.31103.9446965908620.365303409137681
57104.41104.419271921475-0.00927192147514688
58104.8104.7393099502550.0606900497453182
59104.89104.912452312856-0.0224523128559184
60104.9104.934480894305-0.0344808943053465
61104.9104.947437019134-0.0474370191338807
62104.54104.768878862816-0.228878862815691
63104.67104.6453724651280.0246275348724083
64104.87104.6973128102350.17268718976463
65105.04104.967188944690.072811055309856
66105.09105.095484612094-0.00548461209437789
67105.1105.0907828210920.00921717890848583
68105.46105.2124772911180.247522708882187
69105.83105.5518295776760.278170422324422
70106.27106.1584606030160.111539396984128
71106.46106.3886397595340.0713602404661486
72106.52106.5155924894130.00440751058694389
73106.53106.585255121212-0.0552551212124541
74105.96106.401107177441-0.441107177440699
75106106.128769662583-0.128769662582741
76106.15106.0682934770180.0817065229819463
77106.32106.2547880482660.0652119517344261
78106.41106.3760186574160.0339813425838855
79106.41106.416541153731-0.00654115373079378
80106.81106.55726874870.252731251299963
81106.99106.9135754356410.0764245643592147
82107.35107.3267939225010.0232060774986707
83107.53107.4729723058830.0570276941169823
84107.56107.57864312296-0.0186431229599293

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 101.02 & 100.748809589115 & 0.271190410884529 \tabularnewline
14 & 100.92 & 100.897429082051 & 0.0225709179485989 \tabularnewline
15 & 100.93 & 100.930523322077 & -0.000523322077455646 \tabularnewline
16 & 100.98 & 100.984065600126 & -0.00406560012635282 \tabularnewline
17 & 101.07 & 101.076369548473 & -0.00636954847259119 \tabularnewline
18 & 101.1 & 101.105971457559 & -0.00597145755864403 \tabularnewline
19 & 101.11 & 101.073969095001 & 0.0360309049988103 \tabularnewline
20 & 101.19 & 101.173163363777 & 0.0168366362230614 \tabularnewline
21 & 101.31 & 101.301780811795 & 0.00821918820517453 \tabularnewline
22 & 101.52 & 101.603797585223 & -0.0837975852225412 \tabularnewline
23 & 101.61 & 101.622199803509 & -0.012199803508679 \tabularnewline
24 & 101.65 & 101.657654661848 & -0.00765466184797958 \tabularnewline
25 & 101.66 & 101.692822685321 & -0.0328226853214488 \tabularnewline
26 & 101.56 & 101.539538940355 & 0.0204610596447452 \tabularnewline
27 & 101.75 & 101.56574961352 & 0.184250386480002 \tabularnewline
28 & 101.83 & 101.78891893194 & 0.0410810680596683 \tabularnewline
29 & 101.98 & 101.927170936442 & 0.0528290635583204 \tabularnewline
30 & 102.06 & 102.017076579367 & 0.0429234206327891 \tabularnewline
31 & 102.07 & 102.041324319674 & 0.0286756803261312 \tabularnewline
32 & 102.1 & 102.140595139757 & -0.0405951397574711 \tabularnewline
33 & 102.42 & 102.223811519706 & 0.196188480294452 \tabularnewline
34 & 102.91 & 102.701101400211 & 0.208898599789322 \tabularnewline
35 & 103.14 & 103.013260485946 & 0.126739514054023 \tabularnewline
36 & 103.23 & 103.201249966746 & 0.0287500332541981 \tabularnewline
37 & 103.23 & 103.294790340069 & -0.0647903400693224 \tabularnewline
38 & 102.91 & 103.142669476174 & -0.232669476174379 \tabularnewline
39 & 103.11 & 102.975936222171 & 0.134063777828885 \tabularnewline
40 & 103.14 & 103.156603778684 & -0.016603778684356 \tabularnewline
41 & 103.26 & 103.259965205152 & 3.47948476502324e-05 \tabularnewline
42 & 103.3 & 103.314663268191 & -0.0146632681908869 \tabularnewline
43 & 103.32 & 103.296339436013 & 0.0236605639871499 \tabularnewline
44 & 103.44 & 103.3956625227 & 0.0443374772997629 \tabularnewline
45 & 103.54 & 103.594321978194 & -0.0543219781939115 \tabularnewline
46 & 103.98 & 103.855988932136 & 0.124011067863805 \tabularnewline
47 & 104.24 & 104.087140859979 & 0.152859140020695 \tabularnewline
48 & 104.29 & 104.292729172898 & -0.00272917289824193 \tabularnewline
49 & 104.29 & 104.351371211177 & -0.0613712111765068 \tabularnewline
50 & 103.98 & 104.186655542399 & -0.206655542399147 \tabularnewline
51 & 103.98 & 104.084111559321 & -0.104111559321225 \tabularnewline
52 & 103.89 & 104.03122802091 & -0.141228020909637 \tabularnewline
53 & 103.86 & 104.016443630516 & -0.156443630515682 \tabularnewline
54 & 103.88 & 103.915562747973 & -0.0355627479728184 \tabularnewline
55 & 103.88 & 103.867996957045 & 0.0120030429547455 \tabularnewline
56 & 104.31 & 103.944696590862 & 0.365303409137681 \tabularnewline
57 & 104.41 & 104.419271921475 & -0.00927192147514688 \tabularnewline
58 & 104.8 & 104.739309950255 & 0.0606900497453182 \tabularnewline
59 & 104.89 & 104.912452312856 & -0.0224523128559184 \tabularnewline
60 & 104.9 & 104.934480894305 & -0.0344808943053465 \tabularnewline
61 & 104.9 & 104.947437019134 & -0.0474370191338807 \tabularnewline
62 & 104.54 & 104.768878862816 & -0.228878862815691 \tabularnewline
63 & 104.67 & 104.645372465128 & 0.0246275348724083 \tabularnewline
64 & 104.87 & 104.697312810235 & 0.17268718976463 \tabularnewline
65 & 105.04 & 104.96718894469 & 0.072811055309856 \tabularnewline
66 & 105.09 & 105.095484612094 & -0.00548461209437789 \tabularnewline
67 & 105.1 & 105.090782821092 & 0.00921717890848583 \tabularnewline
68 & 105.46 & 105.212477291118 & 0.247522708882187 \tabularnewline
69 & 105.83 & 105.551829577676 & 0.278170422324422 \tabularnewline
70 & 106.27 & 106.158460603016 & 0.111539396984128 \tabularnewline
71 & 106.46 & 106.388639759534 & 0.0713602404661486 \tabularnewline
72 & 106.52 & 106.515592489413 & 0.00440751058694389 \tabularnewline
73 & 106.53 & 106.585255121212 & -0.0552551212124541 \tabularnewline
74 & 105.96 & 106.401107177441 & -0.441107177440699 \tabularnewline
75 & 106 & 106.128769662583 & -0.128769662582741 \tabularnewline
76 & 106.15 & 106.068293477018 & 0.0817065229819463 \tabularnewline
77 & 106.32 & 106.254788048266 & 0.0652119517344261 \tabularnewline
78 & 106.41 & 106.376018657416 & 0.0339813425838855 \tabularnewline
79 & 106.41 & 106.416541153731 & -0.00654115373079378 \tabularnewline
80 & 106.81 & 106.5572687487 & 0.252731251299963 \tabularnewline
81 & 106.99 & 106.913575435641 & 0.0764245643592147 \tabularnewline
82 & 107.35 & 107.326793922501 & 0.0232060774986707 \tabularnewline
83 & 107.53 & 107.472972305883 & 0.0570276941169823 \tabularnewline
84 & 107.56 & 107.57864312296 & -0.0186431229599293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232481&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]101.02[/C][C]100.748809589115[/C][C]0.271190410884529[/C][/ROW]
[ROW][C]14[/C][C]100.92[/C][C]100.897429082051[/C][C]0.0225709179485989[/C][/ROW]
[ROW][C]15[/C][C]100.93[/C][C]100.930523322077[/C][C]-0.000523322077455646[/C][/ROW]
[ROW][C]16[/C][C]100.98[/C][C]100.984065600126[/C][C]-0.00406560012635282[/C][/ROW]
[ROW][C]17[/C][C]101.07[/C][C]101.076369548473[/C][C]-0.00636954847259119[/C][/ROW]
[ROW][C]18[/C][C]101.1[/C][C]101.105971457559[/C][C]-0.00597145755864403[/C][/ROW]
[ROW][C]19[/C][C]101.11[/C][C]101.073969095001[/C][C]0.0360309049988103[/C][/ROW]
[ROW][C]20[/C][C]101.19[/C][C]101.173163363777[/C][C]0.0168366362230614[/C][/ROW]
[ROW][C]21[/C][C]101.31[/C][C]101.301780811795[/C][C]0.00821918820517453[/C][/ROW]
[ROW][C]22[/C][C]101.52[/C][C]101.603797585223[/C][C]-0.0837975852225412[/C][/ROW]
[ROW][C]23[/C][C]101.61[/C][C]101.622199803509[/C][C]-0.012199803508679[/C][/ROW]
[ROW][C]24[/C][C]101.65[/C][C]101.657654661848[/C][C]-0.00765466184797958[/C][/ROW]
[ROW][C]25[/C][C]101.66[/C][C]101.692822685321[/C][C]-0.0328226853214488[/C][/ROW]
[ROW][C]26[/C][C]101.56[/C][C]101.539538940355[/C][C]0.0204610596447452[/C][/ROW]
[ROW][C]27[/C][C]101.75[/C][C]101.56574961352[/C][C]0.184250386480002[/C][/ROW]
[ROW][C]28[/C][C]101.83[/C][C]101.78891893194[/C][C]0.0410810680596683[/C][/ROW]
[ROW][C]29[/C][C]101.98[/C][C]101.927170936442[/C][C]0.0528290635583204[/C][/ROW]
[ROW][C]30[/C][C]102.06[/C][C]102.017076579367[/C][C]0.0429234206327891[/C][/ROW]
[ROW][C]31[/C][C]102.07[/C][C]102.041324319674[/C][C]0.0286756803261312[/C][/ROW]
[ROW][C]32[/C][C]102.1[/C][C]102.140595139757[/C][C]-0.0405951397574711[/C][/ROW]
[ROW][C]33[/C][C]102.42[/C][C]102.223811519706[/C][C]0.196188480294452[/C][/ROW]
[ROW][C]34[/C][C]102.91[/C][C]102.701101400211[/C][C]0.208898599789322[/C][/ROW]
[ROW][C]35[/C][C]103.14[/C][C]103.013260485946[/C][C]0.126739514054023[/C][/ROW]
[ROW][C]36[/C][C]103.23[/C][C]103.201249966746[/C][C]0.0287500332541981[/C][/ROW]
[ROW][C]37[/C][C]103.23[/C][C]103.294790340069[/C][C]-0.0647903400693224[/C][/ROW]
[ROW][C]38[/C][C]102.91[/C][C]103.142669476174[/C][C]-0.232669476174379[/C][/ROW]
[ROW][C]39[/C][C]103.11[/C][C]102.975936222171[/C][C]0.134063777828885[/C][/ROW]
[ROW][C]40[/C][C]103.14[/C][C]103.156603778684[/C][C]-0.016603778684356[/C][/ROW]
[ROW][C]41[/C][C]103.26[/C][C]103.259965205152[/C][C]3.47948476502324e-05[/C][/ROW]
[ROW][C]42[/C][C]103.3[/C][C]103.314663268191[/C][C]-0.0146632681908869[/C][/ROW]
[ROW][C]43[/C][C]103.32[/C][C]103.296339436013[/C][C]0.0236605639871499[/C][/ROW]
[ROW][C]44[/C][C]103.44[/C][C]103.3956625227[/C][C]0.0443374772997629[/C][/ROW]
[ROW][C]45[/C][C]103.54[/C][C]103.594321978194[/C][C]-0.0543219781939115[/C][/ROW]
[ROW][C]46[/C][C]103.98[/C][C]103.855988932136[/C][C]0.124011067863805[/C][/ROW]
[ROW][C]47[/C][C]104.24[/C][C]104.087140859979[/C][C]0.152859140020695[/C][/ROW]
[ROW][C]48[/C][C]104.29[/C][C]104.292729172898[/C][C]-0.00272917289824193[/C][/ROW]
[ROW][C]49[/C][C]104.29[/C][C]104.351371211177[/C][C]-0.0613712111765068[/C][/ROW]
[ROW][C]50[/C][C]103.98[/C][C]104.186655542399[/C][C]-0.206655542399147[/C][/ROW]
[ROW][C]51[/C][C]103.98[/C][C]104.084111559321[/C][C]-0.104111559321225[/C][/ROW]
[ROW][C]52[/C][C]103.89[/C][C]104.03122802091[/C][C]-0.141228020909637[/C][/ROW]
[ROW][C]53[/C][C]103.86[/C][C]104.016443630516[/C][C]-0.156443630515682[/C][/ROW]
[ROW][C]54[/C][C]103.88[/C][C]103.915562747973[/C][C]-0.0355627479728184[/C][/ROW]
[ROW][C]55[/C][C]103.88[/C][C]103.867996957045[/C][C]0.0120030429547455[/C][/ROW]
[ROW][C]56[/C][C]104.31[/C][C]103.944696590862[/C][C]0.365303409137681[/C][/ROW]
[ROW][C]57[/C][C]104.41[/C][C]104.419271921475[/C][C]-0.00927192147514688[/C][/ROW]
[ROW][C]58[/C][C]104.8[/C][C]104.739309950255[/C][C]0.0606900497453182[/C][/ROW]
[ROW][C]59[/C][C]104.89[/C][C]104.912452312856[/C][C]-0.0224523128559184[/C][/ROW]
[ROW][C]60[/C][C]104.9[/C][C]104.934480894305[/C][C]-0.0344808943053465[/C][/ROW]
[ROW][C]61[/C][C]104.9[/C][C]104.947437019134[/C][C]-0.0474370191338807[/C][/ROW]
[ROW][C]62[/C][C]104.54[/C][C]104.768878862816[/C][C]-0.228878862815691[/C][/ROW]
[ROW][C]63[/C][C]104.67[/C][C]104.645372465128[/C][C]0.0246275348724083[/C][/ROW]
[ROW][C]64[/C][C]104.87[/C][C]104.697312810235[/C][C]0.17268718976463[/C][/ROW]
[ROW][C]65[/C][C]105.04[/C][C]104.96718894469[/C][C]0.072811055309856[/C][/ROW]
[ROW][C]66[/C][C]105.09[/C][C]105.095484612094[/C][C]-0.00548461209437789[/C][/ROW]
[ROW][C]67[/C][C]105.1[/C][C]105.090782821092[/C][C]0.00921717890848583[/C][/ROW]
[ROW][C]68[/C][C]105.46[/C][C]105.212477291118[/C][C]0.247522708882187[/C][/ROW]
[ROW][C]69[/C][C]105.83[/C][C]105.551829577676[/C][C]0.278170422324422[/C][/ROW]
[ROW][C]70[/C][C]106.27[/C][C]106.158460603016[/C][C]0.111539396984128[/C][/ROW]
[ROW][C]71[/C][C]106.46[/C][C]106.388639759534[/C][C]0.0713602404661486[/C][/ROW]
[ROW][C]72[/C][C]106.52[/C][C]106.515592489413[/C][C]0.00440751058694389[/C][/ROW]
[ROW][C]73[/C][C]106.53[/C][C]106.585255121212[/C][C]-0.0552551212124541[/C][/ROW]
[ROW][C]74[/C][C]105.96[/C][C]106.401107177441[/C][C]-0.441107177440699[/C][/ROW]
[ROW][C]75[/C][C]106[/C][C]106.128769662583[/C][C]-0.128769662582741[/C][/ROW]
[ROW][C]76[/C][C]106.15[/C][C]106.068293477018[/C][C]0.0817065229819463[/C][/ROW]
[ROW][C]77[/C][C]106.32[/C][C]106.254788048266[/C][C]0.0652119517344261[/C][/ROW]
[ROW][C]78[/C][C]106.41[/C][C]106.376018657416[/C][C]0.0339813425838855[/C][/ROW]
[ROW][C]79[/C][C]106.41[/C][C]106.416541153731[/C][C]-0.00654115373079378[/C][/ROW]
[ROW][C]80[/C][C]106.81[/C][C]106.5572687487[/C][C]0.252731251299963[/C][/ROW]
[ROW][C]81[/C][C]106.99[/C][C]106.913575435641[/C][C]0.0764245643592147[/C][/ROW]
[ROW][C]82[/C][C]107.35[/C][C]107.326793922501[/C][C]0.0232060774986707[/C][/ROW]
[ROW][C]83[/C][C]107.53[/C][C]107.472972305883[/C][C]0.0570276941169823[/C][/ROW]
[ROW][C]84[/C][C]107.56[/C][C]107.57864312296[/C][C]-0.0186431229599293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232481&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232481&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
13101.02100.7488095891150.271190410884529
14100.92100.8974290820510.0225709179485989
15100.93100.930523322077-0.000523322077455646
16100.98100.984065600126-0.00406560012635282
17101.07101.076369548473-0.00636954847259119
18101.1101.105971457559-0.00597145755864403
19101.11101.0739690950010.0360309049988103
20101.19101.1731633637770.0168366362230614
21101.31101.3017808117950.00821918820517453
22101.52101.603797585223-0.0837975852225412
23101.61101.622199803509-0.012199803508679
24101.65101.657654661848-0.00765466184797958
25101.66101.692822685321-0.0328226853214488
26101.56101.5395389403550.0204610596447452
27101.75101.565749613520.184250386480002
28101.83101.788918931940.0410810680596683
29101.98101.9271709364420.0528290635583204
30102.06102.0170765793670.0429234206327891
31102.07102.0413243196740.0286756803261312
32102.1102.140595139757-0.0405951397574711
33102.42102.2238115197060.196188480294452
34102.91102.7011014002110.208898599789322
35103.14103.0132604859460.126739514054023
36103.23103.2012499667460.0287500332541981
37103.23103.294790340069-0.0647903400693224
38102.91103.142669476174-0.232669476174379
39103.11102.9759362221710.134063777828885
40103.14103.156603778684-0.016603778684356
41103.26103.2599652051523.47948476502324e-05
42103.3103.314663268191-0.0146632681908869
43103.32103.2963394360130.0236605639871499
44103.44103.39566252270.0443374772997629
45103.54103.594321978194-0.0543219781939115
46103.98103.8559889321360.124011067863805
47104.24104.0871408599790.152859140020695
48104.29104.292729172898-0.00272917289824193
49104.29104.351371211177-0.0613712111765068
50103.98104.186655542399-0.206655542399147
51103.98104.084111559321-0.104111559321225
52103.89104.03122802091-0.141228020909637
53103.86104.016443630516-0.156443630515682
54103.88103.915562747973-0.0355627479728184
55103.88103.8679969570450.0120030429547455
56104.31103.9446965908620.365303409137681
57104.41104.419271921475-0.00927192147514688
58104.8104.7393099502550.0606900497453182
59104.89104.912452312856-0.0224523128559184
60104.9104.934480894305-0.0344808943053465
61104.9104.947437019134-0.0474370191338807
62104.54104.768878862816-0.228878862815691
63104.67104.6453724651280.0246275348724083
64104.87104.6973128102350.17268718976463
65105.04104.967188944690.072811055309856
66105.09105.095484612094-0.00548461209437789
67105.1105.0907828210920.00921717890848583
68105.46105.2124772911180.247522708882187
69105.83105.5518295776760.278170422324422
70106.27106.1584606030160.111539396984128
71106.46106.3886397595340.0713602404661486
72106.52106.5155924894130.00440751058694389
73106.53106.585255121212-0.0552551212124541
74105.96106.401107177441-0.441107177440699
75106106.128769662583-0.128769662582741
76106.15106.0682934770180.0817065229819463
77106.32106.2547880482660.0652119517344261
78106.41106.3760186574160.0339813425838855
79106.41106.416541153731-0.00654115373079378
80106.81106.55726874870.252731251299963
81106.99106.9135754356410.0764245643592147
82107.35107.3267939225010.0232060774986707
83107.53107.4729723058830.0570276941169823
84107.56107.57864312296-0.0186431229599293







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85107.619188555343107.374687986786107.8636891239
86107.443024185069107.109031552746107.777016817393
87107.614320710663107.20509077369108.023550647637
88107.709422296521107.232843843701108.186000749341
89107.837143917784107.297758160272108.376529675297
90107.910028405839107.311166139047108.508890672631
91107.927480751377107.271592132784108.58336936997
92108.114153428841107.40183092546108.826475932221
93108.230141277231107.462910151896108.997372402567
94108.574099762322107.751188231105109.39701129354
95108.704398379924107.827857762744109.580938997104
96108.749979216926106.118703011101111.381255422752

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 107.619188555343 & 107.374687986786 & 107.8636891239 \tabularnewline
86 & 107.443024185069 & 107.109031552746 & 107.777016817393 \tabularnewline
87 & 107.614320710663 & 107.20509077369 & 108.023550647637 \tabularnewline
88 & 107.709422296521 & 107.232843843701 & 108.186000749341 \tabularnewline
89 & 107.837143917784 & 107.297758160272 & 108.376529675297 \tabularnewline
90 & 107.910028405839 & 107.311166139047 & 108.508890672631 \tabularnewline
91 & 107.927480751377 & 107.271592132784 & 108.58336936997 \tabularnewline
92 & 108.114153428841 & 107.40183092546 & 108.826475932221 \tabularnewline
93 & 108.230141277231 & 107.462910151896 & 108.997372402567 \tabularnewline
94 & 108.574099762322 & 107.751188231105 & 109.39701129354 \tabularnewline
95 & 108.704398379924 & 107.827857762744 & 109.580938997104 \tabularnewline
96 & 108.749979216926 & 106.118703011101 & 111.381255422752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232481&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]107.619188555343[/C][C]107.374687986786[/C][C]107.8636891239[/C][/ROW]
[ROW][C]86[/C][C]107.443024185069[/C][C]107.109031552746[/C][C]107.777016817393[/C][/ROW]
[ROW][C]87[/C][C]107.614320710663[/C][C]107.20509077369[/C][C]108.023550647637[/C][/ROW]
[ROW][C]88[/C][C]107.709422296521[/C][C]107.232843843701[/C][C]108.186000749341[/C][/ROW]
[ROW][C]89[/C][C]107.837143917784[/C][C]107.297758160272[/C][C]108.376529675297[/C][/ROW]
[ROW][C]90[/C][C]107.910028405839[/C][C]107.311166139047[/C][C]108.508890672631[/C][/ROW]
[ROW][C]91[/C][C]107.927480751377[/C][C]107.271592132784[/C][C]108.58336936997[/C][/ROW]
[ROW][C]92[/C][C]108.114153428841[/C][C]107.40183092546[/C][C]108.826475932221[/C][/ROW]
[ROW][C]93[/C][C]108.230141277231[/C][C]107.462910151896[/C][C]108.997372402567[/C][/ROW]
[ROW][C]94[/C][C]108.574099762322[/C][C]107.751188231105[/C][C]109.39701129354[/C][/ROW]
[ROW][C]95[/C][C]108.704398379924[/C][C]107.827857762744[/C][C]109.580938997104[/C][/ROW]
[ROW][C]96[/C][C]108.749979216926[/C][C]106.118703011101[/C][C]111.381255422752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232481&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232481&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
85107.619188555343107.374687986786107.8636891239
86107.443024185069107.109031552746107.777016817393
87107.614320710663107.20509077369108.023550647637
88107.709422296521107.232843843701108.186000749341
89107.837143917784107.297758160272108.376529675297
90107.910028405839107.311166139047108.508890672631
91107.927480751377107.271592132784108.58336936997
92108.114153428841107.40183092546108.826475932221
93108.230141277231107.462910151896108.997372402567
94108.574099762322107.751188231105109.39701129354
95108.704398379924107.827857762744109.580938997104
96108.749979216926106.118703011101111.381255422752



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')