Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 13 Aug 2014 11:15:04 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Aug/13/t1407924914l4qsfgeiurwgyzm.htm/, Retrieved Thu, 16 May 2024 20:54:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235501, Retrieved Thu, 16 May 2024 20:54:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2014-08-13 09:41:06] [ba0170e6f15797e8c541ec0953bc1848]
- RMP     [Exponential Smoothing] [] [2014-08-13 10:15:04] [b3e3d38149b35cb70244b37a39776b3a] [Current]
Feedback Forum

Post a new message
Dataseries X:
106
105
104
102
122
121
106
96
97
97
98
100
106
104
107
112
140
140
134
128
133
139
140
143
152
146
146
155
180
182
177
165
174
174
175
180
184
186
186
192
215
221
222
207
215
212
206
219
222
217
218
225
251
264
264
258
267
258
253
272
275
268
286
293
314
328
326
325
333
332
320
338
344
338
363
375
403
414
411
405
410
416
396
412
422
418
444
453
491
498
489
494
497
500
481
499
509
499
528
537
576
582
584
594
594
598
580
589
595
584
616
622
662
669
679
688
689
690
672
690




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235501&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]2 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=235501&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235501&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.214017549706109
beta0.10820900489298
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.214017549706109 \tabularnewline
beta & 0.10820900489298 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235501&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]0.214017549706109[/C][/ROW]
[ROW][C]beta[/C][C]0.10820900489298[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235501&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235501&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
alpha0.214017549706109
beta0.10820900489298
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310699.96664370070396.03335629929613
1410499.10941027628994.89058972371014
15107102.6035292127364.39647078726387
16112107.6428686984984.35713130150221
17140134.6582549886795.34174501132085
18140134.8432782042345.15672179576555
19134126.2156770038867.7843229961142
20128118.4938205360139.50617946398735
21133124.5645531892338.43544681076733
22139128.77582570894910.2241742910511
23140134.1527858399735.84721416002725
24143139.6382940806913.36170591930937
25152156.809155844972-4.80915584497185
26146151.779235514193-5.77923551419286
27146153.754171302531-7.75417130253078
28155157.838640354209-2.83864035420922
29180194.681509896174-14.6815098961741
30182189.389563361308-7.38956336130821
31177176.629804753050.370195246949692
32165165.063052696506-0.0630526965064462
33174167.9406258613766.05937413862398
34174172.7371930435911.26280695640901
35175171.3050466683073.69495333169311
36180173.5239836624836.47601633751674
37184185.806324477944-1.80632447794386
38186178.3936080215487.6063919784518
39186181.1165821871314.88341781286854
40192193.523438095967-1.52343809596735
41215227.385077622915-12.3850776229145
42221228.595202779074-7.5952027790735
43222220.1442146008181.85578539918234
44207205.188795545671.81120445433032
45215214.7442002190610.255799780939128
46212213.949594363444-1.94959436344354
47206213.208331607693-7.20833160769337
48219215.2012411323823.79875886761769
49222220.4140781351581.58592186484222
50217220.373609549837-3.3736095498372
51218217.4187940369120.581205963087882
52225223.8655638929931.13443610700739
53251252.802303182054-1.80230318205366
54264260.4455193027043.55448069729613
55264261.3065828032552.69341719674526
56258243.1867756087814.8132243912204
57267255.52586413674111.474135863259
58258254.8206709365553.17932906344501
59253250.1305374443532.86946255564672
60272265.8572248957916.14277510420931
61275270.7323493569064.26765064309404
62268266.7481857591791.25181424082075
63286268.54059355868817.4594064413117
64293281.51150827317611.4884917268241
65314318.360928947316-4.36092894731598
66328333.96795014116-5.9679501411598
67326332.789784250469-6.78978425046904
68325320.2225549020014.77744509799862
69333329.5685657886663.43143421133431
70332318.36709854533513.6329014546645
71320314.5185488140785.48145118592174
72338338.01005633122-0.0100563312199711
73344340.7063508665573.29364913344261
74338332.4601031959615.53989680403919
75363351.32552903382111.6744709661792
76375359.28003898078415.7199610192156
77403389.73240524040413.2675947595958
78414411.9813202090462.01867979095391
79411412.200568682043-1.20056868204256
80405410.00035834056-5.00035834056001
81410418.463739625111-8.46373962511143
82416411.7622845439994.23771545600067
83396396.148461924195-0.148461924195431
84412418.125522102415-6.12552210241495
85422422.945009784984-0.945009784984393
86418413.4237834441924.57621655580823
87444441.3776534515832.62234654841689
88453451.5432902181541.45670978184563
89491480.90880025229410.0911997477065
90498494.4461123456323.55388765436777
91489490.708896635724-1.70889663572444
92494483.28132109178710.7186789082133
93497492.8855940266264.11440597337406
94500499.3640161708510.635983829149268
95481474.9529922096996.04700779030054
96499496.5974323885052.40256761149465
97509509.168936066764-0.16893606676382
98499502.89185355801-3.8918535580105
99528532.180996581808-4.18099658180824
100537541.10731996042-4.10731996041989
101576582.199458162337-6.19945816233712
102582587.162080888081-5.16208088808139
103584574.6736680874489.32633191255218
104594578.84625693434515.1537430656554
105594583.68107473956710.3189252604333
106598588.4951269851499.50487301485077
107580565.99388761752314.0061123824769
108589589.257813009789-0.25781300978872
109595600.577217804015-5.57721780401494
110584588.022831655448-4.02283165544759
111616621.765410993726-5.76541099372616
112622631.555493984479-9.55549398447886
113662676.060112863147-14.0601128631474
114669680.500798029579-11.5007980295788
115679677.0793067873831.92069321261715
116688684.1422436850163.85775631498393
117689681.0244471691937.97555283080658
118690683.5470236029536.45297639704711
119672659.39278295611712.6072170438825
120690670.94812927815919.0518707218412

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 106 & 99.9666437007039 & 6.03335629929613 \tabularnewline
14 & 104 & 99.1094102762899 & 4.89058972371014 \tabularnewline
15 & 107 & 102.603529212736 & 4.39647078726387 \tabularnewline
16 & 112 & 107.642868698498 & 4.35713130150221 \tabularnewline
17 & 140 & 134.658254988679 & 5.34174501132085 \tabularnewline
18 & 140 & 134.843278204234 & 5.15672179576555 \tabularnewline
19 & 134 & 126.215677003886 & 7.7843229961142 \tabularnewline
20 & 128 & 118.493820536013 & 9.50617946398735 \tabularnewline
21 & 133 & 124.564553189233 & 8.43544681076733 \tabularnewline
22 & 139 & 128.775825708949 & 10.2241742910511 \tabularnewline
23 & 140 & 134.152785839973 & 5.84721416002725 \tabularnewline
24 & 143 & 139.638294080691 & 3.36170591930937 \tabularnewline
25 & 152 & 156.809155844972 & -4.80915584497185 \tabularnewline
26 & 146 & 151.779235514193 & -5.77923551419286 \tabularnewline
27 & 146 & 153.754171302531 & -7.75417130253078 \tabularnewline
28 & 155 & 157.838640354209 & -2.83864035420922 \tabularnewline
29 & 180 & 194.681509896174 & -14.6815098961741 \tabularnewline
30 & 182 & 189.389563361308 & -7.38956336130821 \tabularnewline
31 & 177 & 176.62980475305 & 0.370195246949692 \tabularnewline
32 & 165 & 165.063052696506 & -0.0630526965064462 \tabularnewline
33 & 174 & 167.940625861376 & 6.05937413862398 \tabularnewline
34 & 174 & 172.737193043591 & 1.26280695640901 \tabularnewline
35 & 175 & 171.305046668307 & 3.69495333169311 \tabularnewline
36 & 180 & 173.523983662483 & 6.47601633751674 \tabularnewline
37 & 184 & 185.806324477944 & -1.80632447794386 \tabularnewline
38 & 186 & 178.393608021548 & 7.6063919784518 \tabularnewline
39 & 186 & 181.116582187131 & 4.88341781286854 \tabularnewline
40 & 192 & 193.523438095967 & -1.52343809596735 \tabularnewline
41 & 215 & 227.385077622915 & -12.3850776229145 \tabularnewline
42 & 221 & 228.595202779074 & -7.5952027790735 \tabularnewline
43 & 222 & 220.144214600818 & 1.85578539918234 \tabularnewline
44 & 207 & 205.18879554567 & 1.81120445433032 \tabularnewline
45 & 215 & 214.744200219061 & 0.255799780939128 \tabularnewline
46 & 212 & 213.949594363444 & -1.94959436344354 \tabularnewline
47 & 206 & 213.208331607693 & -7.20833160769337 \tabularnewline
48 & 219 & 215.201241132382 & 3.79875886761769 \tabularnewline
49 & 222 & 220.414078135158 & 1.58592186484222 \tabularnewline
50 & 217 & 220.373609549837 & -3.3736095498372 \tabularnewline
51 & 218 & 217.418794036912 & 0.581205963087882 \tabularnewline
52 & 225 & 223.865563892993 & 1.13443610700739 \tabularnewline
53 & 251 & 252.802303182054 & -1.80230318205366 \tabularnewline
54 & 264 & 260.445519302704 & 3.55448069729613 \tabularnewline
55 & 264 & 261.306582803255 & 2.69341719674526 \tabularnewline
56 & 258 & 243.18677560878 & 14.8132243912204 \tabularnewline
57 & 267 & 255.525864136741 & 11.474135863259 \tabularnewline
58 & 258 & 254.820670936555 & 3.17932906344501 \tabularnewline
59 & 253 & 250.130537444353 & 2.86946255564672 \tabularnewline
60 & 272 & 265.857224895791 & 6.14277510420931 \tabularnewline
61 & 275 & 270.732349356906 & 4.26765064309404 \tabularnewline
62 & 268 & 266.748185759179 & 1.25181424082075 \tabularnewline
63 & 286 & 268.540593558688 & 17.4594064413117 \tabularnewline
64 & 293 & 281.511508273176 & 11.4884917268241 \tabularnewline
65 & 314 & 318.360928947316 & -4.36092894731598 \tabularnewline
66 & 328 & 333.96795014116 & -5.9679501411598 \tabularnewline
67 & 326 & 332.789784250469 & -6.78978425046904 \tabularnewline
68 & 325 & 320.222554902001 & 4.77744509799862 \tabularnewline
69 & 333 & 329.568565788666 & 3.43143421133431 \tabularnewline
70 & 332 & 318.367098545335 & 13.6329014546645 \tabularnewline
71 & 320 & 314.518548814078 & 5.48145118592174 \tabularnewline
72 & 338 & 338.01005633122 & -0.0100563312199711 \tabularnewline
73 & 344 & 340.706350866557 & 3.29364913344261 \tabularnewline
74 & 338 & 332.460103195961 & 5.53989680403919 \tabularnewline
75 & 363 & 351.325529033821 & 11.6744709661792 \tabularnewline
76 & 375 & 359.280038980784 & 15.7199610192156 \tabularnewline
77 & 403 & 389.732405240404 & 13.2675947595958 \tabularnewline
78 & 414 & 411.981320209046 & 2.01867979095391 \tabularnewline
79 & 411 & 412.200568682043 & -1.20056868204256 \tabularnewline
80 & 405 & 410.00035834056 & -5.00035834056001 \tabularnewline
81 & 410 & 418.463739625111 & -8.46373962511143 \tabularnewline
82 & 416 & 411.762284543999 & 4.23771545600067 \tabularnewline
83 & 396 & 396.148461924195 & -0.148461924195431 \tabularnewline
84 & 412 & 418.125522102415 & -6.12552210241495 \tabularnewline
85 & 422 & 422.945009784984 & -0.945009784984393 \tabularnewline
86 & 418 & 413.423783444192 & 4.57621655580823 \tabularnewline
87 & 444 & 441.377653451583 & 2.62234654841689 \tabularnewline
88 & 453 & 451.543290218154 & 1.45670978184563 \tabularnewline
89 & 491 & 480.908800252294 & 10.0911997477065 \tabularnewline
90 & 498 & 494.446112345632 & 3.55388765436777 \tabularnewline
91 & 489 & 490.708896635724 & -1.70889663572444 \tabularnewline
92 & 494 & 483.281321091787 & 10.7186789082133 \tabularnewline
93 & 497 & 492.885594026626 & 4.11440597337406 \tabularnewline
94 & 500 & 499.364016170851 & 0.635983829149268 \tabularnewline
95 & 481 & 474.952992209699 & 6.04700779030054 \tabularnewline
96 & 499 & 496.597432388505 & 2.40256761149465 \tabularnewline
97 & 509 & 509.168936066764 & -0.16893606676382 \tabularnewline
98 & 499 & 502.89185355801 & -3.8918535580105 \tabularnewline
99 & 528 & 532.180996581808 & -4.18099658180824 \tabularnewline
100 & 537 & 541.10731996042 & -4.10731996041989 \tabularnewline
101 & 576 & 582.199458162337 & -6.19945816233712 \tabularnewline
102 & 582 & 587.162080888081 & -5.16208088808139 \tabularnewline
103 & 584 & 574.673668087448 & 9.32633191255218 \tabularnewline
104 & 594 & 578.846256934345 & 15.1537430656554 \tabularnewline
105 & 594 & 583.681074739567 & 10.3189252604333 \tabularnewline
106 & 598 & 588.495126985149 & 9.50487301485077 \tabularnewline
107 & 580 & 565.993887617523 & 14.0061123824769 \tabularnewline
108 & 589 & 589.257813009789 & -0.25781300978872 \tabularnewline
109 & 595 & 600.577217804015 & -5.57721780401494 \tabularnewline
110 & 584 & 588.022831655448 & -4.02283165544759 \tabularnewline
111 & 616 & 621.765410993726 & -5.76541099372616 \tabularnewline
112 & 622 & 631.555493984479 & -9.55549398447886 \tabularnewline
113 & 662 & 676.060112863147 & -14.0601128631474 \tabularnewline
114 & 669 & 680.500798029579 & -11.5007980295788 \tabularnewline
115 & 679 & 677.079306787383 & 1.92069321261715 \tabularnewline
116 & 688 & 684.142243685016 & 3.85775631498393 \tabularnewline
117 & 689 & 681.024447169193 & 7.97555283080658 \tabularnewline
118 & 690 & 683.547023602953 & 6.45297639704711 \tabularnewline
119 & 672 & 659.392782956117 & 12.6072170438825 \tabularnewline
120 & 690 & 670.948129278159 & 19.0518707218412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235501&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]106[/C][C]99.9666437007039[/C][C]6.03335629929613[/C][/ROW]
[ROW][C]14[/C][C]104[/C][C]99.1094102762899[/C][C]4.89058972371014[/C][/ROW]
[ROW][C]15[/C][C]107[/C][C]102.603529212736[/C][C]4.39647078726387[/C][/ROW]
[ROW][C]16[/C][C]112[/C][C]107.642868698498[/C][C]4.35713130150221[/C][/ROW]
[ROW][C]17[/C][C]140[/C][C]134.658254988679[/C][C]5.34174501132085[/C][/ROW]
[ROW][C]18[/C][C]140[/C][C]134.843278204234[/C][C]5.15672179576555[/C][/ROW]
[ROW][C]19[/C][C]134[/C][C]126.215677003886[/C][C]7.7843229961142[/C][/ROW]
[ROW][C]20[/C][C]128[/C][C]118.493820536013[/C][C]9.50617946398735[/C][/ROW]
[ROW][C]21[/C][C]133[/C][C]124.564553189233[/C][C]8.43544681076733[/C][/ROW]
[ROW][C]22[/C][C]139[/C][C]128.775825708949[/C][C]10.2241742910511[/C][/ROW]
[ROW][C]23[/C][C]140[/C][C]134.152785839973[/C][C]5.84721416002725[/C][/ROW]
[ROW][C]24[/C][C]143[/C][C]139.638294080691[/C][C]3.36170591930937[/C][/ROW]
[ROW][C]25[/C][C]152[/C][C]156.809155844972[/C][C]-4.80915584497185[/C][/ROW]
[ROW][C]26[/C][C]146[/C][C]151.779235514193[/C][C]-5.77923551419286[/C][/ROW]
[ROW][C]27[/C][C]146[/C][C]153.754171302531[/C][C]-7.75417130253078[/C][/ROW]
[ROW][C]28[/C][C]155[/C][C]157.838640354209[/C][C]-2.83864035420922[/C][/ROW]
[ROW][C]29[/C][C]180[/C][C]194.681509896174[/C][C]-14.6815098961741[/C][/ROW]
[ROW][C]30[/C][C]182[/C][C]189.389563361308[/C][C]-7.38956336130821[/C][/ROW]
[ROW][C]31[/C][C]177[/C][C]176.62980475305[/C][C]0.370195246949692[/C][/ROW]
[ROW][C]32[/C][C]165[/C][C]165.063052696506[/C][C]-0.0630526965064462[/C][/ROW]
[ROW][C]33[/C][C]174[/C][C]167.940625861376[/C][C]6.05937413862398[/C][/ROW]
[ROW][C]34[/C][C]174[/C][C]172.737193043591[/C][C]1.26280695640901[/C][/ROW]
[ROW][C]35[/C][C]175[/C][C]171.305046668307[/C][C]3.69495333169311[/C][/ROW]
[ROW][C]36[/C][C]180[/C][C]173.523983662483[/C][C]6.47601633751674[/C][/ROW]
[ROW][C]37[/C][C]184[/C][C]185.806324477944[/C][C]-1.80632447794386[/C][/ROW]
[ROW][C]38[/C][C]186[/C][C]178.393608021548[/C][C]7.6063919784518[/C][/ROW]
[ROW][C]39[/C][C]186[/C][C]181.116582187131[/C][C]4.88341781286854[/C][/ROW]
[ROW][C]40[/C][C]192[/C][C]193.523438095967[/C][C]-1.52343809596735[/C][/ROW]
[ROW][C]41[/C][C]215[/C][C]227.385077622915[/C][C]-12.3850776229145[/C][/ROW]
[ROW][C]42[/C][C]221[/C][C]228.595202779074[/C][C]-7.5952027790735[/C][/ROW]
[ROW][C]43[/C][C]222[/C][C]220.144214600818[/C][C]1.85578539918234[/C][/ROW]
[ROW][C]44[/C][C]207[/C][C]205.18879554567[/C][C]1.81120445433032[/C][/ROW]
[ROW][C]45[/C][C]215[/C][C]214.744200219061[/C][C]0.255799780939128[/C][/ROW]
[ROW][C]46[/C][C]212[/C][C]213.949594363444[/C][C]-1.94959436344354[/C][/ROW]
[ROW][C]47[/C][C]206[/C][C]213.208331607693[/C][C]-7.20833160769337[/C][/ROW]
[ROW][C]48[/C][C]219[/C][C]215.201241132382[/C][C]3.79875886761769[/C][/ROW]
[ROW][C]49[/C][C]222[/C][C]220.414078135158[/C][C]1.58592186484222[/C][/ROW]
[ROW][C]50[/C][C]217[/C][C]220.373609549837[/C][C]-3.3736095498372[/C][/ROW]
[ROW][C]51[/C][C]218[/C][C]217.418794036912[/C][C]0.581205963087882[/C][/ROW]
[ROW][C]52[/C][C]225[/C][C]223.865563892993[/C][C]1.13443610700739[/C][/ROW]
[ROW][C]53[/C][C]251[/C][C]252.802303182054[/C][C]-1.80230318205366[/C][/ROW]
[ROW][C]54[/C][C]264[/C][C]260.445519302704[/C][C]3.55448069729613[/C][/ROW]
[ROW][C]55[/C][C]264[/C][C]261.306582803255[/C][C]2.69341719674526[/C][/ROW]
[ROW][C]56[/C][C]258[/C][C]243.18677560878[/C][C]14.8132243912204[/C][/ROW]
[ROW][C]57[/C][C]267[/C][C]255.525864136741[/C][C]11.474135863259[/C][/ROW]
[ROW][C]58[/C][C]258[/C][C]254.820670936555[/C][C]3.17932906344501[/C][/ROW]
[ROW][C]59[/C][C]253[/C][C]250.130537444353[/C][C]2.86946255564672[/C][/ROW]
[ROW][C]60[/C][C]272[/C][C]265.857224895791[/C][C]6.14277510420931[/C][/ROW]
[ROW][C]61[/C][C]275[/C][C]270.732349356906[/C][C]4.26765064309404[/C][/ROW]
[ROW][C]62[/C][C]268[/C][C]266.748185759179[/C][C]1.25181424082075[/C][/ROW]
[ROW][C]63[/C][C]286[/C][C]268.540593558688[/C][C]17.4594064413117[/C][/ROW]
[ROW][C]64[/C][C]293[/C][C]281.511508273176[/C][C]11.4884917268241[/C][/ROW]
[ROW][C]65[/C][C]314[/C][C]318.360928947316[/C][C]-4.36092894731598[/C][/ROW]
[ROW][C]66[/C][C]328[/C][C]333.96795014116[/C][C]-5.9679501411598[/C][/ROW]
[ROW][C]67[/C][C]326[/C][C]332.789784250469[/C][C]-6.78978425046904[/C][/ROW]
[ROW][C]68[/C][C]325[/C][C]320.222554902001[/C][C]4.77744509799862[/C][/ROW]
[ROW][C]69[/C][C]333[/C][C]329.568565788666[/C][C]3.43143421133431[/C][/ROW]
[ROW][C]70[/C][C]332[/C][C]318.367098545335[/C][C]13.6329014546645[/C][/ROW]
[ROW][C]71[/C][C]320[/C][C]314.518548814078[/C][C]5.48145118592174[/C][/ROW]
[ROW][C]72[/C][C]338[/C][C]338.01005633122[/C][C]-0.0100563312199711[/C][/ROW]
[ROW][C]73[/C][C]344[/C][C]340.706350866557[/C][C]3.29364913344261[/C][/ROW]
[ROW][C]74[/C][C]338[/C][C]332.460103195961[/C][C]5.53989680403919[/C][/ROW]
[ROW][C]75[/C][C]363[/C][C]351.325529033821[/C][C]11.6744709661792[/C][/ROW]
[ROW][C]76[/C][C]375[/C][C]359.280038980784[/C][C]15.7199610192156[/C][/ROW]
[ROW][C]77[/C][C]403[/C][C]389.732405240404[/C][C]13.2675947595958[/C][/ROW]
[ROW][C]78[/C][C]414[/C][C]411.981320209046[/C][C]2.01867979095391[/C][/ROW]
[ROW][C]79[/C][C]411[/C][C]412.200568682043[/C][C]-1.20056868204256[/C][/ROW]
[ROW][C]80[/C][C]405[/C][C]410.00035834056[/C][C]-5.00035834056001[/C][/ROW]
[ROW][C]81[/C][C]410[/C][C]418.463739625111[/C][C]-8.46373962511143[/C][/ROW]
[ROW][C]82[/C][C]416[/C][C]411.762284543999[/C][C]4.23771545600067[/C][/ROW]
[ROW][C]83[/C][C]396[/C][C]396.148461924195[/C][C]-0.148461924195431[/C][/ROW]
[ROW][C]84[/C][C]412[/C][C]418.125522102415[/C][C]-6.12552210241495[/C][/ROW]
[ROW][C]85[/C][C]422[/C][C]422.945009784984[/C][C]-0.945009784984393[/C][/ROW]
[ROW][C]86[/C][C]418[/C][C]413.423783444192[/C][C]4.57621655580823[/C][/ROW]
[ROW][C]87[/C][C]444[/C][C]441.377653451583[/C][C]2.62234654841689[/C][/ROW]
[ROW][C]88[/C][C]453[/C][C]451.543290218154[/C][C]1.45670978184563[/C][/ROW]
[ROW][C]89[/C][C]491[/C][C]480.908800252294[/C][C]10.0911997477065[/C][/ROW]
[ROW][C]90[/C][C]498[/C][C]494.446112345632[/C][C]3.55388765436777[/C][/ROW]
[ROW][C]91[/C][C]489[/C][C]490.708896635724[/C][C]-1.70889663572444[/C][/ROW]
[ROW][C]92[/C][C]494[/C][C]483.281321091787[/C][C]10.7186789082133[/C][/ROW]
[ROW][C]93[/C][C]497[/C][C]492.885594026626[/C][C]4.11440597337406[/C][/ROW]
[ROW][C]94[/C][C]500[/C][C]499.364016170851[/C][C]0.635983829149268[/C][/ROW]
[ROW][C]95[/C][C]481[/C][C]474.952992209699[/C][C]6.04700779030054[/C][/ROW]
[ROW][C]96[/C][C]499[/C][C]496.597432388505[/C][C]2.40256761149465[/C][/ROW]
[ROW][C]97[/C][C]509[/C][C]509.168936066764[/C][C]-0.16893606676382[/C][/ROW]
[ROW][C]98[/C][C]499[/C][C]502.89185355801[/C][C]-3.8918535580105[/C][/ROW]
[ROW][C]99[/C][C]528[/C][C]532.180996581808[/C][C]-4.18099658180824[/C][/ROW]
[ROW][C]100[/C][C]537[/C][C]541.10731996042[/C][C]-4.10731996041989[/C][/ROW]
[ROW][C]101[/C][C]576[/C][C]582.199458162337[/C][C]-6.19945816233712[/C][/ROW]
[ROW][C]102[/C][C]582[/C][C]587.162080888081[/C][C]-5.16208088808139[/C][/ROW]
[ROW][C]103[/C][C]584[/C][C]574.673668087448[/C][C]9.32633191255218[/C][/ROW]
[ROW][C]104[/C][C]594[/C][C]578.846256934345[/C][C]15.1537430656554[/C][/ROW]
[ROW][C]105[/C][C]594[/C][C]583.681074739567[/C][C]10.3189252604333[/C][/ROW]
[ROW][C]106[/C][C]598[/C][C]588.495126985149[/C][C]9.50487301485077[/C][/ROW]
[ROW][C]107[/C][C]580[/C][C]565.993887617523[/C][C]14.0061123824769[/C][/ROW]
[ROW][C]108[/C][C]589[/C][C]589.257813009789[/C][C]-0.25781300978872[/C][/ROW]
[ROW][C]109[/C][C]595[/C][C]600.577217804015[/C][C]-5.57721780401494[/C][/ROW]
[ROW][C]110[/C][C]584[/C][C]588.022831655448[/C][C]-4.02283165544759[/C][/ROW]
[ROW][C]111[/C][C]616[/C][C]621.765410993726[/C][C]-5.76541099372616[/C][/ROW]
[ROW][C]112[/C][C]622[/C][C]631.555493984479[/C][C]-9.55549398447886[/C][/ROW]
[ROW][C]113[/C][C]662[/C][C]676.060112863147[/C][C]-14.0601128631474[/C][/ROW]
[ROW][C]114[/C][C]669[/C][C]680.500798029579[/C][C]-11.5007980295788[/C][/ROW]
[ROW][C]115[/C][C]679[/C][C]677.079306787383[/C][C]1.92069321261715[/C][/ROW]
[ROW][C]116[/C][C]688[/C][C]684.142243685016[/C][C]3.85775631498393[/C][/ROW]
[ROW][C]117[/C][C]689[/C][C]681.024447169193[/C][C]7.97555283080658[/C][/ROW]
[ROW][C]118[/C][C]690[/C][C]683.547023602953[/C][C]6.45297639704711[/C][/ROW]
[ROW][C]119[/C][C]672[/C][C]659.392782956117[/C][C]12.6072170438825[/C][/ROW]
[ROW][C]120[/C][C]690[/C][C]670.948129278159[/C][C]19.0518707218412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235501&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235501&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
1310699.96664370070396.03335629929613
1410499.10941027628994.89058972371014
15107102.6035292127364.39647078726387
16112107.6428686984984.35713130150221
17140134.6582549886795.34174501132085
18140134.8432782042345.15672179576555
19134126.2156770038867.7843229961142
20128118.4938205360139.50617946398735
21133124.5645531892338.43544681076733
22139128.77582570894910.2241742910511
23140134.1527858399735.84721416002725
24143139.6382940806913.36170591930937
25152156.809155844972-4.80915584497185
26146151.779235514193-5.77923551419286
27146153.754171302531-7.75417130253078
28155157.838640354209-2.83864035420922
29180194.681509896174-14.6815098961741
30182189.389563361308-7.38956336130821
31177176.629804753050.370195246949692
32165165.063052696506-0.0630526965064462
33174167.9406258613766.05937413862398
34174172.7371930435911.26280695640901
35175171.3050466683073.69495333169311
36180173.5239836624836.47601633751674
37184185.806324477944-1.80632447794386
38186178.3936080215487.6063919784518
39186181.1165821871314.88341781286854
40192193.523438095967-1.52343809596735
41215227.385077622915-12.3850776229145
42221228.595202779074-7.5952027790735
43222220.1442146008181.85578539918234
44207205.188795545671.81120445433032
45215214.7442002190610.255799780939128
46212213.949594363444-1.94959436344354
47206213.208331607693-7.20833160769337
48219215.2012411323823.79875886761769
49222220.4140781351581.58592186484222
50217220.373609549837-3.3736095498372
51218217.4187940369120.581205963087882
52225223.8655638929931.13443610700739
53251252.802303182054-1.80230318205366
54264260.4455193027043.55448069729613
55264261.3065828032552.69341719674526
56258243.1867756087814.8132243912204
57267255.52586413674111.474135863259
58258254.8206709365553.17932906344501
59253250.1305374443532.86946255564672
60272265.8572248957916.14277510420931
61275270.7323493569064.26765064309404
62268266.7481857591791.25181424082075
63286268.54059355868817.4594064413117
64293281.51150827317611.4884917268241
65314318.360928947316-4.36092894731598
66328333.96795014116-5.9679501411598
67326332.789784250469-6.78978425046904
68325320.2225549020014.77744509799862
69333329.5685657886663.43143421133431
70332318.36709854533513.6329014546645
71320314.5185488140785.48145118592174
72338338.01005633122-0.0100563312199711
73344340.7063508665573.29364913344261
74338332.4601031959615.53989680403919
75363351.32552903382111.6744709661792
76375359.28003898078415.7199610192156
77403389.73240524040413.2675947595958
78414411.9813202090462.01867979095391
79411412.200568682043-1.20056868204256
80405410.00035834056-5.00035834056001
81410418.463739625111-8.46373962511143
82416411.7622845439994.23771545600067
83396396.148461924195-0.148461924195431
84412418.125522102415-6.12552210241495
85422422.945009784984-0.945009784984393
86418413.4237834441924.57621655580823
87444441.3776534515832.62234654841689
88453451.5432902181541.45670978184563
89491480.90880025229410.0911997477065
90498494.4461123456323.55388765436777
91489490.708896635724-1.70889663572444
92494483.28132109178710.7186789082133
93497492.8855940266264.11440597337406
94500499.3640161708510.635983829149268
95481474.9529922096996.04700779030054
96499496.5974323885052.40256761149465
97509509.168936066764-0.16893606676382
98499502.89185355801-3.8918535580105
99528532.180996581808-4.18099658180824
100537541.10731996042-4.10731996041989
101576582.199458162337-6.19945816233712
102582587.162080888081-5.16208088808139
103584574.6736680874489.32633191255218
104594578.84625693434515.1537430656554
105594583.68107473956710.3189252604333
106598588.4951269851499.50487301485077
107580565.99388761752314.0061123824769
108589589.257813009789-0.25781300978872
109595600.577217804015-5.57721780401494
110584588.022831655448-4.02283165544759
111616621.765410993726-5.76541099372616
112622631.555493984479-9.55549398447886
113662676.060112863147-14.0601128631474
114669680.500798029579-11.5007980295788
115679677.0793067873831.92069321261715
116688684.1422436850163.85775631498393
117689681.0244471691937.97555283080658
118690683.5470236029536.45297639704711
119672659.39278295611712.6072170438825
120690670.94812927815919.0518707218412







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121682.194334607137668.574315170837695.814354043438
122669.668996622729655.692765666157683.645227579301
123706.943091930716692.459224662519721.426959198913
124715.467548546383700.467004312821730.468092779946
125764.408856663296748.615401673322780.20231165327
126775.157541669184758.676155095639791.638928242729
127786.404238545153769.162863976209803.645613114096
128795.956705749845777.904728196624814.008683303065
129795.115380781355776.309250527425813.921511035285
130794.466431492631774.870485932603814.062377052658
131770.250554326513750.167961603083790.333147049944
132785.458893884513769.158083521207801.75970424782

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 682.194334607137 & 668.574315170837 & 695.814354043438 \tabularnewline
122 & 669.668996622729 & 655.692765666157 & 683.645227579301 \tabularnewline
123 & 706.943091930716 & 692.459224662519 & 721.426959198913 \tabularnewline
124 & 715.467548546383 & 700.467004312821 & 730.468092779946 \tabularnewline
125 & 764.408856663296 & 748.615401673322 & 780.20231165327 \tabularnewline
126 & 775.157541669184 & 758.676155095639 & 791.638928242729 \tabularnewline
127 & 786.404238545153 & 769.162863976209 & 803.645613114096 \tabularnewline
128 & 795.956705749845 & 777.904728196624 & 814.008683303065 \tabularnewline
129 & 795.115380781355 & 776.309250527425 & 813.921511035285 \tabularnewline
130 & 794.466431492631 & 774.870485932603 & 814.062377052658 \tabularnewline
131 & 770.250554326513 & 750.167961603083 & 790.333147049944 \tabularnewline
132 & 785.458893884513 & 769.158083521207 & 801.75970424782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235501&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]121[/C][C]682.194334607137[/C][C]668.574315170837[/C][C]695.814354043438[/C][/ROW]
[ROW][C]122[/C][C]669.668996622729[/C][C]655.692765666157[/C][C]683.645227579301[/C][/ROW]
[ROW][C]123[/C][C]706.943091930716[/C][C]692.459224662519[/C][C]721.426959198913[/C][/ROW]
[ROW][C]124[/C][C]715.467548546383[/C][C]700.467004312821[/C][C]730.468092779946[/C][/ROW]
[ROW][C]125[/C][C]764.408856663296[/C][C]748.615401673322[/C][C]780.20231165327[/C][/ROW]
[ROW][C]126[/C][C]775.157541669184[/C][C]758.676155095639[/C][C]791.638928242729[/C][/ROW]
[ROW][C]127[/C][C]786.404238545153[/C][C]769.162863976209[/C][C]803.645613114096[/C][/ROW]
[ROW][C]128[/C][C]795.956705749845[/C][C]777.904728196624[/C][C]814.008683303065[/C][/ROW]
[ROW][C]129[/C][C]795.115380781355[/C][C]776.309250527425[/C][C]813.921511035285[/C][/ROW]
[ROW][C]130[/C][C]794.466431492631[/C][C]774.870485932603[/C][C]814.062377052658[/C][/ROW]
[ROW][C]131[/C][C]770.250554326513[/C][C]750.167961603083[/C][C]790.333147049944[/C][/ROW]
[ROW][C]132[/C][C]785.458893884513[/C][C]769.158083521207[/C][C]801.75970424782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235501&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235501&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
121682.194334607137668.574315170837695.814354043438
122669.668996622729655.692765666157683.645227579301
123706.943091930716692.459224662519721.426959198913
124715.467548546383700.467004312821730.468092779946
125764.408856663296748.615401673322780.20231165327
126775.157541669184758.676155095639791.638928242729
127786.404238545153769.162863976209803.645613114096
128795.956705749845777.904728196624814.008683303065
129795.115380781355776.309250527425813.921511035285
130794.466431492631774.870485932603814.062377052658
131770.250554326513750.167961603083790.333147049944
132785.458893884513769.158083521207801.75970424782



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = 48 ;
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')