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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 16:11:17 +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/2016/Dec/07/t1481123501kzt3ulpa6yvz1ui.htm/, Retrieved Tue, 07 May 2024 12:33:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298191, Retrieved Tue, 07 May 2024 12:33:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Paper N2163] [2016-12-07 15:11:17] [1e2703d0f11438bcd65480dae45a3781] [Current]
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Dataseries X:
3875
3755
4670
4335
4945
4600
4395
4345
4390
4490
4395
4690
4590
4630
5375
4655
4975
4810
4445
4660
4215
4825
4250
3945
4390
4315
4835
4835
4970
4690
4700
4855
4610
4900
4250
4105
4740
4565
5155
5320
5430
4690
4540
4575
4660
4850
4200
4360
4655
4585
5315
5115
5100
5735
5260
5050
5165
5190
4720
5275
4605
4825
5595
5160
5320
5540
4970
5445
5305
5145
4895
4555
4980
4930
5810
5210
5450
5510
5010
5495
5125
5190
4565
4255
4875
4650
5295
5045
5430
5325
4920
5445
4895
5175
4545
4220
4595
4360
4750
4985
5140
4995
5150
5240
4875
5170
4715
4370
5160
4930
5600
5385
5425
5375
5365




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298191&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298191&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298191&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.236589197817152
beta0.0070161861618071
gamma0.553785251479608

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.236589197817152 \tabularnewline
beta & 0.0070161861618071 \tabularnewline
gamma & 0.553785251479608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298191&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]0.236589197817152[/C][/ROW]
[ROW][C]beta[/C][C]0.0070161861618071[/C][/ROW]
[ROW][C]gamma[/C][C]0.553785251479608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298191&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298191&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
alpha0.236589197817152
beta0.0070161861618071
gamma0.553785251479608







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1345904428.00480769231161.99519230769
1446304509.06505979974120.934940200259
1553755294.9866462191980.0133537808124
1646554605.5261124760449.4738875239609
1749754947.6723952797727.327604720228
1848104844.62446936316-34.6244693631606
1944454648.5285435813-203.528543581298
2046604502.13389038144157.866109618559
2142154536.92002540157-321.920025401569
2248254535.78457122608289.215428773919
2342504512.84224817773-262.842248177731
2439454753.4360695206-808.436069520603
2543904536.25898808397-146.258988083965
2643154525.28320244928-210.283202449276
2748355213.24454197307-378.244541973072
2848354399.3960448024435.603955197602
2949704821.116742787148.883257213004
3046904718.42103922649-28.421039226494
3147004450.18091234037249.819087659634
3248554562.37616454815292.623835451847
3346104424.9786295603185.021370439698
3449004801.7598078235698.2401921764395
3542504499.53947882718-249.539478827182
3641054511.94004183739-406.940041837386
3747404669.6825409279570.3174590720455
3845654683.22290969407-118.222909694072
3951555322.45299681525-167.452996815253
4053204903.38915022356416.610849776444
4154305200.21556142554229.784438574457
4246905042.6512678483-352.651267848299
4345404815.74315950259-275.743159502594
4445754821.23105096695-246.231050966949
4546604509.49978408721150.500215912788
4648504840.012364677389.98763532262365
4742004368.32347783832-168.323477838321
4843604331.9704739928228.0295260071789
4946554793.68733276828-138.687332768276
5045854677.02128120912-92.0212812091249
5153155300.6313406112214.3686593887778
5251155170.80221651993-55.8022165199291
5351005275.38838257908-175.38838257908
5457354773.56957323354961.430426766464
5552604890.09322267863369.906777321366
5650505061.90348732606-11.9034873260571
5751654974.81677988116190.18322011884
5851905256.86075102532-66.8607510253232
5947204693.02570082426.9742991760013
6052754787.63267775424487.367322245762
6146055290.04754924134-685.047549241337
6248255065.44625487967-240.446254879671
6355955700.2710811058-105.271081105796
6451605513.62455548486-353.624555484857
6553205497.85178371949-177.851783719494
6655405476.713538967463.2864610326033
6749705129.8347181552-159.834718155201
6854455013.18282500357431.817174996429
6953055115.53272549565189.467274504348
7051455287.75853900128-142.758539001279
7148954744.53172765948150.468272340517
7245555062.09399168756-507.093991687564
7349804831.02216625952148.977833740481
7449304990.53769868362-60.5376986836245
7558105724.2062834164585.793716583551
7652105477.2173857036-267.217385703596
7754505555.79081472247-105.790814722465
7855105653.35850872442-143.358508724423
7950105162.63085716243-152.63085716243
8054955297.19447654201197.805523457986
8151255240.71515180068-115.715151800684
8251905198.770466656-8.77046665600028
8345654809.91844781471-244.918447814708
8442554753.99386825854-498.99386825854
8548754800.2686343171274.7313656828819
8646504851.58460251929-201.584602519293
8752955611.45509383862-316.455093838625
8850455117.09797815525-72.0979781552478
8954305307.44451966582122.555480334183
9053255440.89755473132-115.897554731318
9149204950.53582641709-30.5358264170882
9254455260.12993362441184.870066375587
9348955066.01463795397-171.014637953967
9451755054.07762410992120.922375890082
9545454594.16795565058-49.1679556505824
9642204475.56008419547-255.560084195466
9745954820.80267496741-225.802674967413
9843604682.52246849667-322.522468496665
9947505363.340149618-613.340149618002
10049854899.679294032885.3207059671986
10151405207.45376218544-67.4537621854442
10249955192.7190775896-197.719077589601
10351504716.52761214551433.472387854489
10452405225.1778389227714.822161077228
10548754838.3035257743936.6964742256059
10651704997.20275350504172.797246494963
10747154476.01697733981238.983022660193
10843704337.1645377367332.8354622632714
10951604762.53505703902397.46494296098
11049304731.17427338727198.825726612731
11156005413.60583852132186.394161478683
11253855437.06706674077-52.0670667407676
11354255650.06499709918-225.064997099184
11453755545.02359106831-170.023591068312
11553655344.3307116178920.6692883821097

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4590 & 4428.00480769231 & 161.99519230769 \tabularnewline
14 & 4630 & 4509.06505979974 & 120.934940200259 \tabularnewline
15 & 5375 & 5294.98664621919 & 80.0133537808124 \tabularnewline
16 & 4655 & 4605.52611247604 & 49.4738875239609 \tabularnewline
17 & 4975 & 4947.67239527977 & 27.327604720228 \tabularnewline
18 & 4810 & 4844.62446936316 & -34.6244693631606 \tabularnewline
19 & 4445 & 4648.5285435813 & -203.528543581298 \tabularnewline
20 & 4660 & 4502.13389038144 & 157.866109618559 \tabularnewline
21 & 4215 & 4536.92002540157 & -321.920025401569 \tabularnewline
22 & 4825 & 4535.78457122608 & 289.215428773919 \tabularnewline
23 & 4250 & 4512.84224817773 & -262.842248177731 \tabularnewline
24 & 3945 & 4753.4360695206 & -808.436069520603 \tabularnewline
25 & 4390 & 4536.25898808397 & -146.258988083965 \tabularnewline
26 & 4315 & 4525.28320244928 & -210.283202449276 \tabularnewline
27 & 4835 & 5213.24454197307 & -378.244541973072 \tabularnewline
28 & 4835 & 4399.3960448024 & 435.603955197602 \tabularnewline
29 & 4970 & 4821.116742787 & 148.883257213004 \tabularnewline
30 & 4690 & 4718.42103922649 & -28.421039226494 \tabularnewline
31 & 4700 & 4450.18091234037 & 249.819087659634 \tabularnewline
32 & 4855 & 4562.37616454815 & 292.623835451847 \tabularnewline
33 & 4610 & 4424.9786295603 & 185.021370439698 \tabularnewline
34 & 4900 & 4801.75980782356 & 98.2401921764395 \tabularnewline
35 & 4250 & 4499.53947882718 & -249.539478827182 \tabularnewline
36 & 4105 & 4511.94004183739 & -406.940041837386 \tabularnewline
37 & 4740 & 4669.68254092795 & 70.3174590720455 \tabularnewline
38 & 4565 & 4683.22290969407 & -118.222909694072 \tabularnewline
39 & 5155 & 5322.45299681525 & -167.452996815253 \tabularnewline
40 & 5320 & 4903.38915022356 & 416.610849776444 \tabularnewline
41 & 5430 & 5200.21556142554 & 229.784438574457 \tabularnewline
42 & 4690 & 5042.6512678483 & -352.651267848299 \tabularnewline
43 & 4540 & 4815.74315950259 & -275.743159502594 \tabularnewline
44 & 4575 & 4821.23105096695 & -246.231050966949 \tabularnewline
45 & 4660 & 4509.49978408721 & 150.500215912788 \tabularnewline
46 & 4850 & 4840.01236467738 & 9.98763532262365 \tabularnewline
47 & 4200 & 4368.32347783832 & -168.323477838321 \tabularnewline
48 & 4360 & 4331.97047399282 & 28.0295260071789 \tabularnewline
49 & 4655 & 4793.68733276828 & -138.687332768276 \tabularnewline
50 & 4585 & 4677.02128120912 & -92.0212812091249 \tabularnewline
51 & 5315 & 5300.63134061122 & 14.3686593887778 \tabularnewline
52 & 5115 & 5170.80221651993 & -55.8022165199291 \tabularnewline
53 & 5100 & 5275.38838257908 & -175.38838257908 \tabularnewline
54 & 5735 & 4773.56957323354 & 961.430426766464 \tabularnewline
55 & 5260 & 4890.09322267863 & 369.906777321366 \tabularnewline
56 & 5050 & 5061.90348732606 & -11.9034873260571 \tabularnewline
57 & 5165 & 4974.81677988116 & 190.18322011884 \tabularnewline
58 & 5190 & 5256.86075102532 & -66.8607510253232 \tabularnewline
59 & 4720 & 4693.025700824 & 26.9742991760013 \tabularnewline
60 & 5275 & 4787.63267775424 & 487.367322245762 \tabularnewline
61 & 4605 & 5290.04754924134 & -685.047549241337 \tabularnewline
62 & 4825 & 5065.44625487967 & -240.446254879671 \tabularnewline
63 & 5595 & 5700.2710811058 & -105.271081105796 \tabularnewline
64 & 5160 & 5513.62455548486 & -353.624555484857 \tabularnewline
65 & 5320 & 5497.85178371949 & -177.851783719494 \tabularnewline
66 & 5540 & 5476.7135389674 & 63.2864610326033 \tabularnewline
67 & 4970 & 5129.8347181552 & -159.834718155201 \tabularnewline
68 & 5445 & 5013.18282500357 & 431.817174996429 \tabularnewline
69 & 5305 & 5115.53272549565 & 189.467274504348 \tabularnewline
70 & 5145 & 5287.75853900128 & -142.758539001279 \tabularnewline
71 & 4895 & 4744.53172765948 & 150.468272340517 \tabularnewline
72 & 4555 & 5062.09399168756 & -507.093991687564 \tabularnewline
73 & 4980 & 4831.02216625952 & 148.977833740481 \tabularnewline
74 & 4930 & 4990.53769868362 & -60.5376986836245 \tabularnewline
75 & 5810 & 5724.20628341645 & 85.793716583551 \tabularnewline
76 & 5210 & 5477.2173857036 & -267.217385703596 \tabularnewline
77 & 5450 & 5555.79081472247 & -105.790814722465 \tabularnewline
78 & 5510 & 5653.35850872442 & -143.358508724423 \tabularnewline
79 & 5010 & 5162.63085716243 & -152.63085716243 \tabularnewline
80 & 5495 & 5297.19447654201 & 197.805523457986 \tabularnewline
81 & 5125 & 5240.71515180068 & -115.715151800684 \tabularnewline
82 & 5190 & 5198.770466656 & -8.77046665600028 \tabularnewline
83 & 4565 & 4809.91844781471 & -244.918447814708 \tabularnewline
84 & 4255 & 4753.99386825854 & -498.99386825854 \tabularnewline
85 & 4875 & 4800.26863431712 & 74.7313656828819 \tabularnewline
86 & 4650 & 4851.58460251929 & -201.584602519293 \tabularnewline
87 & 5295 & 5611.45509383862 & -316.455093838625 \tabularnewline
88 & 5045 & 5117.09797815525 & -72.0979781552478 \tabularnewline
89 & 5430 & 5307.44451966582 & 122.555480334183 \tabularnewline
90 & 5325 & 5440.89755473132 & -115.897554731318 \tabularnewline
91 & 4920 & 4950.53582641709 & -30.5358264170882 \tabularnewline
92 & 5445 & 5260.12993362441 & 184.870066375587 \tabularnewline
93 & 4895 & 5066.01463795397 & -171.014637953967 \tabularnewline
94 & 5175 & 5054.07762410992 & 120.922375890082 \tabularnewline
95 & 4545 & 4594.16795565058 & -49.1679556505824 \tabularnewline
96 & 4220 & 4475.56008419547 & -255.560084195466 \tabularnewline
97 & 4595 & 4820.80267496741 & -225.802674967413 \tabularnewline
98 & 4360 & 4682.52246849667 & -322.522468496665 \tabularnewline
99 & 4750 & 5363.340149618 & -613.340149618002 \tabularnewline
100 & 4985 & 4899.6792940328 & 85.3207059671986 \tabularnewline
101 & 5140 & 5207.45376218544 & -67.4537621854442 \tabularnewline
102 & 4995 & 5192.7190775896 & -197.719077589601 \tabularnewline
103 & 5150 & 4716.52761214551 & 433.472387854489 \tabularnewline
104 & 5240 & 5225.17783892277 & 14.822161077228 \tabularnewline
105 & 4875 & 4838.30352577439 & 36.6964742256059 \tabularnewline
106 & 5170 & 4997.20275350504 & 172.797246494963 \tabularnewline
107 & 4715 & 4476.01697733981 & 238.983022660193 \tabularnewline
108 & 4370 & 4337.16453773673 & 32.8354622632714 \tabularnewline
109 & 5160 & 4762.53505703902 & 397.46494296098 \tabularnewline
110 & 4930 & 4731.17427338727 & 198.825726612731 \tabularnewline
111 & 5600 & 5413.60583852132 & 186.394161478683 \tabularnewline
112 & 5385 & 5437.06706674077 & -52.0670667407676 \tabularnewline
113 & 5425 & 5650.06499709918 & -225.064997099184 \tabularnewline
114 & 5375 & 5545.02359106831 & -170.023591068312 \tabularnewline
115 & 5365 & 5344.33071161789 & 20.6692883821097 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298191&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]4590[/C][C]4428.00480769231[/C][C]161.99519230769[/C][/ROW]
[ROW][C]14[/C][C]4630[/C][C]4509.06505979974[/C][C]120.934940200259[/C][/ROW]
[ROW][C]15[/C][C]5375[/C][C]5294.98664621919[/C][C]80.0133537808124[/C][/ROW]
[ROW][C]16[/C][C]4655[/C][C]4605.52611247604[/C][C]49.4738875239609[/C][/ROW]
[ROW][C]17[/C][C]4975[/C][C]4947.67239527977[/C][C]27.327604720228[/C][/ROW]
[ROW][C]18[/C][C]4810[/C][C]4844.62446936316[/C][C]-34.6244693631606[/C][/ROW]
[ROW][C]19[/C][C]4445[/C][C]4648.5285435813[/C][C]-203.528543581298[/C][/ROW]
[ROW][C]20[/C][C]4660[/C][C]4502.13389038144[/C][C]157.866109618559[/C][/ROW]
[ROW][C]21[/C][C]4215[/C][C]4536.92002540157[/C][C]-321.920025401569[/C][/ROW]
[ROW][C]22[/C][C]4825[/C][C]4535.78457122608[/C][C]289.215428773919[/C][/ROW]
[ROW][C]23[/C][C]4250[/C][C]4512.84224817773[/C][C]-262.842248177731[/C][/ROW]
[ROW][C]24[/C][C]3945[/C][C]4753.4360695206[/C][C]-808.436069520603[/C][/ROW]
[ROW][C]25[/C][C]4390[/C][C]4536.25898808397[/C][C]-146.258988083965[/C][/ROW]
[ROW][C]26[/C][C]4315[/C][C]4525.28320244928[/C][C]-210.283202449276[/C][/ROW]
[ROW][C]27[/C][C]4835[/C][C]5213.24454197307[/C][C]-378.244541973072[/C][/ROW]
[ROW][C]28[/C][C]4835[/C][C]4399.3960448024[/C][C]435.603955197602[/C][/ROW]
[ROW][C]29[/C][C]4970[/C][C]4821.116742787[/C][C]148.883257213004[/C][/ROW]
[ROW][C]30[/C][C]4690[/C][C]4718.42103922649[/C][C]-28.421039226494[/C][/ROW]
[ROW][C]31[/C][C]4700[/C][C]4450.18091234037[/C][C]249.819087659634[/C][/ROW]
[ROW][C]32[/C][C]4855[/C][C]4562.37616454815[/C][C]292.623835451847[/C][/ROW]
[ROW][C]33[/C][C]4610[/C][C]4424.9786295603[/C][C]185.021370439698[/C][/ROW]
[ROW][C]34[/C][C]4900[/C][C]4801.75980782356[/C][C]98.2401921764395[/C][/ROW]
[ROW][C]35[/C][C]4250[/C][C]4499.53947882718[/C][C]-249.539478827182[/C][/ROW]
[ROW][C]36[/C][C]4105[/C][C]4511.94004183739[/C][C]-406.940041837386[/C][/ROW]
[ROW][C]37[/C][C]4740[/C][C]4669.68254092795[/C][C]70.3174590720455[/C][/ROW]
[ROW][C]38[/C][C]4565[/C][C]4683.22290969407[/C][C]-118.222909694072[/C][/ROW]
[ROW][C]39[/C][C]5155[/C][C]5322.45299681525[/C][C]-167.452996815253[/C][/ROW]
[ROW][C]40[/C][C]5320[/C][C]4903.38915022356[/C][C]416.610849776444[/C][/ROW]
[ROW][C]41[/C][C]5430[/C][C]5200.21556142554[/C][C]229.784438574457[/C][/ROW]
[ROW][C]42[/C][C]4690[/C][C]5042.6512678483[/C][C]-352.651267848299[/C][/ROW]
[ROW][C]43[/C][C]4540[/C][C]4815.74315950259[/C][C]-275.743159502594[/C][/ROW]
[ROW][C]44[/C][C]4575[/C][C]4821.23105096695[/C][C]-246.231050966949[/C][/ROW]
[ROW][C]45[/C][C]4660[/C][C]4509.49978408721[/C][C]150.500215912788[/C][/ROW]
[ROW][C]46[/C][C]4850[/C][C]4840.01236467738[/C][C]9.98763532262365[/C][/ROW]
[ROW][C]47[/C][C]4200[/C][C]4368.32347783832[/C][C]-168.323477838321[/C][/ROW]
[ROW][C]48[/C][C]4360[/C][C]4331.97047399282[/C][C]28.0295260071789[/C][/ROW]
[ROW][C]49[/C][C]4655[/C][C]4793.68733276828[/C][C]-138.687332768276[/C][/ROW]
[ROW][C]50[/C][C]4585[/C][C]4677.02128120912[/C][C]-92.0212812091249[/C][/ROW]
[ROW][C]51[/C][C]5315[/C][C]5300.63134061122[/C][C]14.3686593887778[/C][/ROW]
[ROW][C]52[/C][C]5115[/C][C]5170.80221651993[/C][C]-55.8022165199291[/C][/ROW]
[ROW][C]53[/C][C]5100[/C][C]5275.38838257908[/C][C]-175.38838257908[/C][/ROW]
[ROW][C]54[/C][C]5735[/C][C]4773.56957323354[/C][C]961.430426766464[/C][/ROW]
[ROW][C]55[/C][C]5260[/C][C]4890.09322267863[/C][C]369.906777321366[/C][/ROW]
[ROW][C]56[/C][C]5050[/C][C]5061.90348732606[/C][C]-11.9034873260571[/C][/ROW]
[ROW][C]57[/C][C]5165[/C][C]4974.81677988116[/C][C]190.18322011884[/C][/ROW]
[ROW][C]58[/C][C]5190[/C][C]5256.86075102532[/C][C]-66.8607510253232[/C][/ROW]
[ROW][C]59[/C][C]4720[/C][C]4693.025700824[/C][C]26.9742991760013[/C][/ROW]
[ROW][C]60[/C][C]5275[/C][C]4787.63267775424[/C][C]487.367322245762[/C][/ROW]
[ROW][C]61[/C][C]4605[/C][C]5290.04754924134[/C][C]-685.047549241337[/C][/ROW]
[ROW][C]62[/C][C]4825[/C][C]5065.44625487967[/C][C]-240.446254879671[/C][/ROW]
[ROW][C]63[/C][C]5595[/C][C]5700.2710811058[/C][C]-105.271081105796[/C][/ROW]
[ROW][C]64[/C][C]5160[/C][C]5513.62455548486[/C][C]-353.624555484857[/C][/ROW]
[ROW][C]65[/C][C]5320[/C][C]5497.85178371949[/C][C]-177.851783719494[/C][/ROW]
[ROW][C]66[/C][C]5540[/C][C]5476.7135389674[/C][C]63.2864610326033[/C][/ROW]
[ROW][C]67[/C][C]4970[/C][C]5129.8347181552[/C][C]-159.834718155201[/C][/ROW]
[ROW][C]68[/C][C]5445[/C][C]5013.18282500357[/C][C]431.817174996429[/C][/ROW]
[ROW][C]69[/C][C]5305[/C][C]5115.53272549565[/C][C]189.467274504348[/C][/ROW]
[ROW][C]70[/C][C]5145[/C][C]5287.75853900128[/C][C]-142.758539001279[/C][/ROW]
[ROW][C]71[/C][C]4895[/C][C]4744.53172765948[/C][C]150.468272340517[/C][/ROW]
[ROW][C]72[/C][C]4555[/C][C]5062.09399168756[/C][C]-507.093991687564[/C][/ROW]
[ROW][C]73[/C][C]4980[/C][C]4831.02216625952[/C][C]148.977833740481[/C][/ROW]
[ROW][C]74[/C][C]4930[/C][C]4990.53769868362[/C][C]-60.5376986836245[/C][/ROW]
[ROW][C]75[/C][C]5810[/C][C]5724.20628341645[/C][C]85.793716583551[/C][/ROW]
[ROW][C]76[/C][C]5210[/C][C]5477.2173857036[/C][C]-267.217385703596[/C][/ROW]
[ROW][C]77[/C][C]5450[/C][C]5555.79081472247[/C][C]-105.790814722465[/C][/ROW]
[ROW][C]78[/C][C]5510[/C][C]5653.35850872442[/C][C]-143.358508724423[/C][/ROW]
[ROW][C]79[/C][C]5010[/C][C]5162.63085716243[/C][C]-152.63085716243[/C][/ROW]
[ROW][C]80[/C][C]5495[/C][C]5297.19447654201[/C][C]197.805523457986[/C][/ROW]
[ROW][C]81[/C][C]5125[/C][C]5240.71515180068[/C][C]-115.715151800684[/C][/ROW]
[ROW][C]82[/C][C]5190[/C][C]5198.770466656[/C][C]-8.77046665600028[/C][/ROW]
[ROW][C]83[/C][C]4565[/C][C]4809.91844781471[/C][C]-244.918447814708[/C][/ROW]
[ROW][C]84[/C][C]4255[/C][C]4753.99386825854[/C][C]-498.99386825854[/C][/ROW]
[ROW][C]85[/C][C]4875[/C][C]4800.26863431712[/C][C]74.7313656828819[/C][/ROW]
[ROW][C]86[/C][C]4650[/C][C]4851.58460251929[/C][C]-201.584602519293[/C][/ROW]
[ROW][C]87[/C][C]5295[/C][C]5611.45509383862[/C][C]-316.455093838625[/C][/ROW]
[ROW][C]88[/C][C]5045[/C][C]5117.09797815525[/C][C]-72.0979781552478[/C][/ROW]
[ROW][C]89[/C][C]5430[/C][C]5307.44451966582[/C][C]122.555480334183[/C][/ROW]
[ROW][C]90[/C][C]5325[/C][C]5440.89755473132[/C][C]-115.897554731318[/C][/ROW]
[ROW][C]91[/C][C]4920[/C][C]4950.53582641709[/C][C]-30.5358264170882[/C][/ROW]
[ROW][C]92[/C][C]5445[/C][C]5260.12993362441[/C][C]184.870066375587[/C][/ROW]
[ROW][C]93[/C][C]4895[/C][C]5066.01463795397[/C][C]-171.014637953967[/C][/ROW]
[ROW][C]94[/C][C]5175[/C][C]5054.07762410992[/C][C]120.922375890082[/C][/ROW]
[ROW][C]95[/C][C]4545[/C][C]4594.16795565058[/C][C]-49.1679556505824[/C][/ROW]
[ROW][C]96[/C][C]4220[/C][C]4475.56008419547[/C][C]-255.560084195466[/C][/ROW]
[ROW][C]97[/C][C]4595[/C][C]4820.80267496741[/C][C]-225.802674967413[/C][/ROW]
[ROW][C]98[/C][C]4360[/C][C]4682.52246849667[/C][C]-322.522468496665[/C][/ROW]
[ROW][C]99[/C][C]4750[/C][C]5363.340149618[/C][C]-613.340149618002[/C][/ROW]
[ROW][C]100[/C][C]4985[/C][C]4899.6792940328[/C][C]85.3207059671986[/C][/ROW]
[ROW][C]101[/C][C]5140[/C][C]5207.45376218544[/C][C]-67.4537621854442[/C][/ROW]
[ROW][C]102[/C][C]4995[/C][C]5192.7190775896[/C][C]-197.719077589601[/C][/ROW]
[ROW][C]103[/C][C]5150[/C][C]4716.52761214551[/C][C]433.472387854489[/C][/ROW]
[ROW][C]104[/C][C]5240[/C][C]5225.17783892277[/C][C]14.822161077228[/C][/ROW]
[ROW][C]105[/C][C]4875[/C][C]4838.30352577439[/C][C]36.6964742256059[/C][/ROW]
[ROW][C]106[/C][C]5170[/C][C]4997.20275350504[/C][C]172.797246494963[/C][/ROW]
[ROW][C]107[/C][C]4715[/C][C]4476.01697733981[/C][C]238.983022660193[/C][/ROW]
[ROW][C]108[/C][C]4370[/C][C]4337.16453773673[/C][C]32.8354622632714[/C][/ROW]
[ROW][C]109[/C][C]5160[/C][C]4762.53505703902[/C][C]397.46494296098[/C][/ROW]
[ROW][C]110[/C][C]4930[/C][C]4731.17427338727[/C][C]198.825726612731[/C][/ROW]
[ROW][C]111[/C][C]5600[/C][C]5413.60583852132[/C][C]186.394161478683[/C][/ROW]
[ROW][C]112[/C][C]5385[/C][C]5437.06706674077[/C][C]-52.0670667407676[/C][/ROW]
[ROW][C]113[/C][C]5425[/C][C]5650.06499709918[/C][C]-225.064997099184[/C][/ROW]
[ROW][C]114[/C][C]5375[/C][C]5545.02359106831[/C][C]-170.023591068312[/C][/ROW]
[ROW][C]115[/C][C]5365[/C][C]5344.33071161789[/C][C]20.6692883821097[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298191&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298191&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
1345904428.00480769231161.99519230769
1446304509.06505979974120.934940200259
1553755294.9866462191980.0133537808124
1646554605.5261124760449.4738875239609
1749754947.6723952797727.327604720228
1848104844.62446936316-34.6244693631606
1944454648.5285435813-203.528543581298
2046604502.13389038144157.866109618559
2142154536.92002540157-321.920025401569
2248254535.78457122608289.215428773919
2342504512.84224817773-262.842248177731
2439454753.4360695206-808.436069520603
2543904536.25898808397-146.258988083965
2643154525.28320244928-210.283202449276
2748355213.24454197307-378.244541973072
2848354399.3960448024435.603955197602
2949704821.116742787148.883257213004
3046904718.42103922649-28.421039226494
3147004450.18091234037249.819087659634
3248554562.37616454815292.623835451847
3346104424.9786295603185.021370439698
3449004801.7598078235698.2401921764395
3542504499.53947882718-249.539478827182
3641054511.94004183739-406.940041837386
3747404669.6825409279570.3174590720455
3845654683.22290969407-118.222909694072
3951555322.45299681525-167.452996815253
4053204903.38915022356416.610849776444
4154305200.21556142554229.784438574457
4246905042.6512678483-352.651267848299
4345404815.74315950259-275.743159502594
4445754821.23105096695-246.231050966949
4546604509.49978408721150.500215912788
4648504840.012364677389.98763532262365
4742004368.32347783832-168.323477838321
4843604331.9704739928228.0295260071789
4946554793.68733276828-138.687332768276
5045854677.02128120912-92.0212812091249
5153155300.6313406112214.3686593887778
5251155170.80221651993-55.8022165199291
5351005275.38838257908-175.38838257908
5457354773.56957323354961.430426766464
5552604890.09322267863369.906777321366
5650505061.90348732606-11.9034873260571
5751654974.81677988116190.18322011884
5851905256.86075102532-66.8607510253232
5947204693.02570082426.9742991760013
6052754787.63267775424487.367322245762
6146055290.04754924134-685.047549241337
6248255065.44625487967-240.446254879671
6355955700.2710811058-105.271081105796
6451605513.62455548486-353.624555484857
6553205497.85178371949-177.851783719494
6655405476.713538967463.2864610326033
6749705129.8347181552-159.834718155201
6854455013.18282500357431.817174996429
6953055115.53272549565189.467274504348
7051455287.75853900128-142.758539001279
7148954744.53172765948150.468272340517
7245555062.09399168756-507.093991687564
7349804831.02216625952148.977833740481
7449304990.53769868362-60.5376986836245
7558105724.2062834164585.793716583551
7652105477.2173857036-267.217385703596
7754505555.79081472247-105.790814722465
7855105653.35850872442-143.358508724423
7950105162.63085716243-152.63085716243
8054955297.19447654201197.805523457986
8151255240.71515180068-115.715151800684
8251905198.770466656-8.77046665600028
8345654809.91844781471-244.918447814708
8442554753.99386825854-498.99386825854
8548754800.2686343171274.7313656828819
8646504851.58460251929-201.584602519293
8752955611.45509383862-316.455093838625
8850455117.09797815525-72.0979781552478
8954305307.44451966582122.555480334183
9053255440.89755473132-115.897554731318
9149204950.53582641709-30.5358264170882
9254455260.12993362441184.870066375587
9348955066.01463795397-171.014637953967
9451755054.07762410992120.922375890082
9545454594.16795565058-49.1679556505824
9642204475.56008419547-255.560084195466
9745954820.80267496741-225.802674967413
9843604682.52246849667-322.522468496665
9947505363.340149618-613.340149618002
10049854899.679294032885.3207059671986
10151405207.45376218544-67.4537621854442
10249955192.7190775896-197.719077589601
10351504716.52761214551433.472387854489
10452405225.1778389227714.822161077228
10548754838.3035257743936.6964742256059
10651704997.20275350504172.797246494963
10747154476.01697733981238.983022660193
10843704337.1645377367332.8354622632714
10951604762.53505703902397.46494296098
11049304731.17427338727198.825726612731
11156005413.60583852132186.394161478683
11253855437.06706674077-52.0670667407676
11354255650.06499709918-225.064997099184
11453755545.02359106831-170.023591068312
11553655344.3307116178920.6692883821097







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1165579.740085059665065.139971377166094.34019874216
1175199.996945843164670.993370665625729.0005210207
1185409.082229297014865.863603085035952.30085550898
1194876.038042577764318.777047801675433.29903735385
1204594.138473780064022.993778265815165.28316929431
1215166.484567309244581.602292003275751.36684261522
1224957.041535153714358.556519538695555.52655076874
1235586.778900513294974.81579997726198.74200104938
1245464.620121406924839.294364036446089.94587877739
1255616.177457280284977.596082267546254.75883229301
1265587.405692535274935.668088263336239.14329680721
1275507.591265980194842.789822603546172.39270935684

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
116 & 5579.74008505966 & 5065.13997137716 & 6094.34019874216 \tabularnewline
117 & 5199.99694584316 & 4670.99337066562 & 5729.0005210207 \tabularnewline
118 & 5409.08222929701 & 4865.86360308503 & 5952.30085550898 \tabularnewline
119 & 4876.03804257776 & 4318.77704780167 & 5433.29903735385 \tabularnewline
120 & 4594.13847378006 & 4022.99377826581 & 5165.28316929431 \tabularnewline
121 & 5166.48456730924 & 4581.60229200327 & 5751.36684261522 \tabularnewline
122 & 4957.04153515371 & 4358.55651953869 & 5555.52655076874 \tabularnewline
123 & 5586.77890051329 & 4974.8157999772 & 6198.74200104938 \tabularnewline
124 & 5464.62012140692 & 4839.29436403644 & 6089.94587877739 \tabularnewline
125 & 5616.17745728028 & 4977.59608226754 & 6254.75883229301 \tabularnewline
126 & 5587.40569253527 & 4935.66808826333 & 6239.14329680721 \tabularnewline
127 & 5507.59126598019 & 4842.78982260354 & 6172.39270935684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298191&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]116[/C][C]5579.74008505966[/C][C]5065.13997137716[/C][C]6094.34019874216[/C][/ROW]
[ROW][C]117[/C][C]5199.99694584316[/C][C]4670.99337066562[/C][C]5729.0005210207[/C][/ROW]
[ROW][C]118[/C][C]5409.08222929701[/C][C]4865.86360308503[/C][C]5952.30085550898[/C][/ROW]
[ROW][C]119[/C][C]4876.03804257776[/C][C]4318.77704780167[/C][C]5433.29903735385[/C][/ROW]
[ROW][C]120[/C][C]4594.13847378006[/C][C]4022.99377826581[/C][C]5165.28316929431[/C][/ROW]
[ROW][C]121[/C][C]5166.48456730924[/C][C]4581.60229200327[/C][C]5751.36684261522[/C][/ROW]
[ROW][C]122[/C][C]4957.04153515371[/C][C]4358.55651953869[/C][C]5555.52655076874[/C][/ROW]
[ROW][C]123[/C][C]5586.77890051329[/C][C]4974.8157999772[/C][C]6198.74200104938[/C][/ROW]
[ROW][C]124[/C][C]5464.62012140692[/C][C]4839.29436403644[/C][C]6089.94587877739[/C][/ROW]
[ROW][C]125[/C][C]5616.17745728028[/C][C]4977.59608226754[/C][C]6254.75883229301[/C][/ROW]
[ROW][C]126[/C][C]5587.40569253527[/C][C]4935.66808826333[/C][C]6239.14329680721[/C][/ROW]
[ROW][C]127[/C][C]5507.59126598019[/C][C]4842.78982260354[/C][C]6172.39270935684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298191&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298191&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
1165579.740085059665065.139971377166094.34019874216
1175199.996945843164670.993370665625729.0005210207
1185409.082229297014865.863603085035952.30085550898
1194876.038042577764318.777047801675433.29903735385
1204594.138473780064022.993778265815165.28316929431
1215166.484567309244581.602292003275751.36684261522
1224957.041535153714358.556519538695555.52655076874
1235586.778900513294974.81579997726198.74200104938
1245464.620121406924839.294364036446089.94587877739
1255616.177457280284977.596082267546254.75883229301
1265587.405692535274935.668088263336239.14329680721
1275507.591265980194842.789822603546172.39270935684



Parameters (Session):
par1 = additive ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')