Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 15 Aug 2012 10:06:23 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/15/t1345039616nyn943h00bn0rb8.htm/, Retrieved Tue, 07 May 2024 05:22:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169355, Retrieved Tue, 07 May 2024 05:22:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS A - STA...] [2012-08-15 14:06:23] [606e5654d317e57bd58e5a48c9e4e9a9] [Current]
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Dataseries X:
19064
18993
18921
18772
20246
20168
19064
18330
18401
18401
18480
18622
18843
18843
18701
18330
20246
20538
20097
19064
19506
18843
19142
19285
19434
19064
19142
18622
20246
20759
20318
19506
20389
19434
20318
20246
20467
19655
20538
20467
21792
21493
20318
19726
20538
19434
20246
20389
20688
20026
20389
20610
21422
20759
19876
18921
19805
17375
18551
19213
19876
18921
18921
18921
19434
18701
17739
16934
17518
15238
16635
17447
17596
16784
16855
16635
17375
16855
15830
15089
16342
13621
15388
16193
16193
15238
14355
14284
15089
14355
12959
11997
13030
10601
12809
13984
14355
13543
12517
13251
13543
13322
11113
10088
10821
8613
10893
11705
12367
11263
10230
10821
11113
10529
8321
7359
8242
5813
8463
10088




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169355&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169355&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405343002238673
beta0.0645195510986042
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238673 \tabularnewline
beta & 0.0645195510986042 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169355&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]0.405343002238673[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510986042[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169355&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
alpha0.405343002238673
beta0.0645195510986042
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131884318842.18055555550.819444444456167
141884318800.825808854142.1741911458957
151870118632.336881918868.6631180812401
161833018259.54743834970.4525616509709
172024620194.784180580251.2158194197509
182053820490.354534832547.645465167494
192009719387.8487213139709.151278686135
201906419014.567440153749.4325598462601
211950619180.1249136204325.87508637955
221884319407.4255614215-564.425561421544
231914219328.9212381859-186.921238185907
241928519427.7138505995-142.713850599517
251943419577.1389090191-143.138909019126
261906419510.5861601928-446.586160192761
271914219155.5137615691-13.5137615690983
281862218744.109755927-122.109755927002
292024620578.4486073916-332.448607391598
302075920694.941492880464.0585071195601
312031819971.4482530007346.551746999328
321950619028.3911353585477.608864641476
332038919512.6009611919876.399038808107
341943419428.73233535135.26766464872708
352031819815.636896977502.363103023035
362024620248.1430029821-2.14300298210583
372046720485.9996697037-18.9996697036877
381965520324.270381823-669.270381822989
392053820165.5917850627372.408214937324
402046719885.2617876904581.738212309596
412179221937.4490396096-145.449039609604
422149322428.0451587156-935.045158715624
432031821503.9482512596-1185.94825125958
441972620013.9476648707-287.947664870684
452053820401.2772714185136.722728581546
461943419456.506636145-22.5066361450117
472024620083.9729659891162.027034010862
482038920025.8360917976363.163908202358
492068820358.6150806772329.384919322787
502002619917.3958203871108.604179612947
512038920679.790904678-290.790904678022
522061020224.0991896586385.900810341376
532142221728.3383427159-306.33834271587
542075921643.8327953702-884.832795370246
551987620551.85356388-675.853563879984
561892119776.924623863-855.924623863
571980520146.0139225397-341.013922539678
581737518859.867148558-1484.86714855803
591855118913.0235876548-362.023587654847
601921318657.0821230035555.917876996518
611987618947.9548918045928.045108195496
621892118533.8152472366387.184752763358
631892119094.619236915-173.619236915034
641892119014.8773401231-93.8773401230719
651943419826.5051383773-392.50513837731
661870119274.3214452461-573.32144524606
671773918352.2836740437-613.283674043687
681693417416.6743991956-482.674399195577
691751818174.0526749956-656.052674995597
701523816002.5671144473-764.567114447258
711663516956.7968868138-321.796886813805
721744717205.4713541366241.528645863378
731759617524.424635374271.5753646258163
741678416353.323637071430.676362929033
751685516511.2371048167343.762895183278
761663516615.128848087819.8711519121971
771737517224.7548409973150.245159002719
781685516728.7139535349126.286046465131
791583016028.4563361522-198.456336152176
801508915311.4739029503-222.473902950263
811634216050.8386940613291.16130593872
821362114203.1595510917-582.1595510917
831538815503.7825193006-115.782519300616
841619316185.49589184537.50410815474061
851619316316.9516712724-123.951671272445
861523815283.4501633476-45.450163347592
871435515187.5465361841-832.546536184102
881428414582.1226643135-298.122664313456
891508915092.1612289709-3.16122897093919
901435514467.4600379731-112.460037973091
911295913418.8435733541-459.843573354143
921199712516.3170337979-519.317033797888
931303013367.7217012154-337.721701215432
941060110656.2823706669-55.282370666866
951280912372.0643611103436.935638889699
961398413289.8450940587694.154905941301
971435513578.1302055649776.869794435084
981354312936.6819585132606.318041486829
991251712634.1911583183-117.191158318312
1001325112652.5143564819598.485643518077
1011354313740.8201766849-197.820176684876
1021332213006.5616848288315.438315171206
1031111311970.3490485989-857.349048598891
1041008810906.4666311222-818.466631122232
1051082111771.913007812-950.913007811991
10686138991.15185093047-378.15185093047
1071089310871.59443543921.4055645610242
1081170511765.8656219282-60.8656219282457
1091236711769.5151464484597.484853551568
1101126310921.4630154272341.536984572795
1111023010042.008898529187.991101470998
1121082110578.2027427683242.79725723167
1131111311008.0867127967104.913287203348
1141052910668.9518940503-139.951894050324
11583218706.0342240553-385.034224055298
11673597824.36566716371-465.365667163711
11782428731.05602401281-489.056024012807
11858136467.05767078637-654.057670786373
11984638455.003611972637.9963880273699
120100889276.3058985918811.694101408204

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 18843 & 18842.1805555555 & 0.819444444456167 \tabularnewline
14 & 18843 & 18800.8258088541 & 42.1741911458957 \tabularnewline
15 & 18701 & 18632.3368819188 & 68.6631180812401 \tabularnewline
16 & 18330 & 18259.547438349 & 70.4525616509709 \tabularnewline
17 & 20246 & 20194.7841805802 & 51.2158194197509 \tabularnewline
18 & 20538 & 20490.3545348325 & 47.645465167494 \tabularnewline
19 & 20097 & 19387.8487213139 & 709.151278686135 \tabularnewline
20 & 19064 & 19014.5674401537 & 49.4325598462601 \tabularnewline
21 & 19506 & 19180.1249136204 & 325.87508637955 \tabularnewline
22 & 18843 & 19407.4255614215 & -564.425561421544 \tabularnewline
23 & 19142 & 19328.9212381859 & -186.921238185907 \tabularnewline
24 & 19285 & 19427.7138505995 & -142.713850599517 \tabularnewline
25 & 19434 & 19577.1389090191 & -143.138909019126 \tabularnewline
26 & 19064 & 19510.5861601928 & -446.586160192761 \tabularnewline
27 & 19142 & 19155.5137615691 & -13.5137615690983 \tabularnewline
28 & 18622 & 18744.109755927 & -122.109755927002 \tabularnewline
29 & 20246 & 20578.4486073916 & -332.448607391598 \tabularnewline
30 & 20759 & 20694.9414928804 & 64.0585071195601 \tabularnewline
31 & 20318 & 19971.4482530007 & 346.551746999328 \tabularnewline
32 & 19506 & 19028.3911353585 & 477.608864641476 \tabularnewline
33 & 20389 & 19512.6009611919 & 876.399038808107 \tabularnewline
34 & 19434 & 19428.7323353513 & 5.26766464872708 \tabularnewline
35 & 20318 & 19815.636896977 & 502.363103023035 \tabularnewline
36 & 20246 & 20248.1430029821 & -2.14300298210583 \tabularnewline
37 & 20467 & 20485.9996697037 & -18.9996697036877 \tabularnewline
38 & 19655 & 20324.270381823 & -669.270381822989 \tabularnewline
39 & 20538 & 20165.5917850627 & 372.408214937324 \tabularnewline
40 & 20467 & 19885.2617876904 & 581.738212309596 \tabularnewline
41 & 21792 & 21937.4490396096 & -145.449039609604 \tabularnewline
42 & 21493 & 22428.0451587156 & -935.045158715624 \tabularnewline
43 & 20318 & 21503.9482512596 & -1185.94825125958 \tabularnewline
44 & 19726 & 20013.9476648707 & -287.947664870684 \tabularnewline
45 & 20538 & 20401.2772714185 & 136.722728581546 \tabularnewline
46 & 19434 & 19456.506636145 & -22.5066361450117 \tabularnewline
47 & 20246 & 20083.9729659891 & 162.027034010862 \tabularnewline
48 & 20389 & 20025.8360917976 & 363.163908202358 \tabularnewline
49 & 20688 & 20358.6150806772 & 329.384919322787 \tabularnewline
50 & 20026 & 19917.3958203871 & 108.604179612947 \tabularnewline
51 & 20389 & 20679.790904678 & -290.790904678022 \tabularnewline
52 & 20610 & 20224.0991896586 & 385.900810341376 \tabularnewline
53 & 21422 & 21728.3383427159 & -306.33834271587 \tabularnewline
54 & 20759 & 21643.8327953702 & -884.832795370246 \tabularnewline
55 & 19876 & 20551.85356388 & -675.853563879984 \tabularnewline
56 & 18921 & 19776.924623863 & -855.924623863 \tabularnewline
57 & 19805 & 20146.0139225397 & -341.013922539678 \tabularnewline
58 & 17375 & 18859.867148558 & -1484.86714855803 \tabularnewline
59 & 18551 & 18913.0235876548 & -362.023587654847 \tabularnewline
60 & 19213 & 18657.0821230035 & 555.917876996518 \tabularnewline
61 & 19876 & 18947.9548918045 & 928.045108195496 \tabularnewline
62 & 18921 & 18533.8152472366 & 387.184752763358 \tabularnewline
63 & 18921 & 19094.619236915 & -173.619236915034 \tabularnewline
64 & 18921 & 19014.8773401231 & -93.8773401230719 \tabularnewline
65 & 19434 & 19826.5051383773 & -392.50513837731 \tabularnewline
66 & 18701 & 19274.3214452461 & -573.32144524606 \tabularnewline
67 & 17739 & 18352.2836740437 & -613.283674043687 \tabularnewline
68 & 16934 & 17416.6743991956 & -482.674399195577 \tabularnewline
69 & 17518 & 18174.0526749956 & -656.052674995597 \tabularnewline
70 & 15238 & 16002.5671144473 & -764.567114447258 \tabularnewline
71 & 16635 & 16956.7968868138 & -321.796886813805 \tabularnewline
72 & 17447 & 17205.4713541366 & 241.528645863378 \tabularnewline
73 & 17596 & 17524.4246353742 & 71.5753646258163 \tabularnewline
74 & 16784 & 16353.323637071 & 430.676362929033 \tabularnewline
75 & 16855 & 16511.2371048167 & 343.762895183278 \tabularnewline
76 & 16635 & 16615.1288480878 & 19.8711519121971 \tabularnewline
77 & 17375 & 17224.7548409973 & 150.245159002719 \tabularnewline
78 & 16855 & 16728.7139535349 & 126.286046465131 \tabularnewline
79 & 15830 & 16028.4563361522 & -198.456336152176 \tabularnewline
80 & 15089 & 15311.4739029503 & -222.473902950263 \tabularnewline
81 & 16342 & 16050.8386940613 & 291.16130593872 \tabularnewline
82 & 13621 & 14203.1595510917 & -582.1595510917 \tabularnewline
83 & 15388 & 15503.7825193006 & -115.782519300616 \tabularnewline
84 & 16193 & 16185.4958918453 & 7.50410815474061 \tabularnewline
85 & 16193 & 16316.9516712724 & -123.951671272445 \tabularnewline
86 & 15238 & 15283.4501633476 & -45.450163347592 \tabularnewline
87 & 14355 & 15187.5465361841 & -832.546536184102 \tabularnewline
88 & 14284 & 14582.1226643135 & -298.122664313456 \tabularnewline
89 & 15089 & 15092.1612289709 & -3.16122897093919 \tabularnewline
90 & 14355 & 14467.4600379731 & -112.460037973091 \tabularnewline
91 & 12959 & 13418.8435733541 & -459.843573354143 \tabularnewline
92 & 11997 & 12516.3170337979 & -519.317033797888 \tabularnewline
93 & 13030 & 13367.7217012154 & -337.721701215432 \tabularnewline
94 & 10601 & 10656.2823706669 & -55.282370666866 \tabularnewline
95 & 12809 & 12372.0643611103 & 436.935638889699 \tabularnewline
96 & 13984 & 13289.8450940587 & 694.154905941301 \tabularnewline
97 & 14355 & 13578.1302055649 & 776.869794435084 \tabularnewline
98 & 13543 & 12936.6819585132 & 606.318041486829 \tabularnewline
99 & 12517 & 12634.1911583183 & -117.191158318312 \tabularnewline
100 & 13251 & 12652.5143564819 & 598.485643518077 \tabularnewline
101 & 13543 & 13740.8201766849 & -197.820176684876 \tabularnewline
102 & 13322 & 13006.5616848288 & 315.438315171206 \tabularnewline
103 & 11113 & 11970.3490485989 & -857.349048598891 \tabularnewline
104 & 10088 & 10906.4666311222 & -818.466631122232 \tabularnewline
105 & 10821 & 11771.913007812 & -950.913007811991 \tabularnewline
106 & 8613 & 8991.15185093047 & -378.15185093047 \tabularnewline
107 & 10893 & 10871.594435439 & 21.4055645610242 \tabularnewline
108 & 11705 & 11765.8656219282 & -60.8656219282457 \tabularnewline
109 & 12367 & 11769.5151464484 & 597.484853551568 \tabularnewline
110 & 11263 & 10921.4630154272 & 341.536984572795 \tabularnewline
111 & 10230 & 10042.008898529 & 187.991101470998 \tabularnewline
112 & 10821 & 10578.2027427683 & 242.79725723167 \tabularnewline
113 & 11113 & 11008.0867127967 & 104.913287203348 \tabularnewline
114 & 10529 & 10668.9518940503 & -139.951894050324 \tabularnewline
115 & 8321 & 8706.0342240553 & -385.034224055298 \tabularnewline
116 & 7359 & 7824.36566716371 & -465.365667163711 \tabularnewline
117 & 8242 & 8731.05602401281 & -489.056024012807 \tabularnewline
118 & 5813 & 6467.05767078637 & -654.057670786373 \tabularnewline
119 & 8463 & 8455.00361197263 & 7.9963880273699 \tabularnewline
120 & 10088 & 9276.3058985918 & 811.694101408204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169355&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]18843[/C][C]18842.1805555555[/C][C]0.819444444456167[/C][/ROW]
[ROW][C]14[/C][C]18843[/C][C]18800.8258088541[/C][C]42.1741911458957[/C][/ROW]
[ROW][C]15[/C][C]18701[/C][C]18632.3368819188[/C][C]68.6631180812401[/C][/ROW]
[ROW][C]16[/C][C]18330[/C][C]18259.547438349[/C][C]70.4525616509709[/C][/ROW]
[ROW][C]17[/C][C]20246[/C][C]20194.7841805802[/C][C]51.2158194197509[/C][/ROW]
[ROW][C]18[/C][C]20538[/C][C]20490.3545348325[/C][C]47.645465167494[/C][/ROW]
[ROW][C]19[/C][C]20097[/C][C]19387.8487213139[/C][C]709.151278686135[/C][/ROW]
[ROW][C]20[/C][C]19064[/C][C]19014.5674401537[/C][C]49.4325598462601[/C][/ROW]
[ROW][C]21[/C][C]19506[/C][C]19180.1249136204[/C][C]325.87508637955[/C][/ROW]
[ROW][C]22[/C][C]18843[/C][C]19407.4255614215[/C][C]-564.425561421544[/C][/ROW]
[ROW][C]23[/C][C]19142[/C][C]19328.9212381859[/C][C]-186.921238185907[/C][/ROW]
[ROW][C]24[/C][C]19285[/C][C]19427.7138505995[/C][C]-142.713850599517[/C][/ROW]
[ROW][C]25[/C][C]19434[/C][C]19577.1389090191[/C][C]-143.138909019126[/C][/ROW]
[ROW][C]26[/C][C]19064[/C][C]19510.5861601928[/C][C]-446.586160192761[/C][/ROW]
[ROW][C]27[/C][C]19142[/C][C]19155.5137615691[/C][C]-13.5137615690983[/C][/ROW]
[ROW][C]28[/C][C]18622[/C][C]18744.109755927[/C][C]-122.109755927002[/C][/ROW]
[ROW][C]29[/C][C]20246[/C][C]20578.4486073916[/C][C]-332.448607391598[/C][/ROW]
[ROW][C]30[/C][C]20759[/C][C]20694.9414928804[/C][C]64.0585071195601[/C][/ROW]
[ROW][C]31[/C][C]20318[/C][C]19971.4482530007[/C][C]346.551746999328[/C][/ROW]
[ROW][C]32[/C][C]19506[/C][C]19028.3911353585[/C][C]477.608864641476[/C][/ROW]
[ROW][C]33[/C][C]20389[/C][C]19512.6009611919[/C][C]876.399038808107[/C][/ROW]
[ROW][C]34[/C][C]19434[/C][C]19428.7323353513[/C][C]5.26766464872708[/C][/ROW]
[ROW][C]35[/C][C]20318[/C][C]19815.636896977[/C][C]502.363103023035[/C][/ROW]
[ROW][C]36[/C][C]20246[/C][C]20248.1430029821[/C][C]-2.14300298210583[/C][/ROW]
[ROW][C]37[/C][C]20467[/C][C]20485.9996697037[/C][C]-18.9996697036877[/C][/ROW]
[ROW][C]38[/C][C]19655[/C][C]20324.270381823[/C][C]-669.270381822989[/C][/ROW]
[ROW][C]39[/C][C]20538[/C][C]20165.5917850627[/C][C]372.408214937324[/C][/ROW]
[ROW][C]40[/C][C]20467[/C][C]19885.2617876904[/C][C]581.738212309596[/C][/ROW]
[ROW][C]41[/C][C]21792[/C][C]21937.4490396096[/C][C]-145.449039609604[/C][/ROW]
[ROW][C]42[/C][C]21493[/C][C]22428.0451587156[/C][C]-935.045158715624[/C][/ROW]
[ROW][C]43[/C][C]20318[/C][C]21503.9482512596[/C][C]-1185.94825125958[/C][/ROW]
[ROW][C]44[/C][C]19726[/C][C]20013.9476648707[/C][C]-287.947664870684[/C][/ROW]
[ROW][C]45[/C][C]20538[/C][C]20401.2772714185[/C][C]136.722728581546[/C][/ROW]
[ROW][C]46[/C][C]19434[/C][C]19456.506636145[/C][C]-22.5066361450117[/C][/ROW]
[ROW][C]47[/C][C]20246[/C][C]20083.9729659891[/C][C]162.027034010862[/C][/ROW]
[ROW][C]48[/C][C]20389[/C][C]20025.8360917976[/C][C]363.163908202358[/C][/ROW]
[ROW][C]49[/C][C]20688[/C][C]20358.6150806772[/C][C]329.384919322787[/C][/ROW]
[ROW][C]50[/C][C]20026[/C][C]19917.3958203871[/C][C]108.604179612947[/C][/ROW]
[ROW][C]51[/C][C]20389[/C][C]20679.790904678[/C][C]-290.790904678022[/C][/ROW]
[ROW][C]52[/C][C]20610[/C][C]20224.0991896586[/C][C]385.900810341376[/C][/ROW]
[ROW][C]53[/C][C]21422[/C][C]21728.3383427159[/C][C]-306.33834271587[/C][/ROW]
[ROW][C]54[/C][C]20759[/C][C]21643.8327953702[/C][C]-884.832795370246[/C][/ROW]
[ROW][C]55[/C][C]19876[/C][C]20551.85356388[/C][C]-675.853563879984[/C][/ROW]
[ROW][C]56[/C][C]18921[/C][C]19776.924623863[/C][C]-855.924623863[/C][/ROW]
[ROW][C]57[/C][C]19805[/C][C]20146.0139225397[/C][C]-341.013922539678[/C][/ROW]
[ROW][C]58[/C][C]17375[/C][C]18859.867148558[/C][C]-1484.86714855803[/C][/ROW]
[ROW][C]59[/C][C]18551[/C][C]18913.0235876548[/C][C]-362.023587654847[/C][/ROW]
[ROW][C]60[/C][C]19213[/C][C]18657.0821230035[/C][C]555.917876996518[/C][/ROW]
[ROW][C]61[/C][C]19876[/C][C]18947.9548918045[/C][C]928.045108195496[/C][/ROW]
[ROW][C]62[/C][C]18921[/C][C]18533.8152472366[/C][C]387.184752763358[/C][/ROW]
[ROW][C]63[/C][C]18921[/C][C]19094.619236915[/C][C]-173.619236915034[/C][/ROW]
[ROW][C]64[/C][C]18921[/C][C]19014.8773401231[/C][C]-93.8773401230719[/C][/ROW]
[ROW][C]65[/C][C]19434[/C][C]19826.5051383773[/C][C]-392.50513837731[/C][/ROW]
[ROW][C]66[/C][C]18701[/C][C]19274.3214452461[/C][C]-573.32144524606[/C][/ROW]
[ROW][C]67[/C][C]17739[/C][C]18352.2836740437[/C][C]-613.283674043687[/C][/ROW]
[ROW][C]68[/C][C]16934[/C][C]17416.6743991956[/C][C]-482.674399195577[/C][/ROW]
[ROW][C]69[/C][C]17518[/C][C]18174.0526749956[/C][C]-656.052674995597[/C][/ROW]
[ROW][C]70[/C][C]15238[/C][C]16002.5671144473[/C][C]-764.567114447258[/C][/ROW]
[ROW][C]71[/C][C]16635[/C][C]16956.7968868138[/C][C]-321.796886813805[/C][/ROW]
[ROW][C]72[/C][C]17447[/C][C]17205.4713541366[/C][C]241.528645863378[/C][/ROW]
[ROW][C]73[/C][C]17596[/C][C]17524.4246353742[/C][C]71.5753646258163[/C][/ROW]
[ROW][C]74[/C][C]16784[/C][C]16353.323637071[/C][C]430.676362929033[/C][/ROW]
[ROW][C]75[/C][C]16855[/C][C]16511.2371048167[/C][C]343.762895183278[/C][/ROW]
[ROW][C]76[/C][C]16635[/C][C]16615.1288480878[/C][C]19.8711519121971[/C][/ROW]
[ROW][C]77[/C][C]17375[/C][C]17224.7548409973[/C][C]150.245159002719[/C][/ROW]
[ROW][C]78[/C][C]16855[/C][C]16728.7139535349[/C][C]126.286046465131[/C][/ROW]
[ROW][C]79[/C][C]15830[/C][C]16028.4563361522[/C][C]-198.456336152176[/C][/ROW]
[ROW][C]80[/C][C]15089[/C][C]15311.4739029503[/C][C]-222.473902950263[/C][/ROW]
[ROW][C]81[/C][C]16342[/C][C]16050.8386940613[/C][C]291.16130593872[/C][/ROW]
[ROW][C]82[/C][C]13621[/C][C]14203.1595510917[/C][C]-582.1595510917[/C][/ROW]
[ROW][C]83[/C][C]15388[/C][C]15503.7825193006[/C][C]-115.782519300616[/C][/ROW]
[ROW][C]84[/C][C]16193[/C][C]16185.4958918453[/C][C]7.50410815474061[/C][/ROW]
[ROW][C]85[/C][C]16193[/C][C]16316.9516712724[/C][C]-123.951671272445[/C][/ROW]
[ROW][C]86[/C][C]15238[/C][C]15283.4501633476[/C][C]-45.450163347592[/C][/ROW]
[ROW][C]87[/C][C]14355[/C][C]15187.5465361841[/C][C]-832.546536184102[/C][/ROW]
[ROW][C]88[/C][C]14284[/C][C]14582.1226643135[/C][C]-298.122664313456[/C][/ROW]
[ROW][C]89[/C][C]15089[/C][C]15092.1612289709[/C][C]-3.16122897093919[/C][/ROW]
[ROW][C]90[/C][C]14355[/C][C]14467.4600379731[/C][C]-112.460037973091[/C][/ROW]
[ROW][C]91[/C][C]12959[/C][C]13418.8435733541[/C][C]-459.843573354143[/C][/ROW]
[ROW][C]92[/C][C]11997[/C][C]12516.3170337979[/C][C]-519.317033797888[/C][/ROW]
[ROW][C]93[/C][C]13030[/C][C]13367.7217012154[/C][C]-337.721701215432[/C][/ROW]
[ROW][C]94[/C][C]10601[/C][C]10656.2823706669[/C][C]-55.282370666866[/C][/ROW]
[ROW][C]95[/C][C]12809[/C][C]12372.0643611103[/C][C]436.935638889699[/C][/ROW]
[ROW][C]96[/C][C]13984[/C][C]13289.8450940587[/C][C]694.154905941301[/C][/ROW]
[ROW][C]97[/C][C]14355[/C][C]13578.1302055649[/C][C]776.869794435084[/C][/ROW]
[ROW][C]98[/C][C]13543[/C][C]12936.6819585132[/C][C]606.318041486829[/C][/ROW]
[ROW][C]99[/C][C]12517[/C][C]12634.1911583183[/C][C]-117.191158318312[/C][/ROW]
[ROW][C]100[/C][C]13251[/C][C]12652.5143564819[/C][C]598.485643518077[/C][/ROW]
[ROW][C]101[/C][C]13543[/C][C]13740.8201766849[/C][C]-197.820176684876[/C][/ROW]
[ROW][C]102[/C][C]13322[/C][C]13006.5616848288[/C][C]315.438315171206[/C][/ROW]
[ROW][C]103[/C][C]11113[/C][C]11970.3490485989[/C][C]-857.349048598891[/C][/ROW]
[ROW][C]104[/C][C]10088[/C][C]10906.4666311222[/C][C]-818.466631122232[/C][/ROW]
[ROW][C]105[/C][C]10821[/C][C]11771.913007812[/C][C]-950.913007811991[/C][/ROW]
[ROW][C]106[/C][C]8613[/C][C]8991.15185093047[/C][C]-378.15185093047[/C][/ROW]
[ROW][C]107[/C][C]10893[/C][C]10871.594435439[/C][C]21.4055645610242[/C][/ROW]
[ROW][C]108[/C][C]11705[/C][C]11765.8656219282[/C][C]-60.8656219282457[/C][/ROW]
[ROW][C]109[/C][C]12367[/C][C]11769.5151464484[/C][C]597.484853551568[/C][/ROW]
[ROW][C]110[/C][C]11263[/C][C]10921.4630154272[/C][C]341.536984572795[/C][/ROW]
[ROW][C]111[/C][C]10230[/C][C]10042.008898529[/C][C]187.991101470998[/C][/ROW]
[ROW][C]112[/C][C]10821[/C][C]10578.2027427683[/C][C]242.79725723167[/C][/ROW]
[ROW][C]113[/C][C]11113[/C][C]11008.0867127967[/C][C]104.913287203348[/C][/ROW]
[ROW][C]114[/C][C]10529[/C][C]10668.9518940503[/C][C]-139.951894050324[/C][/ROW]
[ROW][C]115[/C][C]8321[/C][C]8706.0342240553[/C][C]-385.034224055298[/C][/ROW]
[ROW][C]116[/C][C]7359[/C][C]7824.36566716371[/C][C]-465.365667163711[/C][/ROW]
[ROW][C]117[/C][C]8242[/C][C]8731.05602401281[/C][C]-489.056024012807[/C][/ROW]
[ROW][C]118[/C][C]5813[/C][C]6467.05767078637[/C][C]-654.057670786373[/C][/ROW]
[ROW][C]119[/C][C]8463[/C][C]8455.00361197263[/C][C]7.9963880273699[/C][/ROW]
[ROW][C]120[/C][C]10088[/C][C]9276.3058985918[/C][C]811.694101408204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169355&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169355&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
131884318842.18055555550.819444444456167
141884318800.825808854142.1741911458957
151870118632.336881918868.6631180812401
161833018259.54743834970.4525616509709
172024620194.784180580251.2158194197509
182053820490.354534832547.645465167494
192009719387.8487213139709.151278686135
201906419014.567440153749.4325598462601
211950619180.1249136204325.87508637955
221884319407.4255614215-564.425561421544
231914219328.9212381859-186.921238185907
241928519427.7138505995-142.713850599517
251943419577.1389090191-143.138909019126
261906419510.5861601928-446.586160192761
271914219155.5137615691-13.5137615690983
281862218744.109755927-122.109755927002
292024620578.4486073916-332.448607391598
302075920694.941492880464.0585071195601
312031819971.4482530007346.551746999328
321950619028.3911353585477.608864641476
332038919512.6009611919876.399038808107
341943419428.73233535135.26766464872708
352031819815.636896977502.363103023035
362024620248.1430029821-2.14300298210583
372046720485.9996697037-18.9996697036877
381965520324.270381823-669.270381822989
392053820165.5917850627372.408214937324
402046719885.2617876904581.738212309596
412179221937.4490396096-145.449039609604
422149322428.0451587156-935.045158715624
432031821503.9482512596-1185.94825125958
441972620013.9476648707-287.947664870684
452053820401.2772714185136.722728581546
461943419456.506636145-22.5066361450117
472024620083.9729659891162.027034010862
482038920025.8360917976363.163908202358
492068820358.6150806772329.384919322787
502002619917.3958203871108.604179612947
512038920679.790904678-290.790904678022
522061020224.0991896586385.900810341376
532142221728.3383427159-306.33834271587
542075921643.8327953702-884.832795370246
551987620551.85356388-675.853563879984
561892119776.924623863-855.924623863
571980520146.0139225397-341.013922539678
581737518859.867148558-1484.86714855803
591855118913.0235876548-362.023587654847
601921318657.0821230035555.917876996518
611987618947.9548918045928.045108195496
621892118533.8152472366387.184752763358
631892119094.619236915-173.619236915034
641892119014.8773401231-93.8773401230719
651943419826.5051383773-392.50513837731
661870119274.3214452461-573.32144524606
671773918352.2836740437-613.283674043687
681693417416.6743991956-482.674399195577
691751818174.0526749956-656.052674995597
701523816002.5671144473-764.567114447258
711663516956.7968868138-321.796886813805
721744717205.4713541366241.528645863378
731759617524.424635374271.5753646258163
741678416353.323637071430.676362929033
751685516511.2371048167343.762895183278
761663516615.128848087819.8711519121971
771737517224.7548409973150.245159002719
781685516728.7139535349126.286046465131
791583016028.4563361522-198.456336152176
801508915311.4739029503-222.473902950263
811634216050.8386940613291.16130593872
821362114203.1595510917-582.1595510917
831538815503.7825193006-115.782519300616
841619316185.49589184537.50410815474061
851619316316.9516712724-123.951671272445
861523815283.4501633476-45.450163347592
871435515187.5465361841-832.546536184102
881428414582.1226643135-298.122664313456
891508915092.1612289709-3.16122897093919
901435514467.4600379731-112.460037973091
911295913418.8435733541-459.843573354143
921199712516.3170337979-519.317033797888
931303013367.7217012154-337.721701215432
941060110656.2823706669-55.282370666866
951280912372.0643611103436.935638889699
961398413289.8450940587694.154905941301
971435513578.1302055649776.869794435084
981354312936.6819585132606.318041486829
991251712634.1911583183-117.191158318312
1001325112652.5143564819598.485643518077
1011354313740.8201766849-197.820176684876
1021332213006.5616848288315.438315171206
1031111311970.3490485989-857.349048598891
1041008810906.4666311222-818.466631122232
1051082111771.913007812-950.913007811991
10686138991.15185093047-378.15185093047
1071089310871.59443543921.4055645610242
1081170511765.8656219282-60.8656219282457
1091236711769.5151464484597.484853551568
1101126310921.4630154272341.536984572795
1111023010042.008898529187.991101470998
1121082110578.2027427683242.79725723167
1131111311008.0867127967104.913287203348
1141052910668.9518940503-139.951894050324
11583218706.0342240553-385.034224055298
11673597824.36566716371-465.365667163711
11782428731.05602401281-489.056024012807
11858136467.05767078637-654.057670786373
11984638455.003611972637.9963880273699
120100889276.3058985918811.694101408204







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12110029.34333151229116.3718452620610942.3148177623
1228775.487166459147781.149131495449769.82520142283
1237645.937688074886567.3824504588724.49292569175
1248113.25647156616947.762185596459278.75075753574
1258331.115790372757076.072008123349586.15957262216
1267769.485747055836422.379414106589116.59208000508
1275686.858209881964245.262275220927128.454144543
1284892.862087268063354.426137182116431.29803735401
1295965.639183225344328.081657272447603.19670917823
1303806.088603469552067.190259352885544.98694758623
1316474.284318856644631.882692963628316.68594474966
1327791.497664283515843.482333736639739.51299483039

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 10029.3433315122 & 9116.37184526206 & 10942.3148177623 \tabularnewline
122 & 8775.48716645914 & 7781.14913149544 & 9769.82520142283 \tabularnewline
123 & 7645.93768807488 & 6567.382450458 & 8724.49292569175 \tabularnewline
124 & 8113.2564715661 & 6947.76218559645 & 9278.75075753574 \tabularnewline
125 & 8331.11579037275 & 7076.07200812334 & 9586.15957262216 \tabularnewline
126 & 7769.48574705583 & 6422.37941410658 & 9116.59208000508 \tabularnewline
127 & 5686.85820988196 & 4245.26227522092 & 7128.454144543 \tabularnewline
128 & 4892.86208726806 & 3354.42613718211 & 6431.29803735401 \tabularnewline
129 & 5965.63918322534 & 4328.08165727244 & 7603.19670917823 \tabularnewline
130 & 3806.08860346955 & 2067.19025935288 & 5544.98694758623 \tabularnewline
131 & 6474.28431885664 & 4631.88269296362 & 8316.68594474966 \tabularnewline
132 & 7791.49766428351 & 5843.48233373663 & 9739.51299483039 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169355&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]10029.3433315122[/C][C]9116.37184526206[/C][C]10942.3148177623[/C][/ROW]
[ROW][C]122[/C][C]8775.48716645914[/C][C]7781.14913149544[/C][C]9769.82520142283[/C][/ROW]
[ROW][C]123[/C][C]7645.93768807488[/C][C]6567.382450458[/C][C]8724.49292569175[/C][/ROW]
[ROW][C]124[/C][C]8113.2564715661[/C][C]6947.76218559645[/C][C]9278.75075753574[/C][/ROW]
[ROW][C]125[/C][C]8331.11579037275[/C][C]7076.07200812334[/C][C]9586.15957262216[/C][/ROW]
[ROW][C]126[/C][C]7769.48574705583[/C][C]6422.37941410658[/C][C]9116.59208000508[/C][/ROW]
[ROW][C]127[/C][C]5686.85820988196[/C][C]4245.26227522092[/C][C]7128.454144543[/C][/ROW]
[ROW][C]128[/C][C]4892.86208726806[/C][C]3354.42613718211[/C][C]6431.29803735401[/C][/ROW]
[ROW][C]129[/C][C]5965.63918322534[/C][C]4328.08165727244[/C][C]7603.19670917823[/C][/ROW]
[ROW][C]130[/C][C]3806.08860346955[/C][C]2067.19025935288[/C][C]5544.98694758623[/C][/ROW]
[ROW][C]131[/C][C]6474.28431885664[/C][C]4631.88269296362[/C][C]8316.68594474966[/C][/ROW]
[ROW][C]132[/C][C]7791.49766428351[/C][C]5843.48233373663[/C][C]9739.51299483039[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169355&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169355&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
12110029.34333151229116.3718452620610942.3148177623
1228775.487166459147781.149131495449769.82520142283
1237645.937688074886567.3824504588724.49292569175
1248113.25647156616947.762185596459278.75075753574
1258331.115790372757076.072008123349586.15957262216
1267769.485747055836422.379414106589116.59208000508
1275686.858209881964245.262275220927128.454144543
1284892.862087268063354.426137182116431.29803735401
1295965.639183225344328.081657272447603.19670917823
1303806.088603469552067.190259352885544.98694758623
1316474.284318856644631.882692963628316.68594474966
1327791.497664283515843.482333736639739.51299483039



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')