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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, 21 Dec 2016 17:35:38 +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/21/t14823420684lz44mr40ya5whg.htm/, Retrieved Mon, 06 May 2024 12:58:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302442, Retrieved Mon, 06 May 2024 12:58:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Plot & Describe D...] [2016-12-21 13:39:57] [a4b9e35ec68b77b903de481d98cdbf80]
- RMP     [Exponential Smoothing] [Exponentional Smo...] [2016-12-21 16:35:38] [dc40abf8f837a2863894b5e0c13dd016] [Current]
- RMP       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2016-12-23 12:59:01] [a4b9e35ec68b77b903de481d98cdbf80]
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Dataseries X:
4998
4480
4824
4814
4602
4499
4594
4600
4507
4606
4503
4801
4564
4142
4818
4408
4496
4587
4656
4799
4652
4638
4650
5185
5208
4477
4976
4670
4842
4713
4804
4996
4574
4841
4688
4766
4994
4514
4766
4642
4806
4645
4784
4979
4530
4942
4651
5150
4987
4532
5046
4783
4958
4815
5055
5152
4773
5147
4866
5311
5172
4734
5011
4957
4968
5049
5305
5067
5001
5252
4903
5408
5395
5150
5460
4968
5021
5118
5175
5420
5121
5450
5286
5693
5353
5017
5577
4987
5129
5249
5100
5382
5039
5364
5193
5846
5259
4809
5297
5034
5243
5150
5296
5596
4954
5250
5009
5113
5237
4575
5026
4842
5019
5063
5261
5327
5054
5269
5019
5315
5274
4899
5216
5029
5110
5093




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302442&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302442&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302442&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.290849910680853
beta0.00429297776304895
gamma0.28049695162481

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.290849910680853 \tabularnewline
beta & 0.00429297776304895 \tabularnewline
gamma & 0.28049695162481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302442&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]0.290849910680853[/C][/ROW]
[ROW][C]beta[/C][C]0.00429297776304895[/C][/ROW]
[ROW][C]gamma[/C][C]0.28049695162481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302442&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302442&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
alpha0.290849910680853
beta0.00429297776304895
gamma0.28049695162481







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1345644625.40037393162-61.4003739316231
1441424174.04161004062-32.0416100406246
1548184825.72349912652-7.72349912651771
1644084405.426998277812.57300172218766
1744964486.045113129289.9548868707152
1845874557.1560117433829.8439882566199
1946564554.88058395356101.119416046443
2047994621.96186690657177.038133093431
2146524594.5118205710357.488179428974
2246384727.19579466574-89.1957946657394
2346504619.2720437060430.7279562939557
2451854926.68313896924258.316861030764
2552084746.39756353903461.602436460972
2644774454.2422449190722.7577550809301
2749765128.01641353868-152.016413538683
2846704668.936953920711.06304607928814
2948424751.7188763138190.2811236861853
3047134851.38379394824-138.383793948236
3148044815.38190193911-11.3819019391076
3249964865.72790456997130.272095430028
3345744801.72174483792-227.721744837918
3448414822.7447573917418.2552426082621
3546884770.53174103434-82.5317410343396
3647665090.7346096026-324.734609602605
3749944781.03962389644212.960376103556
3845144328.69840525253185.301594747471
3947665014.61044808138-248.610448081383
4046424557.3928469199984.6071530800082
4148064681.83115340725124.168846592755
4246454745.52069543845-100.52069543845
4347844745.4942054535738.5057945464268
4449794838.28976904989140.710230950108
4545304705.88513321281-175.885133212805
4649424790.75365450812151.246345491884
4746514757.17961720823-106.17961720823
4851505022.30384342285127.69615657715
4949874951.6955001556835.3044998443202
5045324442.5014299667589.4985700332527
5150465014.4382556732931.561744326712
5247834705.540784361577.4592156384979
5349584836.31086166994121.689138330055
5448154855.12344628014-40.1234462801413
5550554900.93153927475154.068460725247
5651525048.42639731328103.573602686718
5747734842.95678343256-69.9567834325599
5851475024.5495895662122.4504104338
5948664932.20242082684-66.2024208268449
6053115256.3330997015754.6669002984308
6151725146.8728045350625.1271954649355
6247344646.2525770696587.7474229303461
6350115206.90735191437-195.907351914374
6449574841.44790457393115.552095426067
6549684992.61054659915-24.6105465991541
6650494937.0176337712111.982366228803
6753055066.2157962587238.784203741304
6850675228.93437477972-161.934374779718
6950014912.0208841023288.9791158976786
7052525178.6079945725473.392005427464
7149035034.90040955224-131.900409552241
7254085364.3174444801943.6825555198138
7353955246.12472172135148.875278278653
7451504794.44543572731355.554564272694
7554605377.3960060315382.6039939684661
7649685156.07023497852-188.070234978523
7750215191.83976476369-170.839764763688
7851185121.49960448644-3.49960448644106
7951755242.80157525485-67.8015752548527
8054205236.72720249755183.272797502452
8151215070.6447391118950.3552608881109
8254505323.36661326948126.63338673052
8352865154.8441414622131.155858537802
8456935596.5609982347396.4390017652722
8553535515.5666497517-162.566649751702
8650175014.956945935422.04305406458298
8755775440.89446195776136.105538042243
8849875181.45494694973-194.45494694973
8951295218.9532500462-89.9532500461974
9052495205.684672138643.3153278614009
9151005328.12999790011-228.129997900105
9253825325.4840740387256.5159259612847
9350395096.05453704908-57.0545370490845
9453645332.5343567404331.4656432595739
9551935136.9383676923856.0616323076247
9658465549.52105535006296.478944649942
9752595475.05077895422-216.050778954217
9848094991.42412302767-182.424123027668
9952975389.94166811691-92.9416681169068
10050344997.4098766746136.5901233253899
10152435122.46233607257120.537663927426
10251505196.75470944154-46.7547094415359
10352965238.726959279457.2730407205991
10455965375.7852063669220.214793633098
10549545171.65560056347-217.655600563469
10652505379.11096377582-129.110963775815
10750095141.5816889048-132.581688904803
10851135546.76232437183-433.762324371827
10952375156.6824561595880.3175438404223
11045754765.04395506123-190.043955061235
11150265178.23573796428-152.235737964284
11248424793.2410928646148.7589071353877
11350194937.5634916492181.4365083507901
11450634966.1898785680596.810121431954
11552615069.77327456966191.226725430337
11653275277.5333687874749.4666312125264
11750544935.75969608856118.24030391144
11852695258.0593279329710.9406720670349
11950195060.28471980553-41.2847198055342
12053155431.93492646706-116.934926467057
12152745236.4828142334837.5171857665164
12248994778.78421344229120.215786557706
12352165290.29019516983-74.2901951698268
12450294968.5986453363260.4013546636752
12551105123.47373671277-13.4737367127718
12650935128.10145593048-35.1014559304786

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4564 & 4625.40037393162 & -61.4003739316231 \tabularnewline
14 & 4142 & 4174.04161004062 & -32.0416100406246 \tabularnewline
15 & 4818 & 4825.72349912652 & -7.72349912651771 \tabularnewline
16 & 4408 & 4405.42699827781 & 2.57300172218766 \tabularnewline
17 & 4496 & 4486.04511312928 & 9.9548868707152 \tabularnewline
18 & 4587 & 4557.15601174338 & 29.8439882566199 \tabularnewline
19 & 4656 & 4554.88058395356 & 101.119416046443 \tabularnewline
20 & 4799 & 4621.96186690657 & 177.038133093431 \tabularnewline
21 & 4652 & 4594.51182057103 & 57.488179428974 \tabularnewline
22 & 4638 & 4727.19579466574 & -89.1957946657394 \tabularnewline
23 & 4650 & 4619.27204370604 & 30.7279562939557 \tabularnewline
24 & 5185 & 4926.68313896924 & 258.316861030764 \tabularnewline
25 & 5208 & 4746.39756353903 & 461.602436460972 \tabularnewline
26 & 4477 & 4454.24224491907 & 22.7577550809301 \tabularnewline
27 & 4976 & 5128.01641353868 & -152.016413538683 \tabularnewline
28 & 4670 & 4668.93695392071 & 1.06304607928814 \tabularnewline
29 & 4842 & 4751.71887631381 & 90.2811236861853 \tabularnewline
30 & 4713 & 4851.38379394824 & -138.383793948236 \tabularnewline
31 & 4804 & 4815.38190193911 & -11.3819019391076 \tabularnewline
32 & 4996 & 4865.72790456997 & 130.272095430028 \tabularnewline
33 & 4574 & 4801.72174483792 & -227.721744837918 \tabularnewline
34 & 4841 & 4822.74475739174 & 18.2552426082621 \tabularnewline
35 & 4688 & 4770.53174103434 & -82.5317410343396 \tabularnewline
36 & 4766 & 5090.7346096026 & -324.734609602605 \tabularnewline
37 & 4994 & 4781.03962389644 & 212.960376103556 \tabularnewline
38 & 4514 & 4328.69840525253 & 185.301594747471 \tabularnewline
39 & 4766 & 5014.61044808138 & -248.610448081383 \tabularnewline
40 & 4642 & 4557.39284691999 & 84.6071530800082 \tabularnewline
41 & 4806 & 4681.83115340725 & 124.168846592755 \tabularnewline
42 & 4645 & 4745.52069543845 & -100.52069543845 \tabularnewline
43 & 4784 & 4745.49420545357 & 38.5057945464268 \tabularnewline
44 & 4979 & 4838.28976904989 & 140.710230950108 \tabularnewline
45 & 4530 & 4705.88513321281 & -175.885133212805 \tabularnewline
46 & 4942 & 4790.75365450812 & 151.246345491884 \tabularnewline
47 & 4651 & 4757.17961720823 & -106.17961720823 \tabularnewline
48 & 5150 & 5022.30384342285 & 127.69615657715 \tabularnewline
49 & 4987 & 4951.69550015568 & 35.3044998443202 \tabularnewline
50 & 4532 & 4442.50142996675 & 89.4985700332527 \tabularnewline
51 & 5046 & 5014.43825567329 & 31.561744326712 \tabularnewline
52 & 4783 & 4705.5407843615 & 77.4592156384979 \tabularnewline
53 & 4958 & 4836.31086166994 & 121.689138330055 \tabularnewline
54 & 4815 & 4855.12344628014 & -40.1234462801413 \tabularnewline
55 & 5055 & 4900.93153927475 & 154.068460725247 \tabularnewline
56 & 5152 & 5048.42639731328 & 103.573602686718 \tabularnewline
57 & 4773 & 4842.95678343256 & -69.9567834325599 \tabularnewline
58 & 5147 & 5024.5495895662 & 122.4504104338 \tabularnewline
59 & 4866 & 4932.20242082684 & -66.2024208268449 \tabularnewline
60 & 5311 & 5256.33309970157 & 54.6669002984308 \tabularnewline
61 & 5172 & 5146.87280453506 & 25.1271954649355 \tabularnewline
62 & 4734 & 4646.25257706965 & 87.7474229303461 \tabularnewline
63 & 5011 & 5206.90735191437 & -195.907351914374 \tabularnewline
64 & 4957 & 4841.44790457393 & 115.552095426067 \tabularnewline
65 & 4968 & 4992.61054659915 & -24.6105465991541 \tabularnewline
66 & 5049 & 4937.0176337712 & 111.982366228803 \tabularnewline
67 & 5305 & 5066.2157962587 & 238.784203741304 \tabularnewline
68 & 5067 & 5228.93437477972 & -161.934374779718 \tabularnewline
69 & 5001 & 4912.02088410232 & 88.9791158976786 \tabularnewline
70 & 5252 & 5178.60799457254 & 73.392005427464 \tabularnewline
71 & 4903 & 5034.90040955224 & -131.900409552241 \tabularnewline
72 & 5408 & 5364.31744448019 & 43.6825555198138 \tabularnewline
73 & 5395 & 5246.12472172135 & 148.875278278653 \tabularnewline
74 & 5150 & 4794.44543572731 & 355.554564272694 \tabularnewline
75 & 5460 & 5377.39600603153 & 82.6039939684661 \tabularnewline
76 & 4968 & 5156.07023497852 & -188.070234978523 \tabularnewline
77 & 5021 & 5191.83976476369 & -170.839764763688 \tabularnewline
78 & 5118 & 5121.49960448644 & -3.49960448644106 \tabularnewline
79 & 5175 & 5242.80157525485 & -67.8015752548527 \tabularnewline
80 & 5420 & 5236.72720249755 & 183.272797502452 \tabularnewline
81 & 5121 & 5070.64473911189 & 50.3552608881109 \tabularnewline
82 & 5450 & 5323.36661326948 & 126.63338673052 \tabularnewline
83 & 5286 & 5154.8441414622 & 131.155858537802 \tabularnewline
84 & 5693 & 5596.56099823473 & 96.4390017652722 \tabularnewline
85 & 5353 & 5515.5666497517 & -162.566649751702 \tabularnewline
86 & 5017 & 5014.95694593542 & 2.04305406458298 \tabularnewline
87 & 5577 & 5440.89446195776 & 136.105538042243 \tabularnewline
88 & 4987 & 5181.45494694973 & -194.45494694973 \tabularnewline
89 & 5129 & 5218.9532500462 & -89.9532500461974 \tabularnewline
90 & 5249 & 5205.6846721386 & 43.3153278614009 \tabularnewline
91 & 5100 & 5328.12999790011 & -228.129997900105 \tabularnewline
92 & 5382 & 5325.48407403872 & 56.5159259612847 \tabularnewline
93 & 5039 & 5096.05453704908 & -57.0545370490845 \tabularnewline
94 & 5364 & 5332.53435674043 & 31.4656432595739 \tabularnewline
95 & 5193 & 5136.93836769238 & 56.0616323076247 \tabularnewline
96 & 5846 & 5549.52105535006 & 296.478944649942 \tabularnewline
97 & 5259 & 5475.05077895422 & -216.050778954217 \tabularnewline
98 & 4809 & 4991.42412302767 & -182.424123027668 \tabularnewline
99 & 5297 & 5389.94166811691 & -92.9416681169068 \tabularnewline
100 & 5034 & 4997.40987667461 & 36.5901233253899 \tabularnewline
101 & 5243 & 5122.46233607257 & 120.537663927426 \tabularnewline
102 & 5150 & 5196.75470944154 & -46.7547094415359 \tabularnewline
103 & 5296 & 5238.7269592794 & 57.2730407205991 \tabularnewline
104 & 5596 & 5375.7852063669 & 220.214793633098 \tabularnewline
105 & 4954 & 5171.65560056347 & -217.655600563469 \tabularnewline
106 & 5250 & 5379.11096377582 & -129.110963775815 \tabularnewline
107 & 5009 & 5141.5816889048 & -132.581688904803 \tabularnewline
108 & 5113 & 5546.76232437183 & -433.762324371827 \tabularnewline
109 & 5237 & 5156.68245615958 & 80.3175438404223 \tabularnewline
110 & 4575 & 4765.04395506123 & -190.043955061235 \tabularnewline
111 & 5026 & 5178.23573796428 & -152.235737964284 \tabularnewline
112 & 4842 & 4793.24109286461 & 48.7589071353877 \tabularnewline
113 & 5019 & 4937.56349164921 & 81.4365083507901 \tabularnewline
114 & 5063 & 4966.18987856805 & 96.810121431954 \tabularnewline
115 & 5261 & 5069.77327456966 & 191.226725430337 \tabularnewline
116 & 5327 & 5277.53336878747 & 49.4666312125264 \tabularnewline
117 & 5054 & 4935.75969608856 & 118.24030391144 \tabularnewline
118 & 5269 & 5258.05932793297 & 10.9406720670349 \tabularnewline
119 & 5019 & 5060.28471980553 & -41.2847198055342 \tabularnewline
120 & 5315 & 5431.93492646706 & -116.934926467057 \tabularnewline
121 & 5274 & 5236.48281423348 & 37.5171857665164 \tabularnewline
122 & 4899 & 4778.78421344229 & 120.215786557706 \tabularnewline
123 & 5216 & 5290.29019516983 & -74.2901951698268 \tabularnewline
124 & 5029 & 4968.59864533632 & 60.4013546636752 \tabularnewline
125 & 5110 & 5123.47373671277 & -13.4737367127718 \tabularnewline
126 & 5093 & 5128.10145593048 & -35.1014559304786 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302442&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]4564[/C][C]4625.40037393162[/C][C]-61.4003739316231[/C][/ROW]
[ROW][C]14[/C][C]4142[/C][C]4174.04161004062[/C][C]-32.0416100406246[/C][/ROW]
[ROW][C]15[/C][C]4818[/C][C]4825.72349912652[/C][C]-7.72349912651771[/C][/ROW]
[ROW][C]16[/C][C]4408[/C][C]4405.42699827781[/C][C]2.57300172218766[/C][/ROW]
[ROW][C]17[/C][C]4496[/C][C]4486.04511312928[/C][C]9.9548868707152[/C][/ROW]
[ROW][C]18[/C][C]4587[/C][C]4557.15601174338[/C][C]29.8439882566199[/C][/ROW]
[ROW][C]19[/C][C]4656[/C][C]4554.88058395356[/C][C]101.119416046443[/C][/ROW]
[ROW][C]20[/C][C]4799[/C][C]4621.96186690657[/C][C]177.038133093431[/C][/ROW]
[ROW][C]21[/C][C]4652[/C][C]4594.51182057103[/C][C]57.488179428974[/C][/ROW]
[ROW][C]22[/C][C]4638[/C][C]4727.19579466574[/C][C]-89.1957946657394[/C][/ROW]
[ROW][C]23[/C][C]4650[/C][C]4619.27204370604[/C][C]30.7279562939557[/C][/ROW]
[ROW][C]24[/C][C]5185[/C][C]4926.68313896924[/C][C]258.316861030764[/C][/ROW]
[ROW][C]25[/C][C]5208[/C][C]4746.39756353903[/C][C]461.602436460972[/C][/ROW]
[ROW][C]26[/C][C]4477[/C][C]4454.24224491907[/C][C]22.7577550809301[/C][/ROW]
[ROW][C]27[/C][C]4976[/C][C]5128.01641353868[/C][C]-152.016413538683[/C][/ROW]
[ROW][C]28[/C][C]4670[/C][C]4668.93695392071[/C][C]1.06304607928814[/C][/ROW]
[ROW][C]29[/C][C]4842[/C][C]4751.71887631381[/C][C]90.2811236861853[/C][/ROW]
[ROW][C]30[/C][C]4713[/C][C]4851.38379394824[/C][C]-138.383793948236[/C][/ROW]
[ROW][C]31[/C][C]4804[/C][C]4815.38190193911[/C][C]-11.3819019391076[/C][/ROW]
[ROW][C]32[/C][C]4996[/C][C]4865.72790456997[/C][C]130.272095430028[/C][/ROW]
[ROW][C]33[/C][C]4574[/C][C]4801.72174483792[/C][C]-227.721744837918[/C][/ROW]
[ROW][C]34[/C][C]4841[/C][C]4822.74475739174[/C][C]18.2552426082621[/C][/ROW]
[ROW][C]35[/C][C]4688[/C][C]4770.53174103434[/C][C]-82.5317410343396[/C][/ROW]
[ROW][C]36[/C][C]4766[/C][C]5090.7346096026[/C][C]-324.734609602605[/C][/ROW]
[ROW][C]37[/C][C]4994[/C][C]4781.03962389644[/C][C]212.960376103556[/C][/ROW]
[ROW][C]38[/C][C]4514[/C][C]4328.69840525253[/C][C]185.301594747471[/C][/ROW]
[ROW][C]39[/C][C]4766[/C][C]5014.61044808138[/C][C]-248.610448081383[/C][/ROW]
[ROW][C]40[/C][C]4642[/C][C]4557.39284691999[/C][C]84.6071530800082[/C][/ROW]
[ROW][C]41[/C][C]4806[/C][C]4681.83115340725[/C][C]124.168846592755[/C][/ROW]
[ROW][C]42[/C][C]4645[/C][C]4745.52069543845[/C][C]-100.52069543845[/C][/ROW]
[ROW][C]43[/C][C]4784[/C][C]4745.49420545357[/C][C]38.5057945464268[/C][/ROW]
[ROW][C]44[/C][C]4979[/C][C]4838.28976904989[/C][C]140.710230950108[/C][/ROW]
[ROW][C]45[/C][C]4530[/C][C]4705.88513321281[/C][C]-175.885133212805[/C][/ROW]
[ROW][C]46[/C][C]4942[/C][C]4790.75365450812[/C][C]151.246345491884[/C][/ROW]
[ROW][C]47[/C][C]4651[/C][C]4757.17961720823[/C][C]-106.17961720823[/C][/ROW]
[ROW][C]48[/C][C]5150[/C][C]5022.30384342285[/C][C]127.69615657715[/C][/ROW]
[ROW][C]49[/C][C]4987[/C][C]4951.69550015568[/C][C]35.3044998443202[/C][/ROW]
[ROW][C]50[/C][C]4532[/C][C]4442.50142996675[/C][C]89.4985700332527[/C][/ROW]
[ROW][C]51[/C][C]5046[/C][C]5014.43825567329[/C][C]31.561744326712[/C][/ROW]
[ROW][C]52[/C][C]4783[/C][C]4705.5407843615[/C][C]77.4592156384979[/C][/ROW]
[ROW][C]53[/C][C]4958[/C][C]4836.31086166994[/C][C]121.689138330055[/C][/ROW]
[ROW][C]54[/C][C]4815[/C][C]4855.12344628014[/C][C]-40.1234462801413[/C][/ROW]
[ROW][C]55[/C][C]5055[/C][C]4900.93153927475[/C][C]154.068460725247[/C][/ROW]
[ROW][C]56[/C][C]5152[/C][C]5048.42639731328[/C][C]103.573602686718[/C][/ROW]
[ROW][C]57[/C][C]4773[/C][C]4842.95678343256[/C][C]-69.9567834325599[/C][/ROW]
[ROW][C]58[/C][C]5147[/C][C]5024.5495895662[/C][C]122.4504104338[/C][/ROW]
[ROW][C]59[/C][C]4866[/C][C]4932.20242082684[/C][C]-66.2024208268449[/C][/ROW]
[ROW][C]60[/C][C]5311[/C][C]5256.33309970157[/C][C]54.6669002984308[/C][/ROW]
[ROW][C]61[/C][C]5172[/C][C]5146.87280453506[/C][C]25.1271954649355[/C][/ROW]
[ROW][C]62[/C][C]4734[/C][C]4646.25257706965[/C][C]87.7474229303461[/C][/ROW]
[ROW][C]63[/C][C]5011[/C][C]5206.90735191437[/C][C]-195.907351914374[/C][/ROW]
[ROW][C]64[/C][C]4957[/C][C]4841.44790457393[/C][C]115.552095426067[/C][/ROW]
[ROW][C]65[/C][C]4968[/C][C]4992.61054659915[/C][C]-24.6105465991541[/C][/ROW]
[ROW][C]66[/C][C]5049[/C][C]4937.0176337712[/C][C]111.982366228803[/C][/ROW]
[ROW][C]67[/C][C]5305[/C][C]5066.2157962587[/C][C]238.784203741304[/C][/ROW]
[ROW][C]68[/C][C]5067[/C][C]5228.93437477972[/C][C]-161.934374779718[/C][/ROW]
[ROW][C]69[/C][C]5001[/C][C]4912.02088410232[/C][C]88.9791158976786[/C][/ROW]
[ROW][C]70[/C][C]5252[/C][C]5178.60799457254[/C][C]73.392005427464[/C][/ROW]
[ROW][C]71[/C][C]4903[/C][C]5034.90040955224[/C][C]-131.900409552241[/C][/ROW]
[ROW][C]72[/C][C]5408[/C][C]5364.31744448019[/C][C]43.6825555198138[/C][/ROW]
[ROW][C]73[/C][C]5395[/C][C]5246.12472172135[/C][C]148.875278278653[/C][/ROW]
[ROW][C]74[/C][C]5150[/C][C]4794.44543572731[/C][C]355.554564272694[/C][/ROW]
[ROW][C]75[/C][C]5460[/C][C]5377.39600603153[/C][C]82.6039939684661[/C][/ROW]
[ROW][C]76[/C][C]4968[/C][C]5156.07023497852[/C][C]-188.070234978523[/C][/ROW]
[ROW][C]77[/C][C]5021[/C][C]5191.83976476369[/C][C]-170.839764763688[/C][/ROW]
[ROW][C]78[/C][C]5118[/C][C]5121.49960448644[/C][C]-3.49960448644106[/C][/ROW]
[ROW][C]79[/C][C]5175[/C][C]5242.80157525485[/C][C]-67.8015752548527[/C][/ROW]
[ROW][C]80[/C][C]5420[/C][C]5236.72720249755[/C][C]183.272797502452[/C][/ROW]
[ROW][C]81[/C][C]5121[/C][C]5070.64473911189[/C][C]50.3552608881109[/C][/ROW]
[ROW][C]82[/C][C]5450[/C][C]5323.36661326948[/C][C]126.63338673052[/C][/ROW]
[ROW][C]83[/C][C]5286[/C][C]5154.8441414622[/C][C]131.155858537802[/C][/ROW]
[ROW][C]84[/C][C]5693[/C][C]5596.56099823473[/C][C]96.4390017652722[/C][/ROW]
[ROW][C]85[/C][C]5353[/C][C]5515.5666497517[/C][C]-162.566649751702[/C][/ROW]
[ROW][C]86[/C][C]5017[/C][C]5014.95694593542[/C][C]2.04305406458298[/C][/ROW]
[ROW][C]87[/C][C]5577[/C][C]5440.89446195776[/C][C]136.105538042243[/C][/ROW]
[ROW][C]88[/C][C]4987[/C][C]5181.45494694973[/C][C]-194.45494694973[/C][/ROW]
[ROW][C]89[/C][C]5129[/C][C]5218.9532500462[/C][C]-89.9532500461974[/C][/ROW]
[ROW][C]90[/C][C]5249[/C][C]5205.6846721386[/C][C]43.3153278614009[/C][/ROW]
[ROW][C]91[/C][C]5100[/C][C]5328.12999790011[/C][C]-228.129997900105[/C][/ROW]
[ROW][C]92[/C][C]5382[/C][C]5325.48407403872[/C][C]56.5159259612847[/C][/ROW]
[ROW][C]93[/C][C]5039[/C][C]5096.05453704908[/C][C]-57.0545370490845[/C][/ROW]
[ROW][C]94[/C][C]5364[/C][C]5332.53435674043[/C][C]31.4656432595739[/C][/ROW]
[ROW][C]95[/C][C]5193[/C][C]5136.93836769238[/C][C]56.0616323076247[/C][/ROW]
[ROW][C]96[/C][C]5846[/C][C]5549.52105535006[/C][C]296.478944649942[/C][/ROW]
[ROW][C]97[/C][C]5259[/C][C]5475.05077895422[/C][C]-216.050778954217[/C][/ROW]
[ROW][C]98[/C][C]4809[/C][C]4991.42412302767[/C][C]-182.424123027668[/C][/ROW]
[ROW][C]99[/C][C]5297[/C][C]5389.94166811691[/C][C]-92.9416681169068[/C][/ROW]
[ROW][C]100[/C][C]5034[/C][C]4997.40987667461[/C][C]36.5901233253899[/C][/ROW]
[ROW][C]101[/C][C]5243[/C][C]5122.46233607257[/C][C]120.537663927426[/C][/ROW]
[ROW][C]102[/C][C]5150[/C][C]5196.75470944154[/C][C]-46.7547094415359[/C][/ROW]
[ROW][C]103[/C][C]5296[/C][C]5238.7269592794[/C][C]57.2730407205991[/C][/ROW]
[ROW][C]104[/C][C]5596[/C][C]5375.7852063669[/C][C]220.214793633098[/C][/ROW]
[ROW][C]105[/C][C]4954[/C][C]5171.65560056347[/C][C]-217.655600563469[/C][/ROW]
[ROW][C]106[/C][C]5250[/C][C]5379.11096377582[/C][C]-129.110963775815[/C][/ROW]
[ROW][C]107[/C][C]5009[/C][C]5141.5816889048[/C][C]-132.581688904803[/C][/ROW]
[ROW][C]108[/C][C]5113[/C][C]5546.76232437183[/C][C]-433.762324371827[/C][/ROW]
[ROW][C]109[/C][C]5237[/C][C]5156.68245615958[/C][C]80.3175438404223[/C][/ROW]
[ROW][C]110[/C][C]4575[/C][C]4765.04395506123[/C][C]-190.043955061235[/C][/ROW]
[ROW][C]111[/C][C]5026[/C][C]5178.23573796428[/C][C]-152.235737964284[/C][/ROW]
[ROW][C]112[/C][C]4842[/C][C]4793.24109286461[/C][C]48.7589071353877[/C][/ROW]
[ROW][C]113[/C][C]5019[/C][C]4937.56349164921[/C][C]81.4365083507901[/C][/ROW]
[ROW][C]114[/C][C]5063[/C][C]4966.18987856805[/C][C]96.810121431954[/C][/ROW]
[ROW][C]115[/C][C]5261[/C][C]5069.77327456966[/C][C]191.226725430337[/C][/ROW]
[ROW][C]116[/C][C]5327[/C][C]5277.53336878747[/C][C]49.4666312125264[/C][/ROW]
[ROW][C]117[/C][C]5054[/C][C]4935.75969608856[/C][C]118.24030391144[/C][/ROW]
[ROW][C]118[/C][C]5269[/C][C]5258.05932793297[/C][C]10.9406720670349[/C][/ROW]
[ROW][C]119[/C][C]5019[/C][C]5060.28471980553[/C][C]-41.2847198055342[/C][/ROW]
[ROW][C]120[/C][C]5315[/C][C]5431.93492646706[/C][C]-116.934926467057[/C][/ROW]
[ROW][C]121[/C][C]5274[/C][C]5236.48281423348[/C][C]37.5171857665164[/C][/ROW]
[ROW][C]122[/C][C]4899[/C][C]4778.78421344229[/C][C]120.215786557706[/C][/ROW]
[ROW][C]123[/C][C]5216[/C][C]5290.29019516983[/C][C]-74.2901951698268[/C][/ROW]
[ROW][C]124[/C][C]5029[/C][C]4968.59864533632[/C][C]60.4013546636752[/C][/ROW]
[ROW][C]125[/C][C]5110[/C][C]5123.47373671277[/C][C]-13.4737367127718[/C][/ROW]
[ROW][C]126[/C][C]5093[/C][C]5128.10145593048[/C][C]-35.1014559304786[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302442&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302442&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
1345644625.40037393162-61.4003739316231
1441424174.04161004062-32.0416100406246
1548184825.72349912652-7.72349912651771
1644084405.426998277812.57300172218766
1744964486.045113129289.9548868707152
1845874557.1560117433829.8439882566199
1946564554.88058395356101.119416046443
2047994621.96186690657177.038133093431
2146524594.5118205710357.488179428974
2246384727.19579466574-89.1957946657394
2346504619.2720437060430.7279562939557
2451854926.68313896924258.316861030764
2552084746.39756353903461.602436460972
2644774454.2422449190722.7577550809301
2749765128.01641353868-152.016413538683
2846704668.936953920711.06304607928814
2948424751.7188763138190.2811236861853
3047134851.38379394824-138.383793948236
3148044815.38190193911-11.3819019391076
3249964865.72790456997130.272095430028
3345744801.72174483792-227.721744837918
3448414822.7447573917418.2552426082621
3546884770.53174103434-82.5317410343396
3647665090.7346096026-324.734609602605
3749944781.03962389644212.960376103556
3845144328.69840525253185.301594747471
3947665014.61044808138-248.610448081383
4046424557.3928469199984.6071530800082
4148064681.83115340725124.168846592755
4246454745.52069543845-100.52069543845
4347844745.4942054535738.5057945464268
4449794838.28976904989140.710230950108
4545304705.88513321281-175.885133212805
4649424790.75365450812151.246345491884
4746514757.17961720823-106.17961720823
4851505022.30384342285127.69615657715
4949874951.6955001556835.3044998443202
5045324442.5014299667589.4985700332527
5150465014.4382556732931.561744326712
5247834705.540784361577.4592156384979
5349584836.31086166994121.689138330055
5448154855.12344628014-40.1234462801413
5550554900.93153927475154.068460725247
5651525048.42639731328103.573602686718
5747734842.95678343256-69.9567834325599
5851475024.5495895662122.4504104338
5948664932.20242082684-66.2024208268449
6053115256.3330997015754.6669002984308
6151725146.8728045350625.1271954649355
6247344646.2525770696587.7474229303461
6350115206.90735191437-195.907351914374
6449574841.44790457393115.552095426067
6549684992.61054659915-24.6105465991541
6650494937.0176337712111.982366228803
6753055066.2157962587238.784203741304
6850675228.93437477972-161.934374779718
6950014912.0208841023288.9791158976786
7052525178.6079945725473.392005427464
7149035034.90040955224-131.900409552241
7254085364.3174444801943.6825555198138
7353955246.12472172135148.875278278653
7451504794.44543572731355.554564272694
7554605377.3960060315382.6039939684661
7649685156.07023497852-188.070234978523
7750215191.83976476369-170.839764763688
7851185121.49960448644-3.49960448644106
7951755242.80157525485-67.8015752548527
8054205236.72720249755183.272797502452
8151215070.6447391118950.3552608881109
8254505323.36661326948126.63338673052
8352865154.8441414622131.155858537802
8456935596.5609982347396.4390017652722
8553535515.5666497517-162.566649751702
8650175014.956945935422.04305406458298
8755775440.89446195776136.105538042243
8849875181.45494694973-194.45494694973
8951295218.9532500462-89.9532500461974
9052495205.684672138643.3153278614009
9151005328.12999790011-228.129997900105
9253825325.4840740387256.5159259612847
9350395096.05453704908-57.0545370490845
9453645332.5343567404331.4656432595739
9551935136.9383676923856.0616323076247
9658465549.52105535006296.478944649942
9752595475.05077895422-216.050778954217
9848094991.42412302767-182.424123027668
9952975389.94166811691-92.9416681169068
10050344997.4098766746136.5901233253899
10152435122.46233607257120.537663927426
10251505196.75470944154-46.7547094415359
10352965238.726959279457.2730407205991
10455965375.7852063669220.214793633098
10549545171.65560056347-217.655600563469
10652505379.11096377582-129.110963775815
10750095141.5816889048-132.581688904803
10851135546.76232437183-433.762324371827
10952375156.6824561595880.3175438404223
11045754765.04395506123-190.043955061235
11150265178.23573796428-152.235737964284
11248424793.2410928646148.7589071353877
11350194937.5634916492181.4365083507901
11450634966.1898785680596.810121431954
11552615069.77327456966191.226725430337
11653275277.5333687874749.4666312125264
11750544935.75969608856118.24030391144
11852695258.0593279329710.9406720670349
11950195060.28471980553-41.2847198055342
12053155431.93492646706-116.934926467057
12152745236.4828142334837.5171857665164
12248994778.78421344229120.215786557706
12352165290.29019516983-74.2901951698268
12450294968.5986453363260.4013546636752
12551105123.47373671277-13.4737367127718
12650935128.10145593048-35.1014559304786







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1275212.482435771824934.876462646015490.08840889764
1285336.570585024795047.36410540985625.77706463977
1294994.172319452324693.719272302945294.6253666017
1305260.673383103034949.288968465445572.05779774063
1315049.249695972054727.216640900455371.28275104365
1325417.832588920225085.40608806045750.25908978005
1335287.232698713654944.644368908665629.82102851865
1344835.144283061544482.605370901965187.68319522113
1355272.917472551524910.621486689035635.21345841402
1364999.640079616484627.764973742595371.51518549036
1375122.19196850054740.901968801475503.48196819953
1385126.392629111714735.839777155285516.94548106813

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 5212.48243577182 & 4934.87646264601 & 5490.08840889764 \tabularnewline
128 & 5336.57058502479 & 5047.3641054098 & 5625.77706463977 \tabularnewline
129 & 4994.17231945232 & 4693.71927230294 & 5294.6253666017 \tabularnewline
130 & 5260.67338310303 & 4949.28896846544 & 5572.05779774063 \tabularnewline
131 & 5049.24969597205 & 4727.21664090045 & 5371.28275104365 \tabularnewline
132 & 5417.83258892022 & 5085.4060880604 & 5750.25908978005 \tabularnewline
133 & 5287.23269871365 & 4944.64436890866 & 5629.82102851865 \tabularnewline
134 & 4835.14428306154 & 4482.60537090196 & 5187.68319522113 \tabularnewline
135 & 5272.91747255152 & 4910.62148668903 & 5635.21345841402 \tabularnewline
136 & 4999.64007961648 & 4627.76497374259 & 5371.51518549036 \tabularnewline
137 & 5122.1919685005 & 4740.90196880147 & 5503.48196819953 \tabularnewline
138 & 5126.39262911171 & 4735.83977715528 & 5516.94548106813 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302442&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]127[/C][C]5212.48243577182[/C][C]4934.87646264601[/C][C]5490.08840889764[/C][/ROW]
[ROW][C]128[/C][C]5336.57058502479[/C][C]5047.3641054098[/C][C]5625.77706463977[/C][/ROW]
[ROW][C]129[/C][C]4994.17231945232[/C][C]4693.71927230294[/C][C]5294.6253666017[/C][/ROW]
[ROW][C]130[/C][C]5260.67338310303[/C][C]4949.28896846544[/C][C]5572.05779774063[/C][/ROW]
[ROW][C]131[/C][C]5049.24969597205[/C][C]4727.21664090045[/C][C]5371.28275104365[/C][/ROW]
[ROW][C]132[/C][C]5417.83258892022[/C][C]5085.4060880604[/C][C]5750.25908978005[/C][/ROW]
[ROW][C]133[/C][C]5287.23269871365[/C][C]4944.64436890866[/C][C]5629.82102851865[/C][/ROW]
[ROW][C]134[/C][C]4835.14428306154[/C][C]4482.60537090196[/C][C]5187.68319522113[/C][/ROW]
[ROW][C]135[/C][C]5272.91747255152[/C][C]4910.62148668903[/C][C]5635.21345841402[/C][/ROW]
[ROW][C]136[/C][C]4999.64007961648[/C][C]4627.76497374259[/C][C]5371.51518549036[/C][/ROW]
[ROW][C]137[/C][C]5122.1919685005[/C][C]4740.90196880147[/C][C]5503.48196819953[/C][/ROW]
[ROW][C]138[/C][C]5126.39262911171[/C][C]4735.83977715528[/C][C]5516.94548106813[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302442&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302442&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
1275212.482435771824934.876462646015490.08840889764
1285336.570585024795047.36410540985625.77706463977
1294994.172319452324693.719272302945294.6253666017
1305260.673383103034949.288968465445572.05779774063
1315049.249695972054727.216640900455371.28275104365
1325417.832588920225085.40608806045750.25908978005
1335287.232698713654944.644368908665629.82102851865
1344835.144283061544482.605370901965187.68319522113
1355272.917472551524910.621486689035635.21345841402
1364999.640079616484627.764973742595371.51518549036
1375122.19196850054740.901968801475503.48196819953
1385126.392629111714735.839777155285516.94548106813



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
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')