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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 computationFri, 09 Dec 2016 17:04:27 +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/09/t1481299479nxlb64l1ymsx5ch.htm/, Retrieved Tue, 21 May 2024 00:17:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298584, Retrieved Tue, 21 May 2024 00:17:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Autocorr eerste] [2016-12-07 13:39:31] [5f979cb1c6fa86b57093c7542788c28c]
- RM D    [Exponential Smoothing] [qlfns] [2016-12-09 16:04:27] [4c05fa0998bf98e29c2e453b139976f4] [Current]
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Dataseries X:
5345
5245
5100
5070
5035
5050
5065
5255
5335
5440
5490
5445
5675
5615
5545
5510
5570
5610
5555
5630
5685
5545
5625
5570
5555
5635
5535
5430
5400
5410
5255
5350
5405
5420
5430
5580
5595
5485
5295
5055
4975
4895
4795
4855
4785
4875
5010
4970
4995
5020
4950
4880
4850
4885
4785
5025
5030
5160
5240
5175
5130
5140
5140
5055
5015
5015
4920
5095
5010
5100
5115
5060
5035
5005
4960
5035
4980
4940
4810
5025
5035
5060
5140
4955
5135
5135
5070
5070
5005
5045
4975
5080
5125
5225
5240
5090
5105
5200
5115
4990
4905
4980
4840
4960
4970
5035
5030
4965
4925
4920
4895
4890
4895
4850
4830
4870




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=298584&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=298584&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298584&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
alpha0.726926478093512
beta0.0745516379957872
gamma0.714904520368905

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.726926478093512 \tabularnewline
beta & 0.0745516379957872 \tabularnewline
gamma & 0.714904520368905 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298584&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]0.726926478093512[/C][/ROW]
[ROW][C]beta[/C][C]0.0745516379957872[/C][/ROW]
[ROW][C]gamma[/C][C]0.714904520368905[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298584&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298584&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
alpha0.726926478093512
beta0.0745516379957872
gamma0.714904520368905







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1356755433.53098290599241.469017094014
1456155559.4156272943555.584372705649
1555455549.02145015667-4.02145015666792
1655105541.33028543289-31.3302854328922
1755705616.04803890199-46.0480389019867
1856105656.73822720027-46.7382272002687
1955555456.2687884462198.7312115537907
2056305736.68719894465-106.687198944645
2156855747.20810201792-62.208102017923
2255455808.77409321518-263.774093215184
2356255650.77157127469-25.7715712746922
2455705564.382731200775.61726879922844
2555555825.13063244747-270.130632447472
2656355505.07045501575129.929544984249
2755355503.3516316198531.6483683801453
2854305484.45982259885-54.4598225988502
2954005506.4387010802-106.438701080205
3054105466.76961330978-56.7696133097825
3152555250.538254089164.46174591084309
3253505380.35020515547-30.3502051554715
3354055417.2053399649-12.2053399649039
3454205440.6390502456-20.6390502455952
3554305483.88679199355-53.8867919935492
3655805359.71012094856220.289879051444
3755955710.83327315097-115.83327315097
3854855577.55416486827-92.5541648682656
3952955379.38014655593-84.3801465559263
4050555237.50667274404-182.506672744041
4149755127.49090115386-152.490901153858
4248955032.77938081558-137.779380815584
4347954733.961003904361.0389960957027
4448554865.51798742506-10.5179874250625
4547854888.82030498477-103.820304984766
4648754807.5336396506267.4663603493846
4750104876.63501897006133.364981029938
4849704920.5477952100249.4522047899845
4949955051.05374823338-56.0537482333812
5050204938.2019010793981.7980989206144
5149504850.2410330065699.7589669934414
5248804814.9220324568365.0779675431695
5348504896.01459137273-46.0145913727256
5448854892.61863124855-7.61863124855154
5547854745.3281511130639.671848886941
5650254864.32234717692160.677652823082
5750305020.073410693499.92658930651305
5851605087.2922827020772.7077172979298
5952405205.7336873865634.2663126134394
6051755188.52204732583-13.5220473258287
6151305276.53512761719-146.535127617191
6251405143.79991417363-3.79991417363453
6351405011.4613708436128.538629156403
6450555006.1917039336948.8082960663114
6550155068.78715274483-53.7871527448251
6650155081.83300627284-66.8330062728446
6749204912.117287095667.8827129043384
6850955041.2904258401753.7095741598278
6950105093.7211050606-83.7211050605965
7051005103.91350460642-3.91350460641843
7151155153.79223955323-38.7922395532332
7250605064.82369913502-4.82369913502498
7350355124.34483182162-89.3448318216188
7450055055.29909137069-50.2990913706863
7549604906.7257881978253.2742118021752
7650354818.83189689416216.168103105835
7749804979.779155856060.22084414393612
7849405029.18727888318-89.1872788831752
7948104856.24556141783-46.2455614178325
8050254950.5222088137274.4777911862775
8150354987.8503319121547.1496680878454
8250605112.47857351078-52.4785735107844
8351405121.3353339684618.6646660315364
8449555084.9692618543-129.969261854299
8551355034.44047900229100.559520997713
8651355118.7774511417216.2225488582808
8750705050.0989115921219.9010884078807
8850704979.2556807691790.7443192308328
8950055009.58444067045-4.58444067045093
9050455040.497589181824.50241081817967
9149754951.5744136732223.4255863267845
9250805131.37026352428-51.3702635242835
9351255076.366519324648.6334806753966
9452255187.1896753181437.8103246818619
9552405285.02745896239-45.0274589623941
9650905179.35259694479-89.352596944791
9751055211.56171843622-106.561718436218
9852005125.856151903674.1438480964025
9951155100.122994041814.8770059581957
10049905039.30819882749-49.3081988274926
10149054941.479360217-36.4793602170002
10249804941.5132049351938.4867950648068
10348404873.36213255618-33.3621325561753
10449604986.57194340957-26.571943409569
10549704959.7577595542510.2422404457484
10650355029.119960206995.88003979300811
10750305074.40420893634-44.4042089363375
10849654947.3921108968417.6078891031566
10949255046.65354760155-121.653547601547
11049204977.09655801593-57.0965580159318
11148954829.1203439206665.8796560793435
11248904780.34364054903109.656359450968
11348954796.6829154201998.3170845798095
11448504912.75207104414-62.7520710441404
11548304754.9080377768675.0919622231377
11648704952.08581269249-82.0858126924904

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5675 & 5433.53098290599 & 241.469017094014 \tabularnewline
14 & 5615 & 5559.41562729435 & 55.584372705649 \tabularnewline
15 & 5545 & 5549.02145015667 & -4.02145015666792 \tabularnewline
16 & 5510 & 5541.33028543289 & -31.3302854328922 \tabularnewline
17 & 5570 & 5616.04803890199 & -46.0480389019867 \tabularnewline
18 & 5610 & 5656.73822720027 & -46.7382272002687 \tabularnewline
19 & 5555 & 5456.26878844621 & 98.7312115537907 \tabularnewline
20 & 5630 & 5736.68719894465 & -106.687198944645 \tabularnewline
21 & 5685 & 5747.20810201792 & -62.208102017923 \tabularnewline
22 & 5545 & 5808.77409321518 & -263.774093215184 \tabularnewline
23 & 5625 & 5650.77157127469 & -25.7715712746922 \tabularnewline
24 & 5570 & 5564.38273120077 & 5.61726879922844 \tabularnewline
25 & 5555 & 5825.13063244747 & -270.130632447472 \tabularnewline
26 & 5635 & 5505.07045501575 & 129.929544984249 \tabularnewline
27 & 5535 & 5503.35163161985 & 31.6483683801453 \tabularnewline
28 & 5430 & 5484.45982259885 & -54.4598225988502 \tabularnewline
29 & 5400 & 5506.4387010802 & -106.438701080205 \tabularnewline
30 & 5410 & 5466.76961330978 & -56.7696133097825 \tabularnewline
31 & 5255 & 5250.53825408916 & 4.46174591084309 \tabularnewline
32 & 5350 & 5380.35020515547 & -30.3502051554715 \tabularnewline
33 & 5405 & 5417.2053399649 & -12.2053399649039 \tabularnewline
34 & 5420 & 5440.6390502456 & -20.6390502455952 \tabularnewline
35 & 5430 & 5483.88679199355 & -53.8867919935492 \tabularnewline
36 & 5580 & 5359.71012094856 & 220.289879051444 \tabularnewline
37 & 5595 & 5710.83327315097 & -115.83327315097 \tabularnewline
38 & 5485 & 5577.55416486827 & -92.5541648682656 \tabularnewline
39 & 5295 & 5379.38014655593 & -84.3801465559263 \tabularnewline
40 & 5055 & 5237.50667274404 & -182.506672744041 \tabularnewline
41 & 4975 & 5127.49090115386 & -152.490901153858 \tabularnewline
42 & 4895 & 5032.77938081558 & -137.779380815584 \tabularnewline
43 & 4795 & 4733.9610039043 & 61.0389960957027 \tabularnewline
44 & 4855 & 4865.51798742506 & -10.5179874250625 \tabularnewline
45 & 4785 & 4888.82030498477 & -103.820304984766 \tabularnewline
46 & 4875 & 4807.53363965062 & 67.4663603493846 \tabularnewline
47 & 5010 & 4876.63501897006 & 133.364981029938 \tabularnewline
48 & 4970 & 4920.54779521002 & 49.4522047899845 \tabularnewline
49 & 4995 & 5051.05374823338 & -56.0537482333812 \tabularnewline
50 & 5020 & 4938.20190107939 & 81.7980989206144 \tabularnewline
51 & 4950 & 4850.24103300656 & 99.7589669934414 \tabularnewline
52 & 4880 & 4814.92203245683 & 65.0779675431695 \tabularnewline
53 & 4850 & 4896.01459137273 & -46.0145913727256 \tabularnewline
54 & 4885 & 4892.61863124855 & -7.61863124855154 \tabularnewline
55 & 4785 & 4745.32815111306 & 39.671848886941 \tabularnewline
56 & 5025 & 4864.32234717692 & 160.677652823082 \tabularnewline
57 & 5030 & 5020.07341069349 & 9.92658930651305 \tabularnewline
58 & 5160 & 5087.29228270207 & 72.7077172979298 \tabularnewline
59 & 5240 & 5205.73368738656 & 34.2663126134394 \tabularnewline
60 & 5175 & 5188.52204732583 & -13.5220473258287 \tabularnewline
61 & 5130 & 5276.53512761719 & -146.535127617191 \tabularnewline
62 & 5140 & 5143.79991417363 & -3.79991417363453 \tabularnewline
63 & 5140 & 5011.4613708436 & 128.538629156403 \tabularnewline
64 & 5055 & 5006.19170393369 & 48.8082960663114 \tabularnewline
65 & 5015 & 5068.78715274483 & -53.7871527448251 \tabularnewline
66 & 5015 & 5081.83300627284 & -66.8330062728446 \tabularnewline
67 & 4920 & 4912.11728709566 & 7.8827129043384 \tabularnewline
68 & 5095 & 5041.29042584017 & 53.7095741598278 \tabularnewline
69 & 5010 & 5093.7211050606 & -83.7211050605965 \tabularnewline
70 & 5100 & 5103.91350460642 & -3.91350460641843 \tabularnewline
71 & 5115 & 5153.79223955323 & -38.7922395532332 \tabularnewline
72 & 5060 & 5064.82369913502 & -4.82369913502498 \tabularnewline
73 & 5035 & 5124.34483182162 & -89.3448318216188 \tabularnewline
74 & 5005 & 5055.29909137069 & -50.2990913706863 \tabularnewline
75 & 4960 & 4906.72578819782 & 53.2742118021752 \tabularnewline
76 & 5035 & 4818.83189689416 & 216.168103105835 \tabularnewline
77 & 4980 & 4979.77915585606 & 0.22084414393612 \tabularnewline
78 & 4940 & 5029.18727888318 & -89.1872788831752 \tabularnewline
79 & 4810 & 4856.24556141783 & -46.2455614178325 \tabularnewline
80 & 5025 & 4950.52220881372 & 74.4777911862775 \tabularnewline
81 & 5035 & 4987.85033191215 & 47.1496680878454 \tabularnewline
82 & 5060 & 5112.47857351078 & -52.4785735107844 \tabularnewline
83 & 5140 & 5121.33533396846 & 18.6646660315364 \tabularnewline
84 & 4955 & 5084.9692618543 & -129.969261854299 \tabularnewline
85 & 5135 & 5034.44047900229 & 100.559520997713 \tabularnewline
86 & 5135 & 5118.77745114172 & 16.2225488582808 \tabularnewline
87 & 5070 & 5050.09891159212 & 19.9010884078807 \tabularnewline
88 & 5070 & 4979.25568076917 & 90.7443192308328 \tabularnewline
89 & 5005 & 5009.58444067045 & -4.58444067045093 \tabularnewline
90 & 5045 & 5040.49758918182 & 4.50241081817967 \tabularnewline
91 & 4975 & 4951.57441367322 & 23.4255863267845 \tabularnewline
92 & 5080 & 5131.37026352428 & -51.3702635242835 \tabularnewline
93 & 5125 & 5076.3665193246 & 48.6334806753966 \tabularnewline
94 & 5225 & 5187.18967531814 & 37.8103246818619 \tabularnewline
95 & 5240 & 5285.02745896239 & -45.0274589623941 \tabularnewline
96 & 5090 & 5179.35259694479 & -89.352596944791 \tabularnewline
97 & 5105 & 5211.56171843622 & -106.561718436218 \tabularnewline
98 & 5200 & 5125.8561519036 & 74.1438480964025 \tabularnewline
99 & 5115 & 5100.1229940418 & 14.8770059581957 \tabularnewline
100 & 4990 & 5039.30819882749 & -49.3081988274926 \tabularnewline
101 & 4905 & 4941.479360217 & -36.4793602170002 \tabularnewline
102 & 4980 & 4941.51320493519 & 38.4867950648068 \tabularnewline
103 & 4840 & 4873.36213255618 & -33.3621325561753 \tabularnewline
104 & 4960 & 4986.57194340957 & -26.571943409569 \tabularnewline
105 & 4970 & 4959.75775955425 & 10.2422404457484 \tabularnewline
106 & 5035 & 5029.11996020699 & 5.88003979300811 \tabularnewline
107 & 5030 & 5074.40420893634 & -44.4042089363375 \tabularnewline
108 & 4965 & 4947.39211089684 & 17.6078891031566 \tabularnewline
109 & 4925 & 5046.65354760155 & -121.653547601547 \tabularnewline
110 & 4920 & 4977.09655801593 & -57.0965580159318 \tabularnewline
111 & 4895 & 4829.12034392066 & 65.8796560793435 \tabularnewline
112 & 4890 & 4780.34364054903 & 109.656359450968 \tabularnewline
113 & 4895 & 4796.68291542019 & 98.3170845798095 \tabularnewline
114 & 4850 & 4912.75207104414 & -62.7520710441404 \tabularnewline
115 & 4830 & 4754.90803777686 & 75.0919622231377 \tabularnewline
116 & 4870 & 4952.08581269249 & -82.0858126924904 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298584&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]5675[/C][C]5433.53098290599[/C][C]241.469017094014[/C][/ROW]
[ROW][C]14[/C][C]5615[/C][C]5559.41562729435[/C][C]55.584372705649[/C][/ROW]
[ROW][C]15[/C][C]5545[/C][C]5549.02145015667[/C][C]-4.02145015666792[/C][/ROW]
[ROW][C]16[/C][C]5510[/C][C]5541.33028543289[/C][C]-31.3302854328922[/C][/ROW]
[ROW][C]17[/C][C]5570[/C][C]5616.04803890199[/C][C]-46.0480389019867[/C][/ROW]
[ROW][C]18[/C][C]5610[/C][C]5656.73822720027[/C][C]-46.7382272002687[/C][/ROW]
[ROW][C]19[/C][C]5555[/C][C]5456.26878844621[/C][C]98.7312115537907[/C][/ROW]
[ROW][C]20[/C][C]5630[/C][C]5736.68719894465[/C][C]-106.687198944645[/C][/ROW]
[ROW][C]21[/C][C]5685[/C][C]5747.20810201792[/C][C]-62.208102017923[/C][/ROW]
[ROW][C]22[/C][C]5545[/C][C]5808.77409321518[/C][C]-263.774093215184[/C][/ROW]
[ROW][C]23[/C][C]5625[/C][C]5650.77157127469[/C][C]-25.7715712746922[/C][/ROW]
[ROW][C]24[/C][C]5570[/C][C]5564.38273120077[/C][C]5.61726879922844[/C][/ROW]
[ROW][C]25[/C][C]5555[/C][C]5825.13063244747[/C][C]-270.130632447472[/C][/ROW]
[ROW][C]26[/C][C]5635[/C][C]5505.07045501575[/C][C]129.929544984249[/C][/ROW]
[ROW][C]27[/C][C]5535[/C][C]5503.35163161985[/C][C]31.6483683801453[/C][/ROW]
[ROW][C]28[/C][C]5430[/C][C]5484.45982259885[/C][C]-54.4598225988502[/C][/ROW]
[ROW][C]29[/C][C]5400[/C][C]5506.4387010802[/C][C]-106.438701080205[/C][/ROW]
[ROW][C]30[/C][C]5410[/C][C]5466.76961330978[/C][C]-56.7696133097825[/C][/ROW]
[ROW][C]31[/C][C]5255[/C][C]5250.53825408916[/C][C]4.46174591084309[/C][/ROW]
[ROW][C]32[/C][C]5350[/C][C]5380.35020515547[/C][C]-30.3502051554715[/C][/ROW]
[ROW][C]33[/C][C]5405[/C][C]5417.2053399649[/C][C]-12.2053399649039[/C][/ROW]
[ROW][C]34[/C][C]5420[/C][C]5440.6390502456[/C][C]-20.6390502455952[/C][/ROW]
[ROW][C]35[/C][C]5430[/C][C]5483.88679199355[/C][C]-53.8867919935492[/C][/ROW]
[ROW][C]36[/C][C]5580[/C][C]5359.71012094856[/C][C]220.289879051444[/C][/ROW]
[ROW][C]37[/C][C]5595[/C][C]5710.83327315097[/C][C]-115.83327315097[/C][/ROW]
[ROW][C]38[/C][C]5485[/C][C]5577.55416486827[/C][C]-92.5541648682656[/C][/ROW]
[ROW][C]39[/C][C]5295[/C][C]5379.38014655593[/C][C]-84.3801465559263[/C][/ROW]
[ROW][C]40[/C][C]5055[/C][C]5237.50667274404[/C][C]-182.506672744041[/C][/ROW]
[ROW][C]41[/C][C]4975[/C][C]5127.49090115386[/C][C]-152.490901153858[/C][/ROW]
[ROW][C]42[/C][C]4895[/C][C]5032.77938081558[/C][C]-137.779380815584[/C][/ROW]
[ROW][C]43[/C][C]4795[/C][C]4733.9610039043[/C][C]61.0389960957027[/C][/ROW]
[ROW][C]44[/C][C]4855[/C][C]4865.51798742506[/C][C]-10.5179874250625[/C][/ROW]
[ROW][C]45[/C][C]4785[/C][C]4888.82030498477[/C][C]-103.820304984766[/C][/ROW]
[ROW][C]46[/C][C]4875[/C][C]4807.53363965062[/C][C]67.4663603493846[/C][/ROW]
[ROW][C]47[/C][C]5010[/C][C]4876.63501897006[/C][C]133.364981029938[/C][/ROW]
[ROW][C]48[/C][C]4970[/C][C]4920.54779521002[/C][C]49.4522047899845[/C][/ROW]
[ROW][C]49[/C][C]4995[/C][C]5051.05374823338[/C][C]-56.0537482333812[/C][/ROW]
[ROW][C]50[/C][C]5020[/C][C]4938.20190107939[/C][C]81.7980989206144[/C][/ROW]
[ROW][C]51[/C][C]4950[/C][C]4850.24103300656[/C][C]99.7589669934414[/C][/ROW]
[ROW][C]52[/C][C]4880[/C][C]4814.92203245683[/C][C]65.0779675431695[/C][/ROW]
[ROW][C]53[/C][C]4850[/C][C]4896.01459137273[/C][C]-46.0145913727256[/C][/ROW]
[ROW][C]54[/C][C]4885[/C][C]4892.61863124855[/C][C]-7.61863124855154[/C][/ROW]
[ROW][C]55[/C][C]4785[/C][C]4745.32815111306[/C][C]39.671848886941[/C][/ROW]
[ROW][C]56[/C][C]5025[/C][C]4864.32234717692[/C][C]160.677652823082[/C][/ROW]
[ROW][C]57[/C][C]5030[/C][C]5020.07341069349[/C][C]9.92658930651305[/C][/ROW]
[ROW][C]58[/C][C]5160[/C][C]5087.29228270207[/C][C]72.7077172979298[/C][/ROW]
[ROW][C]59[/C][C]5240[/C][C]5205.73368738656[/C][C]34.2663126134394[/C][/ROW]
[ROW][C]60[/C][C]5175[/C][C]5188.52204732583[/C][C]-13.5220473258287[/C][/ROW]
[ROW][C]61[/C][C]5130[/C][C]5276.53512761719[/C][C]-146.535127617191[/C][/ROW]
[ROW][C]62[/C][C]5140[/C][C]5143.79991417363[/C][C]-3.79991417363453[/C][/ROW]
[ROW][C]63[/C][C]5140[/C][C]5011.4613708436[/C][C]128.538629156403[/C][/ROW]
[ROW][C]64[/C][C]5055[/C][C]5006.19170393369[/C][C]48.8082960663114[/C][/ROW]
[ROW][C]65[/C][C]5015[/C][C]5068.78715274483[/C][C]-53.7871527448251[/C][/ROW]
[ROW][C]66[/C][C]5015[/C][C]5081.83300627284[/C][C]-66.8330062728446[/C][/ROW]
[ROW][C]67[/C][C]4920[/C][C]4912.11728709566[/C][C]7.8827129043384[/C][/ROW]
[ROW][C]68[/C][C]5095[/C][C]5041.29042584017[/C][C]53.7095741598278[/C][/ROW]
[ROW][C]69[/C][C]5010[/C][C]5093.7211050606[/C][C]-83.7211050605965[/C][/ROW]
[ROW][C]70[/C][C]5100[/C][C]5103.91350460642[/C][C]-3.91350460641843[/C][/ROW]
[ROW][C]71[/C][C]5115[/C][C]5153.79223955323[/C][C]-38.7922395532332[/C][/ROW]
[ROW][C]72[/C][C]5060[/C][C]5064.82369913502[/C][C]-4.82369913502498[/C][/ROW]
[ROW][C]73[/C][C]5035[/C][C]5124.34483182162[/C][C]-89.3448318216188[/C][/ROW]
[ROW][C]74[/C][C]5005[/C][C]5055.29909137069[/C][C]-50.2990913706863[/C][/ROW]
[ROW][C]75[/C][C]4960[/C][C]4906.72578819782[/C][C]53.2742118021752[/C][/ROW]
[ROW][C]76[/C][C]5035[/C][C]4818.83189689416[/C][C]216.168103105835[/C][/ROW]
[ROW][C]77[/C][C]4980[/C][C]4979.77915585606[/C][C]0.22084414393612[/C][/ROW]
[ROW][C]78[/C][C]4940[/C][C]5029.18727888318[/C][C]-89.1872788831752[/C][/ROW]
[ROW][C]79[/C][C]4810[/C][C]4856.24556141783[/C][C]-46.2455614178325[/C][/ROW]
[ROW][C]80[/C][C]5025[/C][C]4950.52220881372[/C][C]74.4777911862775[/C][/ROW]
[ROW][C]81[/C][C]5035[/C][C]4987.85033191215[/C][C]47.1496680878454[/C][/ROW]
[ROW][C]82[/C][C]5060[/C][C]5112.47857351078[/C][C]-52.4785735107844[/C][/ROW]
[ROW][C]83[/C][C]5140[/C][C]5121.33533396846[/C][C]18.6646660315364[/C][/ROW]
[ROW][C]84[/C][C]4955[/C][C]5084.9692618543[/C][C]-129.969261854299[/C][/ROW]
[ROW][C]85[/C][C]5135[/C][C]5034.44047900229[/C][C]100.559520997713[/C][/ROW]
[ROW][C]86[/C][C]5135[/C][C]5118.77745114172[/C][C]16.2225488582808[/C][/ROW]
[ROW][C]87[/C][C]5070[/C][C]5050.09891159212[/C][C]19.9010884078807[/C][/ROW]
[ROW][C]88[/C][C]5070[/C][C]4979.25568076917[/C][C]90.7443192308328[/C][/ROW]
[ROW][C]89[/C][C]5005[/C][C]5009.58444067045[/C][C]-4.58444067045093[/C][/ROW]
[ROW][C]90[/C][C]5045[/C][C]5040.49758918182[/C][C]4.50241081817967[/C][/ROW]
[ROW][C]91[/C][C]4975[/C][C]4951.57441367322[/C][C]23.4255863267845[/C][/ROW]
[ROW][C]92[/C][C]5080[/C][C]5131.37026352428[/C][C]-51.3702635242835[/C][/ROW]
[ROW][C]93[/C][C]5125[/C][C]5076.3665193246[/C][C]48.6334806753966[/C][/ROW]
[ROW][C]94[/C][C]5225[/C][C]5187.18967531814[/C][C]37.8103246818619[/C][/ROW]
[ROW][C]95[/C][C]5240[/C][C]5285.02745896239[/C][C]-45.0274589623941[/C][/ROW]
[ROW][C]96[/C][C]5090[/C][C]5179.35259694479[/C][C]-89.352596944791[/C][/ROW]
[ROW][C]97[/C][C]5105[/C][C]5211.56171843622[/C][C]-106.561718436218[/C][/ROW]
[ROW][C]98[/C][C]5200[/C][C]5125.8561519036[/C][C]74.1438480964025[/C][/ROW]
[ROW][C]99[/C][C]5115[/C][C]5100.1229940418[/C][C]14.8770059581957[/C][/ROW]
[ROW][C]100[/C][C]4990[/C][C]5039.30819882749[/C][C]-49.3081988274926[/C][/ROW]
[ROW][C]101[/C][C]4905[/C][C]4941.479360217[/C][C]-36.4793602170002[/C][/ROW]
[ROW][C]102[/C][C]4980[/C][C]4941.51320493519[/C][C]38.4867950648068[/C][/ROW]
[ROW][C]103[/C][C]4840[/C][C]4873.36213255618[/C][C]-33.3621325561753[/C][/ROW]
[ROW][C]104[/C][C]4960[/C][C]4986.57194340957[/C][C]-26.571943409569[/C][/ROW]
[ROW][C]105[/C][C]4970[/C][C]4959.75775955425[/C][C]10.2422404457484[/C][/ROW]
[ROW][C]106[/C][C]5035[/C][C]5029.11996020699[/C][C]5.88003979300811[/C][/ROW]
[ROW][C]107[/C][C]5030[/C][C]5074.40420893634[/C][C]-44.4042089363375[/C][/ROW]
[ROW][C]108[/C][C]4965[/C][C]4947.39211089684[/C][C]17.6078891031566[/C][/ROW]
[ROW][C]109[/C][C]4925[/C][C]5046.65354760155[/C][C]-121.653547601547[/C][/ROW]
[ROW][C]110[/C][C]4920[/C][C]4977.09655801593[/C][C]-57.0965580159318[/C][/ROW]
[ROW][C]111[/C][C]4895[/C][C]4829.12034392066[/C][C]65.8796560793435[/C][/ROW]
[ROW][C]112[/C][C]4890[/C][C]4780.34364054903[/C][C]109.656359450968[/C][/ROW]
[ROW][C]113[/C][C]4895[/C][C]4796.68291542019[/C][C]98.3170845798095[/C][/ROW]
[ROW][C]114[/C][C]4850[/C][C]4912.75207104414[/C][C]-62.7520710441404[/C][/ROW]
[ROW][C]115[/C][C]4830[/C][C]4754.90803777686[/C][C]75.0919622231377[/C][/ROW]
[ROW][C]116[/C][C]4870[/C][C]4952.08581269249[/C][C]-82.0858126924904[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298584&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298584&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
1356755433.53098290599241.469017094014
1456155559.4156272943555.584372705649
1555455549.02145015667-4.02145015666792
1655105541.33028543289-31.3302854328922
1755705616.04803890199-46.0480389019867
1856105656.73822720027-46.7382272002687
1955555456.2687884462198.7312115537907
2056305736.68719894465-106.687198944645
2156855747.20810201792-62.208102017923
2255455808.77409321518-263.774093215184
2356255650.77157127469-25.7715712746922
2455705564.382731200775.61726879922844
2555555825.13063244747-270.130632447472
2656355505.07045501575129.929544984249
2755355503.3516316198531.6483683801453
2854305484.45982259885-54.4598225988502
2954005506.4387010802-106.438701080205
3054105466.76961330978-56.7696133097825
3152555250.538254089164.46174591084309
3253505380.35020515547-30.3502051554715
3354055417.2053399649-12.2053399649039
3454205440.6390502456-20.6390502455952
3554305483.88679199355-53.8867919935492
3655805359.71012094856220.289879051444
3755955710.83327315097-115.83327315097
3854855577.55416486827-92.5541648682656
3952955379.38014655593-84.3801465559263
4050555237.50667274404-182.506672744041
4149755127.49090115386-152.490901153858
4248955032.77938081558-137.779380815584
4347954733.961003904361.0389960957027
4448554865.51798742506-10.5179874250625
4547854888.82030498477-103.820304984766
4648754807.5336396506267.4663603493846
4750104876.63501897006133.364981029938
4849704920.5477952100249.4522047899845
4949955051.05374823338-56.0537482333812
5050204938.2019010793981.7980989206144
5149504850.2410330065699.7589669934414
5248804814.9220324568365.0779675431695
5348504896.01459137273-46.0145913727256
5448854892.61863124855-7.61863124855154
5547854745.3281511130639.671848886941
5650254864.32234717692160.677652823082
5750305020.073410693499.92658930651305
5851605087.2922827020772.7077172979298
5952405205.7336873865634.2663126134394
6051755188.52204732583-13.5220473258287
6151305276.53512761719-146.535127617191
6251405143.79991417363-3.79991417363453
6351405011.4613708436128.538629156403
6450555006.1917039336948.8082960663114
6550155068.78715274483-53.7871527448251
6650155081.83300627284-66.8330062728446
6749204912.117287095667.8827129043384
6850955041.2904258401753.7095741598278
6950105093.7211050606-83.7211050605965
7051005103.91350460642-3.91350460641843
7151155153.79223955323-38.7922395532332
7250605064.82369913502-4.82369913502498
7350355124.34483182162-89.3448318216188
7450055055.29909137069-50.2990913706863
7549604906.7257881978253.2742118021752
7650354818.83189689416216.168103105835
7749804979.779155856060.22084414393612
7849405029.18727888318-89.1872788831752
7948104856.24556141783-46.2455614178325
8050254950.5222088137274.4777911862775
8150354987.8503319121547.1496680878454
8250605112.47857351078-52.4785735107844
8351405121.3353339684618.6646660315364
8449555084.9692618543-129.969261854299
8551355034.44047900229100.559520997713
8651355118.7774511417216.2225488582808
8750705050.0989115921219.9010884078807
8850704979.2556807691790.7443192308328
8950055009.58444067045-4.58444067045093
9050455040.497589181824.50241081817967
9149754951.5744136732223.4255863267845
9250805131.37026352428-51.3702635242835
9351255076.366519324648.6334806753966
9452255187.1896753181437.8103246818619
9552405285.02745896239-45.0274589623941
9650905179.35259694479-89.352596944791
9751055211.56171843622-106.561718436218
9852005125.856151903674.1438480964025
9951155100.122994041814.8770059581957
10049905039.30819882749-49.3081988274926
10149054941.479360217-36.4793602170002
10249804941.5132049351938.4867950648068
10348404873.36213255618-33.3621325561753
10449604986.57194340957-26.571943409569
10549704959.7577595542510.2422404457484
10650355029.119960206995.88003979300811
10750305074.40420893634-44.4042089363375
10849654947.3921108968417.6078891031566
10949255046.65354760155-121.653547601547
11049204977.09655801593-57.0965580159318
11148954829.1203439206665.8796560793435
11248904780.34364054903109.656359450968
11348954796.6829154201998.3170845798095
11448504912.75207104414-62.7520710441404
11548304754.9080377768675.0919622231377
11648704952.08581269249-82.0858126924904







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174892.899773216444719.829284127915065.97026230497
1184954.205685137374734.593724783735173.817645491
1194985.321013116554722.396388625865248.24563760725
1204905.022029026914600.343227581395209.70083047244
1214965.671189068354619.976529653695311.36584848301
1225005.117325255884618.682107640435391.55254287133
1234933.715005937714506.529736523315360.90027535212
1244853.085831167674384.955538109635321.2161242257
1254789.047697697444279.651711462115298.44368393277
1264798.423620141724247.353664778375349.49357550507
1274712.726825498474119.512371215345305.9412797816
1284820.185262164134184.310987838795456.05953648946

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 4892.89977321644 & 4719.82928412791 & 5065.97026230497 \tabularnewline
118 & 4954.20568513737 & 4734.59372478373 & 5173.817645491 \tabularnewline
119 & 4985.32101311655 & 4722.39638862586 & 5248.24563760725 \tabularnewline
120 & 4905.02202902691 & 4600.34322758139 & 5209.70083047244 \tabularnewline
121 & 4965.67118906835 & 4619.97652965369 & 5311.36584848301 \tabularnewline
122 & 5005.11732525588 & 4618.68210764043 & 5391.55254287133 \tabularnewline
123 & 4933.71500593771 & 4506.52973652331 & 5360.90027535212 \tabularnewline
124 & 4853.08583116767 & 4384.95553810963 & 5321.2161242257 \tabularnewline
125 & 4789.04769769744 & 4279.65171146211 & 5298.44368393277 \tabularnewline
126 & 4798.42362014172 & 4247.35366477837 & 5349.49357550507 \tabularnewline
127 & 4712.72682549847 & 4119.51237121534 & 5305.9412797816 \tabularnewline
128 & 4820.18526216413 & 4184.31098783879 & 5456.05953648946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298584&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]117[/C][C]4892.89977321644[/C][C]4719.82928412791[/C][C]5065.97026230497[/C][/ROW]
[ROW][C]118[/C][C]4954.20568513737[/C][C]4734.59372478373[/C][C]5173.817645491[/C][/ROW]
[ROW][C]119[/C][C]4985.32101311655[/C][C]4722.39638862586[/C][C]5248.24563760725[/C][/ROW]
[ROW][C]120[/C][C]4905.02202902691[/C][C]4600.34322758139[/C][C]5209.70083047244[/C][/ROW]
[ROW][C]121[/C][C]4965.67118906835[/C][C]4619.97652965369[/C][C]5311.36584848301[/C][/ROW]
[ROW][C]122[/C][C]5005.11732525588[/C][C]4618.68210764043[/C][C]5391.55254287133[/C][/ROW]
[ROW][C]123[/C][C]4933.71500593771[/C][C]4506.52973652331[/C][C]5360.90027535212[/C][/ROW]
[ROW][C]124[/C][C]4853.08583116767[/C][C]4384.95553810963[/C][C]5321.2161242257[/C][/ROW]
[ROW][C]125[/C][C]4789.04769769744[/C][C]4279.65171146211[/C][C]5298.44368393277[/C][/ROW]
[ROW][C]126[/C][C]4798.42362014172[/C][C]4247.35366477837[/C][C]5349.49357550507[/C][/ROW]
[ROW][C]127[/C][C]4712.72682549847[/C][C]4119.51237121534[/C][C]5305.9412797816[/C][/ROW]
[ROW][C]128[/C][C]4820.18526216413[/C][C]4184.31098783879[/C][C]5456.05953648946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298584&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298584&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
1174892.899773216444719.829284127915065.97026230497
1184954.205685137374734.593724783735173.817645491
1194985.321013116554722.396388625865248.24563760725
1204905.022029026914600.343227581395209.70083047244
1214965.671189068354619.976529653695311.36584848301
1225005.117325255884618.682107640435391.55254287133
1234933.715005937714506.529736523315360.90027535212
1244853.085831167674384.955538109635321.2161242257
1254789.047697697444279.651711462115298.44368393277
1264798.423620141724247.353664778375349.49357550507
1274712.726825498474119.512371215345305.9412797816
1284820.185262164134184.310987838795456.05953648946



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;
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')