Free Statistics

of Irreproducible Research!

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 17:44:56 +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/t14823388213glsdyh0fcb4hmj.htm/, Retrieved Mon, 06 May 2024 18:28:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302421, Retrieved Mon, 06 May 2024 18:28:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N1993 Exponential...] [2016-12-21 16:44:56] [1eb03b74c4069f30e782d39ada1a3213] [Current]
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Dataseries X:
6970
6455
8005
8115
8180
7930
7275
7865
7610
7435
8480
8850
8345
8275
8595
8430
8395
7735
7890
8435
7620
7610
8005
8935
8320
7670
8660
8485
8160
7910
7725
7555
7685
7740
7455
7850
6930
6600
7290
7625
7755
6915
6145
5985
6100
5955
5800
5905
5705
5430
6435
6025
5815
5160
4985
5585
5790
6190
6300
6340
6610
6685
7450
7410
7255
6460
6035
6745
6655
7070
7415
7720
7815
7260
7925
7825
7805
7530
7015
6575
6640
7075
6405
6720
6385
6085
6475
6555
6500
5790
5195
5680
5745
6010
5705
6310
6870
6260
7210
7090
7055
6535
6320
6010
6165
6985
6760
7220
6995
6475
7225
7325
7515
6925
7165
6895
6400
6685
6955
7550
7645
6710
7470
7355
7525
7165




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=302421&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=302421&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302421&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
alpha0.617109375237329
beta0.00560029986365413
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.617109375237329 \tabularnewline
beta & 0.00560029986365413 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302421&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]0.617109375237329[/C][/ROW]
[ROW][C]beta[/C][C]0.00560029986365413[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302421&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302421&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
alpha0.617109375237329
beta0.00560029986365413
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1383458160.94017094017184.059829059826
1482758184.2391245786590.7608754213452
1585958565.4844219234229.5155780765763
1684308440.49501118639-10.4950111863873
1783958440.98675330679-45.9867533067918
1877357798.16727851443-63.1672785144301
1978907692.44390125181197.556098748187
2084358301.00645116809133.993548831908
2176208058.51537032685-438.515370326852
2276107603.91649335366.08350664639875
2380058659.3297761646-654.329776164597
2489358651.18446851835283.815531481654
2583208401.76640761272-81.7664076127203
2676708223.38864257936-553.388642579361
2786608179.53724280232480.462757197683
2884858314.93461651909170.065383480909
2981608411.3091639538-251.309163953802
3079107632.54219710915277.457802890854
3177257835.36464181464-110.364641814638
3275558227.01909210726-672.019092107257
3376857262.58635918804422.413640811961
3477407507.14755967292232.852440327079
3574558448.05970739048-993.059707390485
3678508587.34106103837-737.341061038369
3769307561.50371612381-631.503716123809
3866006855.12220098319-255.122200983188
3972907384.04066418863-94.0406641886284
4076257036.92770088052588.072299119483
4177557222.23185678543532.768143214566
4269157124.81001628878-209.810016288783
4361456871.78110188207-726.781101882074
4459856659.1963769727-674.196376972696
4561006103.66995405695-3.66995405694888
4659556002.43912320736-47.4391232073604
4758006289.75112034568-489.751120345682
4859056828.04129642683-923.041296426829
4957055717.98904529453-12.9890452945301
5054305529.40759381953-99.4075938195265
5164356208.62966862264226.370331377358
5260256314.06139029744-289.061390297439
5358155927.51270544886-112.512705448863
5451605135.9357242501224.0642757498808
5549854818.47765121727166.522348782734
5655855169.56851843228415.431481567719
5757905539.24115435498250.758845645025
5861905575.18243274222614.817567257781
5963006101.03139908734198.968600912663
6063406900.02371314535-560.023713145345
6166106365.28756621393244.71243378607
6266856306.38195231577378.618047684231
6374507410.7221917125939.2778082874147
6474107208.08354442116201.916455578842
6572557198.5577007757656.4422992242353
6664606570.55936393206-110.559363932056
6760356231.12526365864-196.125263658643
6867456459.03017577942285.969824220583
6966556690.61409468865-35.6140946886526
7070706693.09180788911376.908192110892
7174156915.9429733646499.0570266354
7277207613.59170740183106.408292598167
7378157804.6261930049710.3738069950268
7472607657.95261374279-397.952613742794
7579258156.02318890996-231.023188909964
7678257850.80748354091-25.8074835409143
7778057646.21876626654158.781233733458
7875307018.95345210612511.046547893876
7970157034.02615331526-19.0261533152552
8065757560.09267665617-985.092676656174
8166406884.050153736-244.050153736002
8270756915.02019397165159.979806028349
8364057049.19201532443-644.192015324428
8467206885.45801548012-165.458015480118
8563856865.47946730174-480.479467301743
8660856251.3839024844-166.3839024844
8764756948.90624326776-473.906243267756
8865556564.17372548879-9.17372548879484
8965006432.3780596429167.621940357094
9057905875.27244493422-85.2724449342222
9151955308.86622813642-113.866228136417
9256805395.65546124142284.344538758576
9357455780.26717548057-35.2671754805706
9460106089.03438184105-79.0343818410547
9557055761.22837263932-56.2283726393225
9663106139.09692688755170.903073112452
9768706202.69558013849667.304419861507
9862606417.76357888144-157.763578881438
9972107003.4790918014206.5209081986
10070907219.55873782135-129.558737821351
10170557045.433107777189.56689222282148
10265356396.31512884937138.684871150632
10363205960.29655285288359.703447147123
10460106496.56767027161-486.567670271612
10561656285.16806172565-120.168061725652
10669856526.59282281484458.407177185162
10767606542.84538273719217.15461726281
10872207180.9985924901439.0014075098607
10969957357.42200948348-362.422009483479
11064756621.72173762601-146.721737626008
11172257354.36691411874-129.366914118737
11273257233.9589877977491.0410122022577
11375157249.47352074561265.526479254395
11469256808.86935165164116.130648348361
11571656444.6010319964720.398968003597
11668956881.7207609473713.279239052632
11764007123.08911192442-723.089111924416
11866857215.9097520011-530.909752001103
11969556527.78621645822427.213783541779
12075507226.59567726557323.404322734429
12176457425.048396415219.951603585003
12267107133.56149445898-423.561494458982
12374707703.29004479872-233.290044798721
12473557604.06193476948-249.061934769483
12575257476.2488310620548.7511689379462
12671656843.66337865314321.336621346863

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8345 & 8160.94017094017 & 184.059829059826 \tabularnewline
14 & 8275 & 8184.23912457865 & 90.7608754213452 \tabularnewline
15 & 8595 & 8565.48442192342 & 29.5155780765763 \tabularnewline
16 & 8430 & 8440.49501118639 & -10.4950111863873 \tabularnewline
17 & 8395 & 8440.98675330679 & -45.9867533067918 \tabularnewline
18 & 7735 & 7798.16727851443 & -63.1672785144301 \tabularnewline
19 & 7890 & 7692.44390125181 & 197.556098748187 \tabularnewline
20 & 8435 & 8301.00645116809 & 133.993548831908 \tabularnewline
21 & 7620 & 8058.51537032685 & -438.515370326852 \tabularnewline
22 & 7610 & 7603.9164933536 & 6.08350664639875 \tabularnewline
23 & 8005 & 8659.3297761646 & -654.329776164597 \tabularnewline
24 & 8935 & 8651.18446851835 & 283.815531481654 \tabularnewline
25 & 8320 & 8401.76640761272 & -81.7664076127203 \tabularnewline
26 & 7670 & 8223.38864257936 & -553.388642579361 \tabularnewline
27 & 8660 & 8179.53724280232 & 480.462757197683 \tabularnewline
28 & 8485 & 8314.93461651909 & 170.065383480909 \tabularnewline
29 & 8160 & 8411.3091639538 & -251.309163953802 \tabularnewline
30 & 7910 & 7632.54219710915 & 277.457802890854 \tabularnewline
31 & 7725 & 7835.36464181464 & -110.364641814638 \tabularnewline
32 & 7555 & 8227.01909210726 & -672.019092107257 \tabularnewline
33 & 7685 & 7262.58635918804 & 422.413640811961 \tabularnewline
34 & 7740 & 7507.14755967292 & 232.852440327079 \tabularnewline
35 & 7455 & 8448.05970739048 & -993.059707390485 \tabularnewline
36 & 7850 & 8587.34106103837 & -737.341061038369 \tabularnewline
37 & 6930 & 7561.50371612381 & -631.503716123809 \tabularnewline
38 & 6600 & 6855.12220098319 & -255.122200983188 \tabularnewline
39 & 7290 & 7384.04066418863 & -94.0406641886284 \tabularnewline
40 & 7625 & 7036.92770088052 & 588.072299119483 \tabularnewline
41 & 7755 & 7222.23185678543 & 532.768143214566 \tabularnewline
42 & 6915 & 7124.81001628878 & -209.810016288783 \tabularnewline
43 & 6145 & 6871.78110188207 & -726.781101882074 \tabularnewline
44 & 5985 & 6659.1963769727 & -674.196376972696 \tabularnewline
45 & 6100 & 6103.66995405695 & -3.66995405694888 \tabularnewline
46 & 5955 & 6002.43912320736 & -47.4391232073604 \tabularnewline
47 & 5800 & 6289.75112034568 & -489.751120345682 \tabularnewline
48 & 5905 & 6828.04129642683 & -923.041296426829 \tabularnewline
49 & 5705 & 5717.98904529453 & -12.9890452945301 \tabularnewline
50 & 5430 & 5529.40759381953 & -99.4075938195265 \tabularnewline
51 & 6435 & 6208.62966862264 & 226.370331377358 \tabularnewline
52 & 6025 & 6314.06139029744 & -289.061390297439 \tabularnewline
53 & 5815 & 5927.51270544886 & -112.512705448863 \tabularnewline
54 & 5160 & 5135.93572425012 & 24.0642757498808 \tabularnewline
55 & 4985 & 4818.47765121727 & 166.522348782734 \tabularnewline
56 & 5585 & 5169.56851843228 & 415.431481567719 \tabularnewline
57 & 5790 & 5539.24115435498 & 250.758845645025 \tabularnewline
58 & 6190 & 5575.18243274222 & 614.817567257781 \tabularnewline
59 & 6300 & 6101.03139908734 & 198.968600912663 \tabularnewline
60 & 6340 & 6900.02371314535 & -560.023713145345 \tabularnewline
61 & 6610 & 6365.28756621393 & 244.71243378607 \tabularnewline
62 & 6685 & 6306.38195231577 & 378.618047684231 \tabularnewline
63 & 7450 & 7410.72219171259 & 39.2778082874147 \tabularnewline
64 & 7410 & 7208.08354442116 & 201.916455578842 \tabularnewline
65 & 7255 & 7198.55770077576 & 56.4422992242353 \tabularnewline
66 & 6460 & 6570.55936393206 & -110.559363932056 \tabularnewline
67 & 6035 & 6231.12526365864 & -196.125263658643 \tabularnewline
68 & 6745 & 6459.03017577942 & 285.969824220583 \tabularnewline
69 & 6655 & 6690.61409468865 & -35.6140946886526 \tabularnewline
70 & 7070 & 6693.09180788911 & 376.908192110892 \tabularnewline
71 & 7415 & 6915.9429733646 & 499.0570266354 \tabularnewline
72 & 7720 & 7613.59170740183 & 106.408292598167 \tabularnewline
73 & 7815 & 7804.62619300497 & 10.3738069950268 \tabularnewline
74 & 7260 & 7657.95261374279 & -397.952613742794 \tabularnewline
75 & 7925 & 8156.02318890996 & -231.023188909964 \tabularnewline
76 & 7825 & 7850.80748354091 & -25.8074835409143 \tabularnewline
77 & 7805 & 7646.21876626654 & 158.781233733458 \tabularnewline
78 & 7530 & 7018.95345210612 & 511.046547893876 \tabularnewline
79 & 7015 & 7034.02615331526 & -19.0261533152552 \tabularnewline
80 & 6575 & 7560.09267665617 & -985.092676656174 \tabularnewline
81 & 6640 & 6884.050153736 & -244.050153736002 \tabularnewline
82 & 7075 & 6915.02019397165 & 159.979806028349 \tabularnewline
83 & 6405 & 7049.19201532443 & -644.192015324428 \tabularnewline
84 & 6720 & 6885.45801548012 & -165.458015480118 \tabularnewline
85 & 6385 & 6865.47946730174 & -480.479467301743 \tabularnewline
86 & 6085 & 6251.3839024844 & -166.3839024844 \tabularnewline
87 & 6475 & 6948.90624326776 & -473.906243267756 \tabularnewline
88 & 6555 & 6564.17372548879 & -9.17372548879484 \tabularnewline
89 & 6500 & 6432.37805964291 & 67.621940357094 \tabularnewline
90 & 5790 & 5875.27244493422 & -85.2724449342222 \tabularnewline
91 & 5195 & 5308.86622813642 & -113.866228136417 \tabularnewline
92 & 5680 & 5395.65546124142 & 284.344538758576 \tabularnewline
93 & 5745 & 5780.26717548057 & -35.2671754805706 \tabularnewline
94 & 6010 & 6089.03438184105 & -79.0343818410547 \tabularnewline
95 & 5705 & 5761.22837263932 & -56.2283726393225 \tabularnewline
96 & 6310 & 6139.09692688755 & 170.903073112452 \tabularnewline
97 & 6870 & 6202.69558013849 & 667.304419861507 \tabularnewline
98 & 6260 & 6417.76357888144 & -157.763578881438 \tabularnewline
99 & 7210 & 7003.4790918014 & 206.5209081986 \tabularnewline
100 & 7090 & 7219.55873782135 & -129.558737821351 \tabularnewline
101 & 7055 & 7045.43310777718 & 9.56689222282148 \tabularnewline
102 & 6535 & 6396.31512884937 & 138.684871150632 \tabularnewline
103 & 6320 & 5960.29655285288 & 359.703447147123 \tabularnewline
104 & 6010 & 6496.56767027161 & -486.567670271612 \tabularnewline
105 & 6165 & 6285.16806172565 & -120.168061725652 \tabularnewline
106 & 6985 & 6526.59282281484 & 458.407177185162 \tabularnewline
107 & 6760 & 6542.84538273719 & 217.15461726281 \tabularnewline
108 & 7220 & 7180.99859249014 & 39.0014075098607 \tabularnewline
109 & 6995 & 7357.42200948348 & -362.422009483479 \tabularnewline
110 & 6475 & 6621.72173762601 & -146.721737626008 \tabularnewline
111 & 7225 & 7354.36691411874 & -129.366914118737 \tabularnewline
112 & 7325 & 7233.95898779774 & 91.0410122022577 \tabularnewline
113 & 7515 & 7249.47352074561 & 265.526479254395 \tabularnewline
114 & 6925 & 6808.86935165164 & 116.130648348361 \tabularnewline
115 & 7165 & 6444.6010319964 & 720.398968003597 \tabularnewline
116 & 6895 & 6881.72076094737 & 13.279239052632 \tabularnewline
117 & 6400 & 7123.08911192442 & -723.089111924416 \tabularnewline
118 & 6685 & 7215.9097520011 & -530.909752001103 \tabularnewline
119 & 6955 & 6527.78621645822 & 427.213783541779 \tabularnewline
120 & 7550 & 7226.59567726557 & 323.404322734429 \tabularnewline
121 & 7645 & 7425.048396415 & 219.951603585003 \tabularnewline
122 & 6710 & 7133.56149445898 & -423.561494458982 \tabularnewline
123 & 7470 & 7703.29004479872 & -233.290044798721 \tabularnewline
124 & 7355 & 7604.06193476948 & -249.061934769483 \tabularnewline
125 & 7525 & 7476.24883106205 & 48.7511689379462 \tabularnewline
126 & 7165 & 6843.66337865314 & 321.336621346863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302421&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]8345[/C][C]8160.94017094017[/C][C]184.059829059826[/C][/ROW]
[ROW][C]14[/C][C]8275[/C][C]8184.23912457865[/C][C]90.7608754213452[/C][/ROW]
[ROW][C]15[/C][C]8595[/C][C]8565.48442192342[/C][C]29.5155780765763[/C][/ROW]
[ROW][C]16[/C][C]8430[/C][C]8440.49501118639[/C][C]-10.4950111863873[/C][/ROW]
[ROW][C]17[/C][C]8395[/C][C]8440.98675330679[/C][C]-45.9867533067918[/C][/ROW]
[ROW][C]18[/C][C]7735[/C][C]7798.16727851443[/C][C]-63.1672785144301[/C][/ROW]
[ROW][C]19[/C][C]7890[/C][C]7692.44390125181[/C][C]197.556098748187[/C][/ROW]
[ROW][C]20[/C][C]8435[/C][C]8301.00645116809[/C][C]133.993548831908[/C][/ROW]
[ROW][C]21[/C][C]7620[/C][C]8058.51537032685[/C][C]-438.515370326852[/C][/ROW]
[ROW][C]22[/C][C]7610[/C][C]7603.9164933536[/C][C]6.08350664639875[/C][/ROW]
[ROW][C]23[/C][C]8005[/C][C]8659.3297761646[/C][C]-654.329776164597[/C][/ROW]
[ROW][C]24[/C][C]8935[/C][C]8651.18446851835[/C][C]283.815531481654[/C][/ROW]
[ROW][C]25[/C][C]8320[/C][C]8401.76640761272[/C][C]-81.7664076127203[/C][/ROW]
[ROW][C]26[/C][C]7670[/C][C]8223.38864257936[/C][C]-553.388642579361[/C][/ROW]
[ROW][C]27[/C][C]8660[/C][C]8179.53724280232[/C][C]480.462757197683[/C][/ROW]
[ROW][C]28[/C][C]8485[/C][C]8314.93461651909[/C][C]170.065383480909[/C][/ROW]
[ROW][C]29[/C][C]8160[/C][C]8411.3091639538[/C][C]-251.309163953802[/C][/ROW]
[ROW][C]30[/C][C]7910[/C][C]7632.54219710915[/C][C]277.457802890854[/C][/ROW]
[ROW][C]31[/C][C]7725[/C][C]7835.36464181464[/C][C]-110.364641814638[/C][/ROW]
[ROW][C]32[/C][C]7555[/C][C]8227.01909210726[/C][C]-672.019092107257[/C][/ROW]
[ROW][C]33[/C][C]7685[/C][C]7262.58635918804[/C][C]422.413640811961[/C][/ROW]
[ROW][C]34[/C][C]7740[/C][C]7507.14755967292[/C][C]232.852440327079[/C][/ROW]
[ROW][C]35[/C][C]7455[/C][C]8448.05970739048[/C][C]-993.059707390485[/C][/ROW]
[ROW][C]36[/C][C]7850[/C][C]8587.34106103837[/C][C]-737.341061038369[/C][/ROW]
[ROW][C]37[/C][C]6930[/C][C]7561.50371612381[/C][C]-631.503716123809[/C][/ROW]
[ROW][C]38[/C][C]6600[/C][C]6855.12220098319[/C][C]-255.122200983188[/C][/ROW]
[ROW][C]39[/C][C]7290[/C][C]7384.04066418863[/C][C]-94.0406641886284[/C][/ROW]
[ROW][C]40[/C][C]7625[/C][C]7036.92770088052[/C][C]588.072299119483[/C][/ROW]
[ROW][C]41[/C][C]7755[/C][C]7222.23185678543[/C][C]532.768143214566[/C][/ROW]
[ROW][C]42[/C][C]6915[/C][C]7124.81001628878[/C][C]-209.810016288783[/C][/ROW]
[ROW][C]43[/C][C]6145[/C][C]6871.78110188207[/C][C]-726.781101882074[/C][/ROW]
[ROW][C]44[/C][C]5985[/C][C]6659.1963769727[/C][C]-674.196376972696[/C][/ROW]
[ROW][C]45[/C][C]6100[/C][C]6103.66995405695[/C][C]-3.66995405694888[/C][/ROW]
[ROW][C]46[/C][C]5955[/C][C]6002.43912320736[/C][C]-47.4391232073604[/C][/ROW]
[ROW][C]47[/C][C]5800[/C][C]6289.75112034568[/C][C]-489.751120345682[/C][/ROW]
[ROW][C]48[/C][C]5905[/C][C]6828.04129642683[/C][C]-923.041296426829[/C][/ROW]
[ROW][C]49[/C][C]5705[/C][C]5717.98904529453[/C][C]-12.9890452945301[/C][/ROW]
[ROW][C]50[/C][C]5430[/C][C]5529.40759381953[/C][C]-99.4075938195265[/C][/ROW]
[ROW][C]51[/C][C]6435[/C][C]6208.62966862264[/C][C]226.370331377358[/C][/ROW]
[ROW][C]52[/C][C]6025[/C][C]6314.06139029744[/C][C]-289.061390297439[/C][/ROW]
[ROW][C]53[/C][C]5815[/C][C]5927.51270544886[/C][C]-112.512705448863[/C][/ROW]
[ROW][C]54[/C][C]5160[/C][C]5135.93572425012[/C][C]24.0642757498808[/C][/ROW]
[ROW][C]55[/C][C]4985[/C][C]4818.47765121727[/C][C]166.522348782734[/C][/ROW]
[ROW][C]56[/C][C]5585[/C][C]5169.56851843228[/C][C]415.431481567719[/C][/ROW]
[ROW][C]57[/C][C]5790[/C][C]5539.24115435498[/C][C]250.758845645025[/C][/ROW]
[ROW][C]58[/C][C]6190[/C][C]5575.18243274222[/C][C]614.817567257781[/C][/ROW]
[ROW][C]59[/C][C]6300[/C][C]6101.03139908734[/C][C]198.968600912663[/C][/ROW]
[ROW][C]60[/C][C]6340[/C][C]6900.02371314535[/C][C]-560.023713145345[/C][/ROW]
[ROW][C]61[/C][C]6610[/C][C]6365.28756621393[/C][C]244.71243378607[/C][/ROW]
[ROW][C]62[/C][C]6685[/C][C]6306.38195231577[/C][C]378.618047684231[/C][/ROW]
[ROW][C]63[/C][C]7450[/C][C]7410.72219171259[/C][C]39.2778082874147[/C][/ROW]
[ROW][C]64[/C][C]7410[/C][C]7208.08354442116[/C][C]201.916455578842[/C][/ROW]
[ROW][C]65[/C][C]7255[/C][C]7198.55770077576[/C][C]56.4422992242353[/C][/ROW]
[ROW][C]66[/C][C]6460[/C][C]6570.55936393206[/C][C]-110.559363932056[/C][/ROW]
[ROW][C]67[/C][C]6035[/C][C]6231.12526365864[/C][C]-196.125263658643[/C][/ROW]
[ROW][C]68[/C][C]6745[/C][C]6459.03017577942[/C][C]285.969824220583[/C][/ROW]
[ROW][C]69[/C][C]6655[/C][C]6690.61409468865[/C][C]-35.6140946886526[/C][/ROW]
[ROW][C]70[/C][C]7070[/C][C]6693.09180788911[/C][C]376.908192110892[/C][/ROW]
[ROW][C]71[/C][C]7415[/C][C]6915.9429733646[/C][C]499.0570266354[/C][/ROW]
[ROW][C]72[/C][C]7720[/C][C]7613.59170740183[/C][C]106.408292598167[/C][/ROW]
[ROW][C]73[/C][C]7815[/C][C]7804.62619300497[/C][C]10.3738069950268[/C][/ROW]
[ROW][C]74[/C][C]7260[/C][C]7657.95261374279[/C][C]-397.952613742794[/C][/ROW]
[ROW][C]75[/C][C]7925[/C][C]8156.02318890996[/C][C]-231.023188909964[/C][/ROW]
[ROW][C]76[/C][C]7825[/C][C]7850.80748354091[/C][C]-25.8074835409143[/C][/ROW]
[ROW][C]77[/C][C]7805[/C][C]7646.21876626654[/C][C]158.781233733458[/C][/ROW]
[ROW][C]78[/C][C]7530[/C][C]7018.95345210612[/C][C]511.046547893876[/C][/ROW]
[ROW][C]79[/C][C]7015[/C][C]7034.02615331526[/C][C]-19.0261533152552[/C][/ROW]
[ROW][C]80[/C][C]6575[/C][C]7560.09267665617[/C][C]-985.092676656174[/C][/ROW]
[ROW][C]81[/C][C]6640[/C][C]6884.050153736[/C][C]-244.050153736002[/C][/ROW]
[ROW][C]82[/C][C]7075[/C][C]6915.02019397165[/C][C]159.979806028349[/C][/ROW]
[ROW][C]83[/C][C]6405[/C][C]7049.19201532443[/C][C]-644.192015324428[/C][/ROW]
[ROW][C]84[/C][C]6720[/C][C]6885.45801548012[/C][C]-165.458015480118[/C][/ROW]
[ROW][C]85[/C][C]6385[/C][C]6865.47946730174[/C][C]-480.479467301743[/C][/ROW]
[ROW][C]86[/C][C]6085[/C][C]6251.3839024844[/C][C]-166.3839024844[/C][/ROW]
[ROW][C]87[/C][C]6475[/C][C]6948.90624326776[/C][C]-473.906243267756[/C][/ROW]
[ROW][C]88[/C][C]6555[/C][C]6564.17372548879[/C][C]-9.17372548879484[/C][/ROW]
[ROW][C]89[/C][C]6500[/C][C]6432.37805964291[/C][C]67.621940357094[/C][/ROW]
[ROW][C]90[/C][C]5790[/C][C]5875.27244493422[/C][C]-85.2724449342222[/C][/ROW]
[ROW][C]91[/C][C]5195[/C][C]5308.86622813642[/C][C]-113.866228136417[/C][/ROW]
[ROW][C]92[/C][C]5680[/C][C]5395.65546124142[/C][C]284.344538758576[/C][/ROW]
[ROW][C]93[/C][C]5745[/C][C]5780.26717548057[/C][C]-35.2671754805706[/C][/ROW]
[ROW][C]94[/C][C]6010[/C][C]6089.03438184105[/C][C]-79.0343818410547[/C][/ROW]
[ROW][C]95[/C][C]5705[/C][C]5761.22837263932[/C][C]-56.2283726393225[/C][/ROW]
[ROW][C]96[/C][C]6310[/C][C]6139.09692688755[/C][C]170.903073112452[/C][/ROW]
[ROW][C]97[/C][C]6870[/C][C]6202.69558013849[/C][C]667.304419861507[/C][/ROW]
[ROW][C]98[/C][C]6260[/C][C]6417.76357888144[/C][C]-157.763578881438[/C][/ROW]
[ROW][C]99[/C][C]7210[/C][C]7003.4790918014[/C][C]206.5209081986[/C][/ROW]
[ROW][C]100[/C][C]7090[/C][C]7219.55873782135[/C][C]-129.558737821351[/C][/ROW]
[ROW][C]101[/C][C]7055[/C][C]7045.43310777718[/C][C]9.56689222282148[/C][/ROW]
[ROW][C]102[/C][C]6535[/C][C]6396.31512884937[/C][C]138.684871150632[/C][/ROW]
[ROW][C]103[/C][C]6320[/C][C]5960.29655285288[/C][C]359.703447147123[/C][/ROW]
[ROW][C]104[/C][C]6010[/C][C]6496.56767027161[/C][C]-486.567670271612[/C][/ROW]
[ROW][C]105[/C][C]6165[/C][C]6285.16806172565[/C][C]-120.168061725652[/C][/ROW]
[ROW][C]106[/C][C]6985[/C][C]6526.59282281484[/C][C]458.407177185162[/C][/ROW]
[ROW][C]107[/C][C]6760[/C][C]6542.84538273719[/C][C]217.15461726281[/C][/ROW]
[ROW][C]108[/C][C]7220[/C][C]7180.99859249014[/C][C]39.0014075098607[/C][/ROW]
[ROW][C]109[/C][C]6995[/C][C]7357.42200948348[/C][C]-362.422009483479[/C][/ROW]
[ROW][C]110[/C][C]6475[/C][C]6621.72173762601[/C][C]-146.721737626008[/C][/ROW]
[ROW][C]111[/C][C]7225[/C][C]7354.36691411874[/C][C]-129.366914118737[/C][/ROW]
[ROW][C]112[/C][C]7325[/C][C]7233.95898779774[/C][C]91.0410122022577[/C][/ROW]
[ROW][C]113[/C][C]7515[/C][C]7249.47352074561[/C][C]265.526479254395[/C][/ROW]
[ROW][C]114[/C][C]6925[/C][C]6808.86935165164[/C][C]116.130648348361[/C][/ROW]
[ROW][C]115[/C][C]7165[/C][C]6444.6010319964[/C][C]720.398968003597[/C][/ROW]
[ROW][C]116[/C][C]6895[/C][C]6881.72076094737[/C][C]13.279239052632[/C][/ROW]
[ROW][C]117[/C][C]6400[/C][C]7123.08911192442[/C][C]-723.089111924416[/C][/ROW]
[ROW][C]118[/C][C]6685[/C][C]7215.9097520011[/C][C]-530.909752001103[/C][/ROW]
[ROW][C]119[/C][C]6955[/C][C]6527.78621645822[/C][C]427.213783541779[/C][/ROW]
[ROW][C]120[/C][C]7550[/C][C]7226.59567726557[/C][C]323.404322734429[/C][/ROW]
[ROW][C]121[/C][C]7645[/C][C]7425.048396415[/C][C]219.951603585003[/C][/ROW]
[ROW][C]122[/C][C]6710[/C][C]7133.56149445898[/C][C]-423.561494458982[/C][/ROW]
[ROW][C]123[/C][C]7470[/C][C]7703.29004479872[/C][C]-233.290044798721[/C][/ROW]
[ROW][C]124[/C][C]7355[/C][C]7604.06193476948[/C][C]-249.061934769483[/C][/ROW]
[ROW][C]125[/C][C]7525[/C][C]7476.24883106205[/C][C]48.7511689379462[/C][/ROW]
[ROW][C]126[/C][C]7165[/C][C]6843.66337865314[/C][C]321.336621346863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302421&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302421&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
1383458160.94017094017184.059829059826
1482758184.2391245786590.7608754213452
1585958565.4844219234229.5155780765763
1684308440.49501118639-10.4950111863873
1783958440.98675330679-45.9867533067918
1877357798.16727851443-63.1672785144301
1978907692.44390125181197.556098748187
2084358301.00645116809133.993548831908
2176208058.51537032685-438.515370326852
2276107603.91649335366.08350664639875
2380058659.3297761646-654.329776164597
2489358651.18446851835283.815531481654
2583208401.76640761272-81.7664076127203
2676708223.38864257936-553.388642579361
2786608179.53724280232480.462757197683
2884858314.93461651909170.065383480909
2981608411.3091639538-251.309163953802
3079107632.54219710915277.457802890854
3177257835.36464181464-110.364641814638
3275558227.01909210726-672.019092107257
3376857262.58635918804422.413640811961
3477407507.14755967292232.852440327079
3574558448.05970739048-993.059707390485
3678508587.34106103837-737.341061038369
3769307561.50371612381-631.503716123809
3866006855.12220098319-255.122200983188
3972907384.04066418863-94.0406641886284
4076257036.92770088052588.072299119483
4177557222.23185678543532.768143214566
4269157124.81001628878-209.810016288783
4361456871.78110188207-726.781101882074
4459856659.1963769727-674.196376972696
4561006103.66995405695-3.66995405694888
4659556002.43912320736-47.4391232073604
4758006289.75112034568-489.751120345682
4859056828.04129642683-923.041296426829
4957055717.98904529453-12.9890452945301
5054305529.40759381953-99.4075938195265
5164356208.62966862264226.370331377358
5260256314.06139029744-289.061390297439
5358155927.51270544886-112.512705448863
5451605135.9357242501224.0642757498808
5549854818.47765121727166.522348782734
5655855169.56851843228415.431481567719
5757905539.24115435498250.758845645025
5861905575.18243274222614.817567257781
5963006101.03139908734198.968600912663
6063406900.02371314535-560.023713145345
6166106365.28756621393244.71243378607
6266856306.38195231577378.618047684231
6374507410.7221917125939.2778082874147
6474107208.08354442116201.916455578842
6572557198.5577007757656.4422992242353
6664606570.55936393206-110.559363932056
6760356231.12526365864-196.125263658643
6867456459.03017577942285.969824220583
6966556690.61409468865-35.6140946886526
7070706693.09180788911376.908192110892
7174156915.9429733646499.0570266354
7277207613.59170740183106.408292598167
7378157804.6261930049710.3738069950268
7472607657.95261374279-397.952613742794
7579258156.02318890996-231.023188909964
7678257850.80748354091-25.8074835409143
7778057646.21876626654158.781233733458
7875307018.95345210612511.046547893876
7970157034.02615331526-19.0261533152552
8065757560.09267665617-985.092676656174
8166406884.050153736-244.050153736002
8270756915.02019397165159.979806028349
8364057049.19201532443-644.192015324428
8467206885.45801548012-165.458015480118
8563856865.47946730174-480.479467301743
8660856251.3839024844-166.3839024844
8764756948.90624326776-473.906243267756
8865556564.17372548879-9.17372548879484
8965006432.3780596429167.621940357094
9057905875.27244493422-85.2724449342222
9151955308.86622813642-113.866228136417
9256805395.65546124142284.344538758576
9357455780.26717548057-35.2671754805706
9460106089.03438184105-79.0343818410547
9557055761.22837263932-56.2283726393225
9663106139.09692688755170.903073112452
9768706202.69558013849667.304419861507
9862606417.76357888144-157.763578881438
9972107003.4790918014206.5209081986
10070907219.55873782135-129.558737821351
10170557045.433107777189.56689222282148
10265356396.31512884937138.684871150632
10363205960.29655285288359.703447147123
10460106496.56767027161-486.567670271612
10561656285.16806172565-120.168061725652
10669856526.59282281484458.407177185162
10767606542.84538273719217.15461726281
10872207180.9985924901439.0014075098607
10969957357.42200948348-362.422009483479
11064756621.72173762601-146.721737626008
11172257354.36691411874-129.366914118737
11273257233.9589877977491.0410122022577
11375157249.47352074561265.526479254395
11469256808.86935165164116.130648348361
11571656444.6010319964720.398968003597
11668956881.7207609473713.279239052632
11764007123.08911192442-723.089111924416
11866857215.9097520011-530.909752001103
11969556527.78621645822427.213783541779
12075507226.59567726557323.404322734429
12176457425.048396415219.951603585003
12267107133.56149445898-423.561494458982
12374707703.29004479872-233.290044798721
12473557604.06193476948-249.061934769483
12575257476.2488310620548.7511689379462
12671656843.66337865314321.336621346863







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1276837.102510600856125.766502300037548.43851890166
1286556.122317990795718.94862109767393.29601488399
1296504.51604537915556.941706197927452.09038456028
1307116.813082230866069.376691589388164.24947287234
1317124.677925465765985.138773665258264.21707726628
1327520.128110413976294.490042453688745.76617837425
1337478.302253696046171.377364843668785.22714254842
1346802.834210665975418.582232118858187.0861892131
1357706.411699697686248.158160054089164.66523934129
1367745.528419718836216.112096529999274.94474290766
1377886.722638809956288.599258531749484.84601908817
1387329.533335745825664.850897570418994.21577392122

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 6837.10251060085 & 6125.76650230003 & 7548.43851890166 \tabularnewline
128 & 6556.12231799079 & 5718.9486210976 & 7393.29601488399 \tabularnewline
129 & 6504.5160453791 & 5556.94170619792 & 7452.09038456028 \tabularnewline
130 & 7116.81308223086 & 6069.37669158938 & 8164.24947287234 \tabularnewline
131 & 7124.67792546576 & 5985.13877366525 & 8264.21707726628 \tabularnewline
132 & 7520.12811041397 & 6294.49004245368 & 8745.76617837425 \tabularnewline
133 & 7478.30225369604 & 6171.37736484366 & 8785.22714254842 \tabularnewline
134 & 6802.83421066597 & 5418.58223211885 & 8187.0861892131 \tabularnewline
135 & 7706.41169969768 & 6248.15816005408 & 9164.66523934129 \tabularnewline
136 & 7745.52841971883 & 6216.11209652999 & 9274.94474290766 \tabularnewline
137 & 7886.72263880995 & 6288.59925853174 & 9484.84601908817 \tabularnewline
138 & 7329.53333574582 & 5664.85089757041 & 8994.21577392122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302421&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]6837.10251060085[/C][C]6125.76650230003[/C][C]7548.43851890166[/C][/ROW]
[ROW][C]128[/C][C]6556.12231799079[/C][C]5718.9486210976[/C][C]7393.29601488399[/C][/ROW]
[ROW][C]129[/C][C]6504.5160453791[/C][C]5556.94170619792[/C][C]7452.09038456028[/C][/ROW]
[ROW][C]130[/C][C]7116.81308223086[/C][C]6069.37669158938[/C][C]8164.24947287234[/C][/ROW]
[ROW][C]131[/C][C]7124.67792546576[/C][C]5985.13877366525[/C][C]8264.21707726628[/C][/ROW]
[ROW][C]132[/C][C]7520.12811041397[/C][C]6294.49004245368[/C][C]8745.76617837425[/C][/ROW]
[ROW][C]133[/C][C]7478.30225369604[/C][C]6171.37736484366[/C][C]8785.22714254842[/C][/ROW]
[ROW][C]134[/C][C]6802.83421066597[/C][C]5418.58223211885[/C][C]8187.0861892131[/C][/ROW]
[ROW][C]135[/C][C]7706.41169969768[/C][C]6248.15816005408[/C][C]9164.66523934129[/C][/ROW]
[ROW][C]136[/C][C]7745.52841971883[/C][C]6216.11209652999[/C][C]9274.94474290766[/C][/ROW]
[ROW][C]137[/C][C]7886.72263880995[/C][C]6288.59925853174[/C][C]9484.84601908817[/C][/ROW]
[ROW][C]138[/C][C]7329.53333574582[/C][C]5664.85089757041[/C][C]8994.21577392122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302421&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302421&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
1276837.102510600856125.766502300037548.43851890166
1286556.122317990795718.94862109767393.29601488399
1296504.51604537915556.941706197927452.09038456028
1307116.813082230866069.376691589388164.24947287234
1317124.677925465765985.138773665258264.21707726628
1327520.128110413976294.490042453688745.76617837425
1337478.302253696046171.377364843668785.22714254842
1346802.834210665975418.582232118858187.0861892131
1357706.411699697686248.158160054089164.66523934129
1367745.528419718836216.112096529999274.94474290766
1377886.722638809956288.599258531749484.84601908817
1387329.533335745825664.850897570418994.21577392122



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')