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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 computationThu, 22 Dec 2011 15:48:43 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t1324586943btrrgt6bt43c0oa.htm/, Retrieved Fri, 03 May 2024 10:22:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159969, Retrieved Fri, 03 May 2024 10:22:25 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-22 20:48:43] [c7041fab4904771a5085f5eb0f28763f] [Current]
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Dataseries X:
4581945
3874038
4086290
4364364
3793586
4533914
4823043
3981535
4746356
5284534
4264830
3924674
3734753
3762290
3609739
3877594
3636415
3578195
3604342
3459513
3366571
3371277
3724848
3350830
3305159
3390736
3349758
3253655
3734250
3455433
2966726
2993716
3009320
3169713
3170061
3368934
3292638
3337344
3208306
3359130
3223078
3437159
3400156
3657576
3765613
3481921
3604800
3981340
3734078
4018173
3887417
3919880
4014466
4197758
3896531
3964742
4201847
4050512
3997402
4314479
4925744
5130631
4444855
3967319
3931250
4235952
4169219
3779064
3558810
3699466
3650693
3525633
3470276
3859094
3661155
3356365
3344440
3338684
3404294
3289319
3469252
3571850
3639914
3091730
3078149
3188115
3246082
3486992
3378187
3282306
3288345
3325749
3352262
3531954
3722622
3809365
3750617
3615286
3696556
4123959
4136163
3933392
4035576
4551202
4032195
3970893
4489016
5426127
4578224
4126390
4892100
4128697
4408721
4199465
4074767
4161758
3891319
4470302
4283111
3845962
3911471
3798478
3644313
3784029
3647134
3994662
3607836
3566008
3511412
3258665
3486573
3369443
3465544
3905224
3733881
3220642
3225812
3354461
3352261
3450652




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159969&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159969&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159969&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.488346435508068
beta0.0385663763172275
gamma0.396964600926703

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.488346435508068 \tabularnewline
beta & 0.0385663763172275 \tabularnewline
gamma & 0.396964600926703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159969&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]0.488346435508068[/C][/ROW]
[ROW][C]beta[/C][C]0.0385663763172275[/C][/ROW]
[ROW][C]gamma[/C][C]0.396964600926703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159969&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159969&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
alpha0.488346435508068
beta0.0385663763172275
gamma0.396964600926703







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
537935863623823.70625169762.29375
645339144484296.7657946749617.2342053251
748230434346079.14247085476963.857529153
839815354964537.36357245-983002.363572448
947463563846501.80139993899854.198600066
1052845345047461.68105212237072.318947877
1142648305099466.73762518-834636.737625181
1239246744768057.77634966-843383.776349663
1337347534090437.51857734-355684.518577339
1437622904509805.66936111-747515.669361109
1536097393810936.80789601-201197.80789601
1638775943746638.10331921130955.896680786
1736364153621788.6269139514626.3730860502
1835781954127286.62765481-549091.62765481
1936043423624890.2557174-20548.2557173953
2034595133708287.71181621-248774.711816212
2133665713359232.299989617338.70001038862
2233712773731399.9542592-360122.954259202
2337248483416920.72079791307927.279202095
2433508303608843.14741895-258013.147418953
2533051593301590.770866583568.22913342156
2633907363591507.40470637-200771.404706368
2733497583487759.50974634-138001.509746338
2832536553335794.45603951-82139.4560395055
2937342503159698.57612373574551.42387627
3034554333689843.33125211-234410.331252115
3129667263584677.1290825-617951.129082496
3229937163202897.23965529-209181.239655291
3330093203088968.48750936-79648.4875093615
3431697133113837.2457732755875.7542267255
3531700613056505.14294179113555.857058212
3633689343112729.94720797256204.052792033
3732926383258895.864538633742.135461397
3833373443375316.44262336-37972.4426233582
3932083063290753.51210435-82447.5121043506
4033591303283426.624900675703.3750994029
4132230783296055.1160656-72977.1160655972
4234371593343577.2842988993581.7157011139
4334001563314486.1444816285669.8555183797
4436575763424807.86613358232768.133866417
4537656133490325.56687285275287.433127149
4634819213754695.54879014-272774.548790136
4736048003551133.3774811553666.6225188514
4839813403681145.2917469300194.708253101
4937340783794938.40832262-60860.4083226221
5040181733784216.76206598233956.237934023
5138874173904342.27357205-16925.2735720533
5239198804058547.87087187-138667.870871872
5340144663885020.34240809129445.657591914
5441977584031027.52713217166730.472867828
5538965314070015.15043434-173484.150434342
5639647424122737.95386613-157995.953866131
5742018473993562.81585903208284.184140971
5840505124186463.29041496-135951.290414963
5939974024003656.20730483-6254.20730482601
6043144794139459.79241388175019.20758612
6149257444251846.75509557673897.244904427
6251306314615520.62704995515110.372950052
6344448554802571.70079706-357716.700797059
6439673194822510.57047323-855191.57047323
6539312504532673.92940708-601423.929407076
6642359524216829.0894886719122.9105113251
6741692193950577.45717243218641.542827569
6837790644127981.98040992-348917.980409922
6935588104123504.06269049-564694.062690491
7036994663938905.62273154-239439.622731537
7136506933569311.3508596381381.6491403701
7235256333544225.8465049-18592.8465048983
7334702763643272.79981991-172996.799819907
7438590943709435.038899149658.961100996
7536611553595760.1633465394.8366599996
7633563653543003.81895724-186638.818957245
7733444403525902.36974351-181462.369743512
7833386843650582.1014586-311898.101458604
7934042943282817.42397517121476.576024835
8032893193195739.1778943693579.8221056359
8134692523311291.37327548157960.626724523
8235718503576385.62746932-4535.62746932404
8336399143453682.22296515186231.777034855
8430917303400720.35556143-308990.35556143
8530781493333332.68260575-255183.682605746
8631881153356461.54556872-168346.545568723
8732460823182219.4483291863862.5516708209
8834869922956321.91434232530670.085657675
8933781873313128.6266544465058.3733455567
9032823063519535.88065353-237229.880653534
9132883453366773.10450923-78428.1045092316
9233257493171475.72314633154273.276853674
9333522623248086.58115518104175.418844821
9435319543411121.76988493120832.230115068
9537226223471137.50398445251484.496015545
9638093653496095.03921642313269.960783579
9737506173655050.2516076795566.7483923263
9836152863831976.61470237-216690.61470237
9936965563762056.06588146-65500.0658814558
10041239593647149.68413644476809.315863563
10141361633847216.69639333288946.303606668
10239333924064264.53956463-130872.539564632
10340355764077684.62391555-42108.6239155494
10445512024095513.10217715455688.897822854
10540321954257875.8771626-225680.877162597
10639708934139412.68688601-168519.686886012
10744890164152841.60640962336174.393590377
10854261274463999.56401966962127.43598034
10945782244752315.52049272-174091.520492717
11041263904688654.9644251-562264.964425104
11148921004622890.90412592269209.095874076
11241286975037805.22046387-909108.220463873
11344087214155614.29577786253106.704222141
11441994654203858.88931035-4393.8893103525
11540747674572041.00089972-497274.000899722
11641617584351516.68060166-189758.680601661
11738913194048417.89098315-157098.89098315
11844703023828058.60435537642243.395644626
11942831114408113.34947131-125002.349471315
12038459624435054.45360402-589092.453604016
12139114713939263.92220853-27792.9222085322
12237984783942527.16324198-144049.16324198
12336443133966079.20428578-321766.204285777
12437840293782279.486841111749.51315889368
12536471343679765.60083116-32631.6008311617
12639946623647698.59986819346963.400131814
12736078363874831.99266638-266995.992666378
12835660083784412.31815092-218404.318150918
12935114123564182.13992894-52770.1399289449
13032586653595778.32440016-337113.324400156
13134865733347660.12814847138912.871851535
13233694433456493.88489192-87050.8848919203
13334655443327685.15992739137858.840072609
13439052243391845.89758866513378.102411336
13537338813668989.0459290664891.9540709374
13632206423707627.72435722-486985.724357225
13732258123433508.91569529-207696.915695295
13833544613402997.34489112-48536.3448911184
13933522613301864.8495305850396.1504694237
14034506523208285.13386933242366.866130671

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 3793586 & 3623823.70625 & 169762.29375 \tabularnewline
6 & 4533914 & 4484296.76579467 & 49617.2342053251 \tabularnewline
7 & 4823043 & 4346079.14247085 & 476963.857529153 \tabularnewline
8 & 3981535 & 4964537.36357245 & -983002.363572448 \tabularnewline
9 & 4746356 & 3846501.80139993 & 899854.198600066 \tabularnewline
10 & 5284534 & 5047461.68105212 & 237072.318947877 \tabularnewline
11 & 4264830 & 5099466.73762518 & -834636.737625181 \tabularnewline
12 & 3924674 & 4768057.77634966 & -843383.776349663 \tabularnewline
13 & 3734753 & 4090437.51857734 & -355684.518577339 \tabularnewline
14 & 3762290 & 4509805.66936111 & -747515.669361109 \tabularnewline
15 & 3609739 & 3810936.80789601 & -201197.80789601 \tabularnewline
16 & 3877594 & 3746638.10331921 & 130955.896680786 \tabularnewline
17 & 3636415 & 3621788.62691395 & 14626.3730860502 \tabularnewline
18 & 3578195 & 4127286.62765481 & -549091.62765481 \tabularnewline
19 & 3604342 & 3624890.2557174 & -20548.2557173953 \tabularnewline
20 & 3459513 & 3708287.71181621 & -248774.711816212 \tabularnewline
21 & 3366571 & 3359232.29998961 & 7338.70001038862 \tabularnewline
22 & 3371277 & 3731399.9542592 & -360122.954259202 \tabularnewline
23 & 3724848 & 3416920.72079791 & 307927.279202095 \tabularnewline
24 & 3350830 & 3608843.14741895 & -258013.147418953 \tabularnewline
25 & 3305159 & 3301590.77086658 & 3568.22913342156 \tabularnewline
26 & 3390736 & 3591507.40470637 & -200771.404706368 \tabularnewline
27 & 3349758 & 3487759.50974634 & -138001.509746338 \tabularnewline
28 & 3253655 & 3335794.45603951 & -82139.4560395055 \tabularnewline
29 & 3734250 & 3159698.57612373 & 574551.42387627 \tabularnewline
30 & 3455433 & 3689843.33125211 & -234410.331252115 \tabularnewline
31 & 2966726 & 3584677.1290825 & -617951.129082496 \tabularnewline
32 & 2993716 & 3202897.23965529 & -209181.239655291 \tabularnewline
33 & 3009320 & 3088968.48750936 & -79648.4875093615 \tabularnewline
34 & 3169713 & 3113837.24577327 & 55875.7542267255 \tabularnewline
35 & 3170061 & 3056505.14294179 & 113555.857058212 \tabularnewline
36 & 3368934 & 3112729.94720797 & 256204.052792033 \tabularnewline
37 & 3292638 & 3258895.8645386 & 33742.135461397 \tabularnewline
38 & 3337344 & 3375316.44262336 & -37972.4426233582 \tabularnewline
39 & 3208306 & 3290753.51210435 & -82447.5121043506 \tabularnewline
40 & 3359130 & 3283426.6249006 & 75703.3750994029 \tabularnewline
41 & 3223078 & 3296055.1160656 & -72977.1160655972 \tabularnewline
42 & 3437159 & 3343577.28429889 & 93581.7157011139 \tabularnewline
43 & 3400156 & 3314486.14448162 & 85669.8555183797 \tabularnewline
44 & 3657576 & 3424807.86613358 & 232768.133866417 \tabularnewline
45 & 3765613 & 3490325.56687285 & 275287.433127149 \tabularnewline
46 & 3481921 & 3754695.54879014 & -272774.548790136 \tabularnewline
47 & 3604800 & 3551133.37748115 & 53666.6225188514 \tabularnewline
48 & 3981340 & 3681145.2917469 & 300194.708253101 \tabularnewline
49 & 3734078 & 3794938.40832262 & -60860.4083226221 \tabularnewline
50 & 4018173 & 3784216.76206598 & 233956.237934023 \tabularnewline
51 & 3887417 & 3904342.27357205 & -16925.2735720533 \tabularnewline
52 & 3919880 & 4058547.87087187 & -138667.870871872 \tabularnewline
53 & 4014466 & 3885020.34240809 & 129445.657591914 \tabularnewline
54 & 4197758 & 4031027.52713217 & 166730.472867828 \tabularnewline
55 & 3896531 & 4070015.15043434 & -173484.150434342 \tabularnewline
56 & 3964742 & 4122737.95386613 & -157995.953866131 \tabularnewline
57 & 4201847 & 3993562.81585903 & 208284.184140971 \tabularnewline
58 & 4050512 & 4186463.29041496 & -135951.290414963 \tabularnewline
59 & 3997402 & 4003656.20730483 & -6254.20730482601 \tabularnewline
60 & 4314479 & 4139459.79241388 & 175019.20758612 \tabularnewline
61 & 4925744 & 4251846.75509557 & 673897.244904427 \tabularnewline
62 & 5130631 & 4615520.62704995 & 515110.372950052 \tabularnewline
63 & 4444855 & 4802571.70079706 & -357716.700797059 \tabularnewline
64 & 3967319 & 4822510.57047323 & -855191.57047323 \tabularnewline
65 & 3931250 & 4532673.92940708 & -601423.929407076 \tabularnewline
66 & 4235952 & 4216829.08948867 & 19122.9105113251 \tabularnewline
67 & 4169219 & 3950577.45717243 & 218641.542827569 \tabularnewline
68 & 3779064 & 4127981.98040992 & -348917.980409922 \tabularnewline
69 & 3558810 & 4123504.06269049 & -564694.062690491 \tabularnewline
70 & 3699466 & 3938905.62273154 & -239439.622731537 \tabularnewline
71 & 3650693 & 3569311.35085963 & 81381.6491403701 \tabularnewline
72 & 3525633 & 3544225.8465049 & -18592.8465048983 \tabularnewline
73 & 3470276 & 3643272.79981991 & -172996.799819907 \tabularnewline
74 & 3859094 & 3709435.038899 & 149658.961100996 \tabularnewline
75 & 3661155 & 3595760.16334 & 65394.8366599996 \tabularnewline
76 & 3356365 & 3543003.81895724 & -186638.818957245 \tabularnewline
77 & 3344440 & 3525902.36974351 & -181462.369743512 \tabularnewline
78 & 3338684 & 3650582.1014586 & -311898.101458604 \tabularnewline
79 & 3404294 & 3282817.42397517 & 121476.576024835 \tabularnewline
80 & 3289319 & 3195739.17789436 & 93579.8221056359 \tabularnewline
81 & 3469252 & 3311291.37327548 & 157960.626724523 \tabularnewline
82 & 3571850 & 3576385.62746932 & -4535.62746932404 \tabularnewline
83 & 3639914 & 3453682.22296515 & 186231.777034855 \tabularnewline
84 & 3091730 & 3400720.35556143 & -308990.35556143 \tabularnewline
85 & 3078149 & 3333332.68260575 & -255183.682605746 \tabularnewline
86 & 3188115 & 3356461.54556872 & -168346.545568723 \tabularnewline
87 & 3246082 & 3182219.44832918 & 63862.5516708209 \tabularnewline
88 & 3486992 & 2956321.91434232 & 530670.085657675 \tabularnewline
89 & 3378187 & 3313128.62665444 & 65058.3733455567 \tabularnewline
90 & 3282306 & 3519535.88065353 & -237229.880653534 \tabularnewline
91 & 3288345 & 3366773.10450923 & -78428.1045092316 \tabularnewline
92 & 3325749 & 3171475.72314633 & 154273.276853674 \tabularnewline
93 & 3352262 & 3248086.58115518 & 104175.418844821 \tabularnewline
94 & 3531954 & 3411121.76988493 & 120832.230115068 \tabularnewline
95 & 3722622 & 3471137.50398445 & 251484.496015545 \tabularnewline
96 & 3809365 & 3496095.03921642 & 313269.960783579 \tabularnewline
97 & 3750617 & 3655050.25160767 & 95566.7483923263 \tabularnewline
98 & 3615286 & 3831976.61470237 & -216690.61470237 \tabularnewline
99 & 3696556 & 3762056.06588146 & -65500.0658814558 \tabularnewline
100 & 4123959 & 3647149.68413644 & 476809.315863563 \tabularnewline
101 & 4136163 & 3847216.69639333 & 288946.303606668 \tabularnewline
102 & 3933392 & 4064264.53956463 & -130872.539564632 \tabularnewline
103 & 4035576 & 4077684.62391555 & -42108.6239155494 \tabularnewline
104 & 4551202 & 4095513.10217715 & 455688.897822854 \tabularnewline
105 & 4032195 & 4257875.8771626 & -225680.877162597 \tabularnewline
106 & 3970893 & 4139412.68688601 & -168519.686886012 \tabularnewline
107 & 4489016 & 4152841.60640962 & 336174.393590377 \tabularnewline
108 & 5426127 & 4463999.56401966 & 962127.43598034 \tabularnewline
109 & 4578224 & 4752315.52049272 & -174091.520492717 \tabularnewline
110 & 4126390 & 4688654.9644251 & -562264.964425104 \tabularnewline
111 & 4892100 & 4622890.90412592 & 269209.095874076 \tabularnewline
112 & 4128697 & 5037805.22046387 & -909108.220463873 \tabularnewline
113 & 4408721 & 4155614.29577786 & 253106.704222141 \tabularnewline
114 & 4199465 & 4203858.88931035 & -4393.8893103525 \tabularnewline
115 & 4074767 & 4572041.00089972 & -497274.000899722 \tabularnewline
116 & 4161758 & 4351516.68060166 & -189758.680601661 \tabularnewline
117 & 3891319 & 4048417.89098315 & -157098.89098315 \tabularnewline
118 & 4470302 & 3828058.60435537 & 642243.395644626 \tabularnewline
119 & 4283111 & 4408113.34947131 & -125002.349471315 \tabularnewline
120 & 3845962 & 4435054.45360402 & -589092.453604016 \tabularnewline
121 & 3911471 & 3939263.92220853 & -27792.9222085322 \tabularnewline
122 & 3798478 & 3942527.16324198 & -144049.16324198 \tabularnewline
123 & 3644313 & 3966079.20428578 & -321766.204285777 \tabularnewline
124 & 3784029 & 3782279.48684111 & 1749.51315889368 \tabularnewline
125 & 3647134 & 3679765.60083116 & -32631.6008311617 \tabularnewline
126 & 3994662 & 3647698.59986819 & 346963.400131814 \tabularnewline
127 & 3607836 & 3874831.99266638 & -266995.992666378 \tabularnewline
128 & 3566008 & 3784412.31815092 & -218404.318150918 \tabularnewline
129 & 3511412 & 3564182.13992894 & -52770.1399289449 \tabularnewline
130 & 3258665 & 3595778.32440016 & -337113.324400156 \tabularnewline
131 & 3486573 & 3347660.12814847 & 138912.871851535 \tabularnewline
132 & 3369443 & 3456493.88489192 & -87050.8848919203 \tabularnewline
133 & 3465544 & 3327685.15992739 & 137858.840072609 \tabularnewline
134 & 3905224 & 3391845.89758866 & 513378.102411336 \tabularnewline
135 & 3733881 & 3668989.04592906 & 64891.9540709374 \tabularnewline
136 & 3220642 & 3707627.72435722 & -486985.724357225 \tabularnewline
137 & 3225812 & 3433508.91569529 & -207696.915695295 \tabularnewline
138 & 3354461 & 3402997.34489112 & -48536.3448911184 \tabularnewline
139 & 3352261 & 3301864.84953058 & 50396.1504694237 \tabularnewline
140 & 3450652 & 3208285.13386933 & 242366.866130671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159969&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]5[/C][C]3793586[/C][C]3623823.70625[/C][C]169762.29375[/C][/ROW]
[ROW][C]6[/C][C]4533914[/C][C]4484296.76579467[/C][C]49617.2342053251[/C][/ROW]
[ROW][C]7[/C][C]4823043[/C][C]4346079.14247085[/C][C]476963.857529153[/C][/ROW]
[ROW][C]8[/C][C]3981535[/C][C]4964537.36357245[/C][C]-983002.363572448[/C][/ROW]
[ROW][C]9[/C][C]4746356[/C][C]3846501.80139993[/C][C]899854.198600066[/C][/ROW]
[ROW][C]10[/C][C]5284534[/C][C]5047461.68105212[/C][C]237072.318947877[/C][/ROW]
[ROW][C]11[/C][C]4264830[/C][C]5099466.73762518[/C][C]-834636.737625181[/C][/ROW]
[ROW][C]12[/C][C]3924674[/C][C]4768057.77634966[/C][C]-843383.776349663[/C][/ROW]
[ROW][C]13[/C][C]3734753[/C][C]4090437.51857734[/C][C]-355684.518577339[/C][/ROW]
[ROW][C]14[/C][C]3762290[/C][C]4509805.66936111[/C][C]-747515.669361109[/C][/ROW]
[ROW][C]15[/C][C]3609739[/C][C]3810936.80789601[/C][C]-201197.80789601[/C][/ROW]
[ROW][C]16[/C][C]3877594[/C][C]3746638.10331921[/C][C]130955.896680786[/C][/ROW]
[ROW][C]17[/C][C]3636415[/C][C]3621788.62691395[/C][C]14626.3730860502[/C][/ROW]
[ROW][C]18[/C][C]3578195[/C][C]4127286.62765481[/C][C]-549091.62765481[/C][/ROW]
[ROW][C]19[/C][C]3604342[/C][C]3624890.2557174[/C][C]-20548.2557173953[/C][/ROW]
[ROW][C]20[/C][C]3459513[/C][C]3708287.71181621[/C][C]-248774.711816212[/C][/ROW]
[ROW][C]21[/C][C]3366571[/C][C]3359232.29998961[/C][C]7338.70001038862[/C][/ROW]
[ROW][C]22[/C][C]3371277[/C][C]3731399.9542592[/C][C]-360122.954259202[/C][/ROW]
[ROW][C]23[/C][C]3724848[/C][C]3416920.72079791[/C][C]307927.279202095[/C][/ROW]
[ROW][C]24[/C][C]3350830[/C][C]3608843.14741895[/C][C]-258013.147418953[/C][/ROW]
[ROW][C]25[/C][C]3305159[/C][C]3301590.77086658[/C][C]3568.22913342156[/C][/ROW]
[ROW][C]26[/C][C]3390736[/C][C]3591507.40470637[/C][C]-200771.404706368[/C][/ROW]
[ROW][C]27[/C][C]3349758[/C][C]3487759.50974634[/C][C]-138001.509746338[/C][/ROW]
[ROW][C]28[/C][C]3253655[/C][C]3335794.45603951[/C][C]-82139.4560395055[/C][/ROW]
[ROW][C]29[/C][C]3734250[/C][C]3159698.57612373[/C][C]574551.42387627[/C][/ROW]
[ROW][C]30[/C][C]3455433[/C][C]3689843.33125211[/C][C]-234410.331252115[/C][/ROW]
[ROW][C]31[/C][C]2966726[/C][C]3584677.1290825[/C][C]-617951.129082496[/C][/ROW]
[ROW][C]32[/C][C]2993716[/C][C]3202897.23965529[/C][C]-209181.239655291[/C][/ROW]
[ROW][C]33[/C][C]3009320[/C][C]3088968.48750936[/C][C]-79648.4875093615[/C][/ROW]
[ROW][C]34[/C][C]3169713[/C][C]3113837.24577327[/C][C]55875.7542267255[/C][/ROW]
[ROW][C]35[/C][C]3170061[/C][C]3056505.14294179[/C][C]113555.857058212[/C][/ROW]
[ROW][C]36[/C][C]3368934[/C][C]3112729.94720797[/C][C]256204.052792033[/C][/ROW]
[ROW][C]37[/C][C]3292638[/C][C]3258895.8645386[/C][C]33742.135461397[/C][/ROW]
[ROW][C]38[/C][C]3337344[/C][C]3375316.44262336[/C][C]-37972.4426233582[/C][/ROW]
[ROW][C]39[/C][C]3208306[/C][C]3290753.51210435[/C][C]-82447.5121043506[/C][/ROW]
[ROW][C]40[/C][C]3359130[/C][C]3283426.6249006[/C][C]75703.3750994029[/C][/ROW]
[ROW][C]41[/C][C]3223078[/C][C]3296055.1160656[/C][C]-72977.1160655972[/C][/ROW]
[ROW][C]42[/C][C]3437159[/C][C]3343577.28429889[/C][C]93581.7157011139[/C][/ROW]
[ROW][C]43[/C][C]3400156[/C][C]3314486.14448162[/C][C]85669.8555183797[/C][/ROW]
[ROW][C]44[/C][C]3657576[/C][C]3424807.86613358[/C][C]232768.133866417[/C][/ROW]
[ROW][C]45[/C][C]3765613[/C][C]3490325.56687285[/C][C]275287.433127149[/C][/ROW]
[ROW][C]46[/C][C]3481921[/C][C]3754695.54879014[/C][C]-272774.548790136[/C][/ROW]
[ROW][C]47[/C][C]3604800[/C][C]3551133.37748115[/C][C]53666.6225188514[/C][/ROW]
[ROW][C]48[/C][C]3981340[/C][C]3681145.2917469[/C][C]300194.708253101[/C][/ROW]
[ROW][C]49[/C][C]3734078[/C][C]3794938.40832262[/C][C]-60860.4083226221[/C][/ROW]
[ROW][C]50[/C][C]4018173[/C][C]3784216.76206598[/C][C]233956.237934023[/C][/ROW]
[ROW][C]51[/C][C]3887417[/C][C]3904342.27357205[/C][C]-16925.2735720533[/C][/ROW]
[ROW][C]52[/C][C]3919880[/C][C]4058547.87087187[/C][C]-138667.870871872[/C][/ROW]
[ROW][C]53[/C][C]4014466[/C][C]3885020.34240809[/C][C]129445.657591914[/C][/ROW]
[ROW][C]54[/C][C]4197758[/C][C]4031027.52713217[/C][C]166730.472867828[/C][/ROW]
[ROW][C]55[/C][C]3896531[/C][C]4070015.15043434[/C][C]-173484.150434342[/C][/ROW]
[ROW][C]56[/C][C]3964742[/C][C]4122737.95386613[/C][C]-157995.953866131[/C][/ROW]
[ROW][C]57[/C][C]4201847[/C][C]3993562.81585903[/C][C]208284.184140971[/C][/ROW]
[ROW][C]58[/C][C]4050512[/C][C]4186463.29041496[/C][C]-135951.290414963[/C][/ROW]
[ROW][C]59[/C][C]3997402[/C][C]4003656.20730483[/C][C]-6254.20730482601[/C][/ROW]
[ROW][C]60[/C][C]4314479[/C][C]4139459.79241388[/C][C]175019.20758612[/C][/ROW]
[ROW][C]61[/C][C]4925744[/C][C]4251846.75509557[/C][C]673897.244904427[/C][/ROW]
[ROW][C]62[/C][C]5130631[/C][C]4615520.62704995[/C][C]515110.372950052[/C][/ROW]
[ROW][C]63[/C][C]4444855[/C][C]4802571.70079706[/C][C]-357716.700797059[/C][/ROW]
[ROW][C]64[/C][C]3967319[/C][C]4822510.57047323[/C][C]-855191.57047323[/C][/ROW]
[ROW][C]65[/C][C]3931250[/C][C]4532673.92940708[/C][C]-601423.929407076[/C][/ROW]
[ROW][C]66[/C][C]4235952[/C][C]4216829.08948867[/C][C]19122.9105113251[/C][/ROW]
[ROW][C]67[/C][C]4169219[/C][C]3950577.45717243[/C][C]218641.542827569[/C][/ROW]
[ROW][C]68[/C][C]3779064[/C][C]4127981.98040992[/C][C]-348917.980409922[/C][/ROW]
[ROW][C]69[/C][C]3558810[/C][C]4123504.06269049[/C][C]-564694.062690491[/C][/ROW]
[ROW][C]70[/C][C]3699466[/C][C]3938905.62273154[/C][C]-239439.622731537[/C][/ROW]
[ROW][C]71[/C][C]3650693[/C][C]3569311.35085963[/C][C]81381.6491403701[/C][/ROW]
[ROW][C]72[/C][C]3525633[/C][C]3544225.8465049[/C][C]-18592.8465048983[/C][/ROW]
[ROW][C]73[/C][C]3470276[/C][C]3643272.79981991[/C][C]-172996.799819907[/C][/ROW]
[ROW][C]74[/C][C]3859094[/C][C]3709435.038899[/C][C]149658.961100996[/C][/ROW]
[ROW][C]75[/C][C]3661155[/C][C]3595760.16334[/C][C]65394.8366599996[/C][/ROW]
[ROW][C]76[/C][C]3356365[/C][C]3543003.81895724[/C][C]-186638.818957245[/C][/ROW]
[ROW][C]77[/C][C]3344440[/C][C]3525902.36974351[/C][C]-181462.369743512[/C][/ROW]
[ROW][C]78[/C][C]3338684[/C][C]3650582.1014586[/C][C]-311898.101458604[/C][/ROW]
[ROW][C]79[/C][C]3404294[/C][C]3282817.42397517[/C][C]121476.576024835[/C][/ROW]
[ROW][C]80[/C][C]3289319[/C][C]3195739.17789436[/C][C]93579.8221056359[/C][/ROW]
[ROW][C]81[/C][C]3469252[/C][C]3311291.37327548[/C][C]157960.626724523[/C][/ROW]
[ROW][C]82[/C][C]3571850[/C][C]3576385.62746932[/C][C]-4535.62746932404[/C][/ROW]
[ROW][C]83[/C][C]3639914[/C][C]3453682.22296515[/C][C]186231.777034855[/C][/ROW]
[ROW][C]84[/C][C]3091730[/C][C]3400720.35556143[/C][C]-308990.35556143[/C][/ROW]
[ROW][C]85[/C][C]3078149[/C][C]3333332.68260575[/C][C]-255183.682605746[/C][/ROW]
[ROW][C]86[/C][C]3188115[/C][C]3356461.54556872[/C][C]-168346.545568723[/C][/ROW]
[ROW][C]87[/C][C]3246082[/C][C]3182219.44832918[/C][C]63862.5516708209[/C][/ROW]
[ROW][C]88[/C][C]3486992[/C][C]2956321.91434232[/C][C]530670.085657675[/C][/ROW]
[ROW][C]89[/C][C]3378187[/C][C]3313128.62665444[/C][C]65058.3733455567[/C][/ROW]
[ROW][C]90[/C][C]3282306[/C][C]3519535.88065353[/C][C]-237229.880653534[/C][/ROW]
[ROW][C]91[/C][C]3288345[/C][C]3366773.10450923[/C][C]-78428.1045092316[/C][/ROW]
[ROW][C]92[/C][C]3325749[/C][C]3171475.72314633[/C][C]154273.276853674[/C][/ROW]
[ROW][C]93[/C][C]3352262[/C][C]3248086.58115518[/C][C]104175.418844821[/C][/ROW]
[ROW][C]94[/C][C]3531954[/C][C]3411121.76988493[/C][C]120832.230115068[/C][/ROW]
[ROW][C]95[/C][C]3722622[/C][C]3471137.50398445[/C][C]251484.496015545[/C][/ROW]
[ROW][C]96[/C][C]3809365[/C][C]3496095.03921642[/C][C]313269.960783579[/C][/ROW]
[ROW][C]97[/C][C]3750617[/C][C]3655050.25160767[/C][C]95566.7483923263[/C][/ROW]
[ROW][C]98[/C][C]3615286[/C][C]3831976.61470237[/C][C]-216690.61470237[/C][/ROW]
[ROW][C]99[/C][C]3696556[/C][C]3762056.06588146[/C][C]-65500.0658814558[/C][/ROW]
[ROW][C]100[/C][C]4123959[/C][C]3647149.68413644[/C][C]476809.315863563[/C][/ROW]
[ROW][C]101[/C][C]4136163[/C][C]3847216.69639333[/C][C]288946.303606668[/C][/ROW]
[ROW][C]102[/C][C]3933392[/C][C]4064264.53956463[/C][C]-130872.539564632[/C][/ROW]
[ROW][C]103[/C][C]4035576[/C][C]4077684.62391555[/C][C]-42108.6239155494[/C][/ROW]
[ROW][C]104[/C][C]4551202[/C][C]4095513.10217715[/C][C]455688.897822854[/C][/ROW]
[ROW][C]105[/C][C]4032195[/C][C]4257875.8771626[/C][C]-225680.877162597[/C][/ROW]
[ROW][C]106[/C][C]3970893[/C][C]4139412.68688601[/C][C]-168519.686886012[/C][/ROW]
[ROW][C]107[/C][C]4489016[/C][C]4152841.60640962[/C][C]336174.393590377[/C][/ROW]
[ROW][C]108[/C][C]5426127[/C][C]4463999.56401966[/C][C]962127.43598034[/C][/ROW]
[ROW][C]109[/C][C]4578224[/C][C]4752315.52049272[/C][C]-174091.520492717[/C][/ROW]
[ROW][C]110[/C][C]4126390[/C][C]4688654.9644251[/C][C]-562264.964425104[/C][/ROW]
[ROW][C]111[/C][C]4892100[/C][C]4622890.90412592[/C][C]269209.095874076[/C][/ROW]
[ROW][C]112[/C][C]4128697[/C][C]5037805.22046387[/C][C]-909108.220463873[/C][/ROW]
[ROW][C]113[/C][C]4408721[/C][C]4155614.29577786[/C][C]253106.704222141[/C][/ROW]
[ROW][C]114[/C][C]4199465[/C][C]4203858.88931035[/C][C]-4393.8893103525[/C][/ROW]
[ROW][C]115[/C][C]4074767[/C][C]4572041.00089972[/C][C]-497274.000899722[/C][/ROW]
[ROW][C]116[/C][C]4161758[/C][C]4351516.68060166[/C][C]-189758.680601661[/C][/ROW]
[ROW][C]117[/C][C]3891319[/C][C]4048417.89098315[/C][C]-157098.89098315[/C][/ROW]
[ROW][C]118[/C][C]4470302[/C][C]3828058.60435537[/C][C]642243.395644626[/C][/ROW]
[ROW][C]119[/C][C]4283111[/C][C]4408113.34947131[/C][C]-125002.349471315[/C][/ROW]
[ROW][C]120[/C][C]3845962[/C][C]4435054.45360402[/C][C]-589092.453604016[/C][/ROW]
[ROW][C]121[/C][C]3911471[/C][C]3939263.92220853[/C][C]-27792.9222085322[/C][/ROW]
[ROW][C]122[/C][C]3798478[/C][C]3942527.16324198[/C][C]-144049.16324198[/C][/ROW]
[ROW][C]123[/C][C]3644313[/C][C]3966079.20428578[/C][C]-321766.204285777[/C][/ROW]
[ROW][C]124[/C][C]3784029[/C][C]3782279.48684111[/C][C]1749.51315889368[/C][/ROW]
[ROW][C]125[/C][C]3647134[/C][C]3679765.60083116[/C][C]-32631.6008311617[/C][/ROW]
[ROW][C]126[/C][C]3994662[/C][C]3647698.59986819[/C][C]346963.400131814[/C][/ROW]
[ROW][C]127[/C][C]3607836[/C][C]3874831.99266638[/C][C]-266995.992666378[/C][/ROW]
[ROW][C]128[/C][C]3566008[/C][C]3784412.31815092[/C][C]-218404.318150918[/C][/ROW]
[ROW][C]129[/C][C]3511412[/C][C]3564182.13992894[/C][C]-52770.1399289449[/C][/ROW]
[ROW][C]130[/C][C]3258665[/C][C]3595778.32440016[/C][C]-337113.324400156[/C][/ROW]
[ROW][C]131[/C][C]3486573[/C][C]3347660.12814847[/C][C]138912.871851535[/C][/ROW]
[ROW][C]132[/C][C]3369443[/C][C]3456493.88489192[/C][C]-87050.8848919203[/C][/ROW]
[ROW][C]133[/C][C]3465544[/C][C]3327685.15992739[/C][C]137858.840072609[/C][/ROW]
[ROW][C]134[/C][C]3905224[/C][C]3391845.89758866[/C][C]513378.102411336[/C][/ROW]
[ROW][C]135[/C][C]3733881[/C][C]3668989.04592906[/C][C]64891.9540709374[/C][/ROW]
[ROW][C]136[/C][C]3220642[/C][C]3707627.72435722[/C][C]-486985.724357225[/C][/ROW]
[ROW][C]137[/C][C]3225812[/C][C]3433508.91569529[/C][C]-207696.915695295[/C][/ROW]
[ROW][C]138[/C][C]3354461[/C][C]3402997.34489112[/C][C]-48536.3448911184[/C][/ROW]
[ROW][C]139[/C][C]3352261[/C][C]3301864.84953058[/C][C]50396.1504694237[/C][/ROW]
[ROW][C]140[/C][C]3450652[/C][C]3208285.13386933[/C][C]242366.866130671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159969&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159969&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
537935863623823.70625169762.29375
645339144484296.7657946749617.2342053251
748230434346079.14247085476963.857529153
839815354964537.36357245-983002.363572448
947463563846501.80139993899854.198600066
1052845345047461.68105212237072.318947877
1142648305099466.73762518-834636.737625181
1239246744768057.77634966-843383.776349663
1337347534090437.51857734-355684.518577339
1437622904509805.66936111-747515.669361109
1536097393810936.80789601-201197.80789601
1638775943746638.10331921130955.896680786
1736364153621788.6269139514626.3730860502
1835781954127286.62765481-549091.62765481
1936043423624890.2557174-20548.2557173953
2034595133708287.71181621-248774.711816212
2133665713359232.299989617338.70001038862
2233712773731399.9542592-360122.954259202
2337248483416920.72079791307927.279202095
2433508303608843.14741895-258013.147418953
2533051593301590.770866583568.22913342156
2633907363591507.40470637-200771.404706368
2733497583487759.50974634-138001.509746338
2832536553335794.45603951-82139.4560395055
2937342503159698.57612373574551.42387627
3034554333689843.33125211-234410.331252115
3129667263584677.1290825-617951.129082496
3229937163202897.23965529-209181.239655291
3330093203088968.48750936-79648.4875093615
3431697133113837.2457732755875.7542267255
3531700613056505.14294179113555.857058212
3633689343112729.94720797256204.052792033
3732926383258895.864538633742.135461397
3833373443375316.44262336-37972.4426233582
3932083063290753.51210435-82447.5121043506
4033591303283426.624900675703.3750994029
4132230783296055.1160656-72977.1160655972
4234371593343577.2842988993581.7157011139
4334001563314486.1444816285669.8555183797
4436575763424807.86613358232768.133866417
4537656133490325.56687285275287.433127149
4634819213754695.54879014-272774.548790136
4736048003551133.3774811553666.6225188514
4839813403681145.2917469300194.708253101
4937340783794938.40832262-60860.4083226221
5040181733784216.76206598233956.237934023
5138874173904342.27357205-16925.2735720533
5239198804058547.87087187-138667.870871872
5340144663885020.34240809129445.657591914
5441977584031027.52713217166730.472867828
5538965314070015.15043434-173484.150434342
5639647424122737.95386613-157995.953866131
5742018473993562.81585903208284.184140971
5840505124186463.29041496-135951.290414963
5939974024003656.20730483-6254.20730482601
6043144794139459.79241388175019.20758612
6149257444251846.75509557673897.244904427
6251306314615520.62704995515110.372950052
6344448554802571.70079706-357716.700797059
6439673194822510.57047323-855191.57047323
6539312504532673.92940708-601423.929407076
6642359524216829.0894886719122.9105113251
6741692193950577.45717243218641.542827569
6837790644127981.98040992-348917.980409922
6935588104123504.06269049-564694.062690491
7036994663938905.62273154-239439.622731537
7136506933569311.3508596381381.6491403701
7235256333544225.8465049-18592.8465048983
7334702763643272.79981991-172996.799819907
7438590943709435.038899149658.961100996
7536611553595760.1633465394.8366599996
7633563653543003.81895724-186638.818957245
7733444403525902.36974351-181462.369743512
7833386843650582.1014586-311898.101458604
7934042943282817.42397517121476.576024835
8032893193195739.1778943693579.8221056359
8134692523311291.37327548157960.626724523
8235718503576385.62746932-4535.62746932404
8336399143453682.22296515186231.777034855
8430917303400720.35556143-308990.35556143
8530781493333332.68260575-255183.682605746
8631881153356461.54556872-168346.545568723
8732460823182219.4483291863862.5516708209
8834869922956321.91434232530670.085657675
8933781873313128.6266544465058.3733455567
9032823063519535.88065353-237229.880653534
9132883453366773.10450923-78428.1045092316
9233257493171475.72314633154273.276853674
9333522623248086.58115518104175.418844821
9435319543411121.76988493120832.230115068
9537226223471137.50398445251484.496015545
9638093653496095.03921642313269.960783579
9737506173655050.2516076795566.7483923263
9836152863831976.61470237-216690.61470237
9936965563762056.06588146-65500.0658814558
10041239593647149.68413644476809.315863563
10141361633847216.69639333288946.303606668
10239333924064264.53956463-130872.539564632
10340355764077684.62391555-42108.6239155494
10445512024095513.10217715455688.897822854
10540321954257875.8771626-225680.877162597
10639708934139412.68688601-168519.686886012
10744890164152841.60640962336174.393590377
10854261274463999.56401966962127.43598034
10945782244752315.52049272-174091.520492717
11041263904688654.9644251-562264.964425104
11148921004622890.90412592269209.095874076
11241286975037805.22046387-909108.220463873
11344087214155614.29577786253106.704222141
11441994654203858.88931035-4393.8893103525
11540747674572041.00089972-497274.000899722
11641617584351516.68060166-189758.680601661
11738913194048417.89098315-157098.89098315
11844703023828058.60435537642243.395644626
11942831114408113.34947131-125002.349471315
12038459624435054.45360402-589092.453604016
12139114713939263.92220853-27792.9222085322
12237984783942527.16324198-144049.16324198
12336443133966079.20428578-321766.204285777
12437840293782279.486841111749.51315889368
12536471343679765.60083116-32631.6008311617
12639946623647698.59986819346963.400131814
12736078363874831.99266638-266995.992666378
12835660083784412.31815092-218404.318150918
12935114123564182.13992894-52770.1399289449
13032586653595778.32440016-337113.324400156
13134865733347660.12814847138912.871851535
13233694433456493.88489192-87050.8848919203
13334655443327685.15992739137858.840072609
13439052243391845.89758866513378.102411336
13537338813668989.0459290664891.9540709374
13632206423707627.72435722-486985.724357225
13732258123433508.91569529-207696.915695295
13833544613402997.34489112-48536.3448911184
13933522613301864.8495305850396.1504694237
14034506523208285.13386933242366.866130671







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1413347756.94533112692343.282100974003170.60856122
1423455599.969043542720708.578365984190491.3597211
1433403777.867066092592037.419315794215518.31481639
1443329142.904397762442326.458405474215959.35039005

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
141 & 3347756.9453311 & 2692343.28210097 & 4003170.60856122 \tabularnewline
142 & 3455599.96904354 & 2720708.57836598 & 4190491.3597211 \tabularnewline
143 & 3403777.86706609 & 2592037.41931579 & 4215518.31481639 \tabularnewline
144 & 3329142.90439776 & 2442326.45840547 & 4215959.35039005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159969&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]141[/C][C]3347756.9453311[/C][C]2692343.28210097[/C][C]4003170.60856122[/C][/ROW]
[ROW][C]142[/C][C]3455599.96904354[/C][C]2720708.57836598[/C][C]4190491.3597211[/C][/ROW]
[ROW][C]143[/C][C]3403777.86706609[/C][C]2592037.41931579[/C][C]4215518.31481639[/C][/ROW]
[ROW][C]144[/C][C]3329142.90439776[/C][C]2442326.45840547[/C][C]4215959.35039005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159969&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159969&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
1413347756.94533112692343.282100974003170.60856122
1423455599.969043542720708.578365984190491.3597211
1433403777.867066092592037.419315794215518.31481639
1443329142.904397762442326.458405474215959.35039005



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')