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 computationMon, 19 Dec 2016 19:26:58 +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/19/t14821720404nlooa0tjvixttj.htm/, Retrieved Sat, 18 May 2024 00:57:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301439, Retrieved Sat, 18 May 2024 00:57:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N2141 - Exponenti...] [2016-12-19 18:26:58] [f8e2c3c70b883e93ecb746821352be11] [Current]
Feedback Forum

Post a new message
Dataseries X:
4976
4994
5478
4712
4388
4210
3844
3850
3770
3584
3490
3060
3324
3406
4346
4076
4310
4148
3958
4296
4370
4476
4406
4076
4430
4534
5200
4960
5188
4958
4554
4310
3890
4214
3720
3606
4360
4262
4788
4780
4836
4492
4514
4770
4664
4906
4684
4320
4588
4372
4674
4794
4558
4260
3994
3394
3334
3412
3198
3196
3536
3272
3562
3900
3744
3886
3708
3700
3878
4152
3830
3864
3880
4230
4394
4076
4224
4026
3950
4086
4166
4270
4162
4030
4128
3958
4216
4096
4168
3948
3394
3660
3808
3684
3610
3598
3918
3764
3872
3710
4056
4010
3656
3884
3886
3880
3642
3272
3602
3198
3802
3402
3344
3508
3426
3394
3448
3554
3522
3472
3692
3690
3802
3814
3408
3650




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301439&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301439&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301439&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.631833576020012
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.631833576020012 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301439&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]0.631833576020012[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301439&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301439&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
alpha0.631833576020012
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1333243576.82371794872-252.823717948719
1434063473.87083117413-67.870831174132
1543464325.5273882455620.4726117544433
1640764004.4189654471371.5810345528712
1743104206.43589352351103.564106476491
1841484027.49413363883120.505866361172
1939583727.25674648616230.743253513842
2042964012.17104186926283.828958130739
2143704222.96000116933147.039998830667
2244764201.65443648812274.345563511882
2344064308.8681353200297.1318646799846
2440763944.19560243256131.804397567445
2544304194.34913585455235.650864145454
2645344468.1243340079865.8756659920236
2752005436.81150812914-236.811508129137
2849604971.95874506846-11.9587450684594
2951885132.9675286647855.0324713352165
3049584929.5992393513628.4007606486375
3145544611.75245850354-57.7524585035362
3243104733.92985052952-423.929850529519
3338904447.17192880867-557.171928808665
3442144027.79125811258186.208741887419
3537204014.07301997925-294.07301997925
3636063414.98936830455191.010631695446
3743603740.7841706013619.215829398698
3842624194.4030648020467.5969351979611
3947885052.73854012008-264.738540120085
4047804653.02377826701126.97622173299
4148364926.48025535313-90.4802553531263
4244924621.36723789184-129.367237891839
4345144172.11861573504341.881384264956
4447704411.98386677154358.016133228462
4546644570.2304127392893.7695872607183
4649064835.8242511072370.1757488927733
4746844571.96885330452112.031146695476
4843204408.06696286477-88.0669628647738
4945884715.18194697152-127.181946971524
5043724494.1141093172-122.114109317198
5146745110.2290134592-436.229013459205
5247944746.3770356745347.6229643254719
5345584889.63528682393-331.635286823934
5442604417.83554215258-157.835542152578
5539944124.09760953646-130.097609536459
5633944071.69095794079-677.690957940787
5733343478.25628290777-144.256282907771
5834123584.770925442-172.770925441996
5931983182.8234137454715.1765862545321
6031962884.05615458652311.943845413482
6135363429.51057431176106.489425688242
6232723357.94996332506-85.9499633250612
6335623881.26802817621-319.268028176212
6439003769.45398037434130.546019625658
6537443825.47564799799-81.4756479979892
6638863575.72239298619310.277607013807
6737083587.96624084973120.033759150266
6837003491.99550152893208.004498471073
6938783654.56569071913223.434309280874
7041523982.90146101193169.098538988075
7138303866.15451883554-36.1545188355426
7238643644.21428454536219.785715454635
7338804055.79868445826-175.798684458265
7442303735.02924568385494.970754316153
7543944539.49264736018-145.492647360179
7640764703.08214927872-627.08214927872
7742244202.3496424747521.6503575252518
7840264161.98525529357-135.985255293574
7939503822.2238458684127.776154131596
8040863763.53288416623322.467115833773
8141664004.10513647384161.894863526157
8242704273.55361244625-3.55361244625146
8341623972.15195971169189.848040288309
8440303987.2363313536342.7636686463748
8541284141.33136449908-13.3313644990785
8639584170.1690190695-212.169019069501
8742164292.04064869636-76.0406486963611
8840964322.20717054475-226.207170544747
8941684313.6024622408-145.602462240799
9039484109.52598798401-161.52598798401
9133943850.73518098086-456.735180980857
9236603494.40900734146165.590992658538
9338083576.74434582861231.255654171394
9436843829.10472443827-145.104724438269
9536103509.47032130328100.529678696715
9635983413.9688260058184.0311739942
9739183636.6691044744281.330895525603
9837643778.47892027859-14.4789202785919
9938724075.37568729076-203.375687290765
10037103969.80138500097-259.80138500097
10140563969.6466712557886.3533287442224
10240103906.26514636557103.734853634426
10336563706.38893258861-50.3889325886084
10438843835.9255640711748.074435928831
10538863868.1855198892717.8144801107319
10638803847.123343501832.8766564982006
10736423730.37789255755-88.3778925575502
10832723546.26069789788-274.260697897884
10936023515.2192746184786.7807253815349
11031983425.19851864242-227.198518642422
11138023518.14645391858283.853546081417
11234023699.64589314528-297.645893145281
11333443803.02229158993-459.022291589934
11435083401.45343209201106.546567907987
11534263146.61055057527279.389449424732
11633943520.7631427395-126.7631427395
11734483431.4141462815716.5858537184345
11835543415.12107010499138.87892989501
11935223320.70956091014201.290439089864
12034723251.17873637349220.821263626512
12136923665.8700489844626.1299510155409
12236903421.93148187613268.068518123873
12338024015.95797121414-213.957971214136
12438143668.83481019757145.165189802425
12534083992.58074715223-584.580747152233
12636503719.90330419262-69.9033041926245

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3324 & 3576.82371794872 & -252.823717948719 \tabularnewline
14 & 3406 & 3473.87083117413 & -67.870831174132 \tabularnewline
15 & 4346 & 4325.52738824556 & 20.4726117544433 \tabularnewline
16 & 4076 & 4004.41896544713 & 71.5810345528712 \tabularnewline
17 & 4310 & 4206.43589352351 & 103.564106476491 \tabularnewline
18 & 4148 & 4027.49413363883 & 120.505866361172 \tabularnewline
19 & 3958 & 3727.25674648616 & 230.743253513842 \tabularnewline
20 & 4296 & 4012.17104186926 & 283.828958130739 \tabularnewline
21 & 4370 & 4222.96000116933 & 147.039998830667 \tabularnewline
22 & 4476 & 4201.65443648812 & 274.345563511882 \tabularnewline
23 & 4406 & 4308.86813532002 & 97.1318646799846 \tabularnewline
24 & 4076 & 3944.19560243256 & 131.804397567445 \tabularnewline
25 & 4430 & 4194.34913585455 & 235.650864145454 \tabularnewline
26 & 4534 & 4468.12433400798 & 65.8756659920236 \tabularnewline
27 & 5200 & 5436.81150812914 & -236.811508129137 \tabularnewline
28 & 4960 & 4971.95874506846 & -11.9587450684594 \tabularnewline
29 & 5188 & 5132.96752866478 & 55.0324713352165 \tabularnewline
30 & 4958 & 4929.59923935136 & 28.4007606486375 \tabularnewline
31 & 4554 & 4611.75245850354 & -57.7524585035362 \tabularnewline
32 & 4310 & 4733.92985052952 & -423.929850529519 \tabularnewline
33 & 3890 & 4447.17192880867 & -557.171928808665 \tabularnewline
34 & 4214 & 4027.79125811258 & 186.208741887419 \tabularnewline
35 & 3720 & 4014.07301997925 & -294.07301997925 \tabularnewline
36 & 3606 & 3414.98936830455 & 191.010631695446 \tabularnewline
37 & 4360 & 3740.7841706013 & 619.215829398698 \tabularnewline
38 & 4262 & 4194.40306480204 & 67.5969351979611 \tabularnewline
39 & 4788 & 5052.73854012008 & -264.738540120085 \tabularnewline
40 & 4780 & 4653.02377826701 & 126.97622173299 \tabularnewline
41 & 4836 & 4926.48025535313 & -90.4802553531263 \tabularnewline
42 & 4492 & 4621.36723789184 & -129.367237891839 \tabularnewline
43 & 4514 & 4172.11861573504 & 341.881384264956 \tabularnewline
44 & 4770 & 4411.98386677154 & 358.016133228462 \tabularnewline
45 & 4664 & 4570.23041273928 & 93.7695872607183 \tabularnewline
46 & 4906 & 4835.82425110723 & 70.1757488927733 \tabularnewline
47 & 4684 & 4571.96885330452 & 112.031146695476 \tabularnewline
48 & 4320 & 4408.06696286477 & -88.0669628647738 \tabularnewline
49 & 4588 & 4715.18194697152 & -127.181946971524 \tabularnewline
50 & 4372 & 4494.1141093172 & -122.114109317198 \tabularnewline
51 & 4674 & 5110.2290134592 & -436.229013459205 \tabularnewline
52 & 4794 & 4746.37703567453 & 47.6229643254719 \tabularnewline
53 & 4558 & 4889.63528682393 & -331.635286823934 \tabularnewline
54 & 4260 & 4417.83554215258 & -157.835542152578 \tabularnewline
55 & 3994 & 4124.09760953646 & -130.097609536459 \tabularnewline
56 & 3394 & 4071.69095794079 & -677.690957940787 \tabularnewline
57 & 3334 & 3478.25628290777 & -144.256282907771 \tabularnewline
58 & 3412 & 3584.770925442 & -172.770925441996 \tabularnewline
59 & 3198 & 3182.82341374547 & 15.1765862545321 \tabularnewline
60 & 3196 & 2884.05615458652 & 311.943845413482 \tabularnewline
61 & 3536 & 3429.51057431176 & 106.489425688242 \tabularnewline
62 & 3272 & 3357.94996332506 & -85.9499633250612 \tabularnewline
63 & 3562 & 3881.26802817621 & -319.268028176212 \tabularnewline
64 & 3900 & 3769.45398037434 & 130.546019625658 \tabularnewline
65 & 3744 & 3825.47564799799 & -81.4756479979892 \tabularnewline
66 & 3886 & 3575.72239298619 & 310.277607013807 \tabularnewline
67 & 3708 & 3587.96624084973 & 120.033759150266 \tabularnewline
68 & 3700 & 3491.99550152893 & 208.004498471073 \tabularnewline
69 & 3878 & 3654.56569071913 & 223.434309280874 \tabularnewline
70 & 4152 & 3982.90146101193 & 169.098538988075 \tabularnewline
71 & 3830 & 3866.15451883554 & -36.1545188355426 \tabularnewline
72 & 3864 & 3644.21428454536 & 219.785715454635 \tabularnewline
73 & 3880 & 4055.79868445826 & -175.798684458265 \tabularnewline
74 & 4230 & 3735.02924568385 & 494.970754316153 \tabularnewline
75 & 4394 & 4539.49264736018 & -145.492647360179 \tabularnewline
76 & 4076 & 4703.08214927872 & -627.08214927872 \tabularnewline
77 & 4224 & 4202.34964247475 & 21.6503575252518 \tabularnewline
78 & 4026 & 4161.98525529357 & -135.985255293574 \tabularnewline
79 & 3950 & 3822.2238458684 & 127.776154131596 \tabularnewline
80 & 4086 & 3763.53288416623 & 322.467115833773 \tabularnewline
81 & 4166 & 4004.10513647384 & 161.894863526157 \tabularnewline
82 & 4270 & 4273.55361244625 & -3.55361244625146 \tabularnewline
83 & 4162 & 3972.15195971169 & 189.848040288309 \tabularnewline
84 & 4030 & 3987.23633135363 & 42.7636686463748 \tabularnewline
85 & 4128 & 4141.33136449908 & -13.3313644990785 \tabularnewline
86 & 3958 & 4170.1690190695 & -212.169019069501 \tabularnewline
87 & 4216 & 4292.04064869636 & -76.0406486963611 \tabularnewline
88 & 4096 & 4322.20717054475 & -226.207170544747 \tabularnewline
89 & 4168 & 4313.6024622408 & -145.602462240799 \tabularnewline
90 & 3948 & 4109.52598798401 & -161.52598798401 \tabularnewline
91 & 3394 & 3850.73518098086 & -456.735180980857 \tabularnewline
92 & 3660 & 3494.40900734146 & 165.590992658538 \tabularnewline
93 & 3808 & 3576.74434582861 & 231.255654171394 \tabularnewline
94 & 3684 & 3829.10472443827 & -145.104724438269 \tabularnewline
95 & 3610 & 3509.47032130328 & 100.529678696715 \tabularnewline
96 & 3598 & 3413.9688260058 & 184.0311739942 \tabularnewline
97 & 3918 & 3636.6691044744 & 281.330895525603 \tabularnewline
98 & 3764 & 3778.47892027859 & -14.4789202785919 \tabularnewline
99 & 3872 & 4075.37568729076 & -203.375687290765 \tabularnewline
100 & 3710 & 3969.80138500097 & -259.80138500097 \tabularnewline
101 & 4056 & 3969.64667125578 & 86.3533287442224 \tabularnewline
102 & 4010 & 3906.26514636557 & 103.734853634426 \tabularnewline
103 & 3656 & 3706.38893258861 & -50.3889325886084 \tabularnewline
104 & 3884 & 3835.92556407117 & 48.074435928831 \tabularnewline
105 & 3886 & 3868.18551988927 & 17.8144801107319 \tabularnewline
106 & 3880 & 3847.1233435018 & 32.8766564982006 \tabularnewline
107 & 3642 & 3730.37789255755 & -88.3778925575502 \tabularnewline
108 & 3272 & 3546.26069789788 & -274.260697897884 \tabularnewline
109 & 3602 & 3515.21927461847 & 86.7807253815349 \tabularnewline
110 & 3198 & 3425.19851864242 & -227.198518642422 \tabularnewline
111 & 3802 & 3518.14645391858 & 283.853546081417 \tabularnewline
112 & 3402 & 3699.64589314528 & -297.645893145281 \tabularnewline
113 & 3344 & 3803.02229158993 & -459.022291589934 \tabularnewline
114 & 3508 & 3401.45343209201 & 106.546567907987 \tabularnewline
115 & 3426 & 3146.61055057527 & 279.389449424732 \tabularnewline
116 & 3394 & 3520.7631427395 & -126.7631427395 \tabularnewline
117 & 3448 & 3431.41414628157 & 16.5858537184345 \tabularnewline
118 & 3554 & 3415.12107010499 & 138.87892989501 \tabularnewline
119 & 3522 & 3320.70956091014 & 201.290439089864 \tabularnewline
120 & 3472 & 3251.17873637349 & 220.821263626512 \tabularnewline
121 & 3692 & 3665.87004898446 & 26.1299510155409 \tabularnewline
122 & 3690 & 3421.93148187613 & 268.068518123873 \tabularnewline
123 & 3802 & 4015.95797121414 & -213.957971214136 \tabularnewline
124 & 3814 & 3668.83481019757 & 145.165189802425 \tabularnewline
125 & 3408 & 3992.58074715223 & -584.580747152233 \tabularnewline
126 & 3650 & 3719.90330419262 & -69.9033041926245 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301439&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]3324[/C][C]3576.82371794872[/C][C]-252.823717948719[/C][/ROW]
[ROW][C]14[/C][C]3406[/C][C]3473.87083117413[/C][C]-67.870831174132[/C][/ROW]
[ROW][C]15[/C][C]4346[/C][C]4325.52738824556[/C][C]20.4726117544433[/C][/ROW]
[ROW][C]16[/C][C]4076[/C][C]4004.41896544713[/C][C]71.5810345528712[/C][/ROW]
[ROW][C]17[/C][C]4310[/C][C]4206.43589352351[/C][C]103.564106476491[/C][/ROW]
[ROW][C]18[/C][C]4148[/C][C]4027.49413363883[/C][C]120.505866361172[/C][/ROW]
[ROW][C]19[/C][C]3958[/C][C]3727.25674648616[/C][C]230.743253513842[/C][/ROW]
[ROW][C]20[/C][C]4296[/C][C]4012.17104186926[/C][C]283.828958130739[/C][/ROW]
[ROW][C]21[/C][C]4370[/C][C]4222.96000116933[/C][C]147.039998830667[/C][/ROW]
[ROW][C]22[/C][C]4476[/C][C]4201.65443648812[/C][C]274.345563511882[/C][/ROW]
[ROW][C]23[/C][C]4406[/C][C]4308.86813532002[/C][C]97.1318646799846[/C][/ROW]
[ROW][C]24[/C][C]4076[/C][C]3944.19560243256[/C][C]131.804397567445[/C][/ROW]
[ROW][C]25[/C][C]4430[/C][C]4194.34913585455[/C][C]235.650864145454[/C][/ROW]
[ROW][C]26[/C][C]4534[/C][C]4468.12433400798[/C][C]65.8756659920236[/C][/ROW]
[ROW][C]27[/C][C]5200[/C][C]5436.81150812914[/C][C]-236.811508129137[/C][/ROW]
[ROW][C]28[/C][C]4960[/C][C]4971.95874506846[/C][C]-11.9587450684594[/C][/ROW]
[ROW][C]29[/C][C]5188[/C][C]5132.96752866478[/C][C]55.0324713352165[/C][/ROW]
[ROW][C]30[/C][C]4958[/C][C]4929.59923935136[/C][C]28.4007606486375[/C][/ROW]
[ROW][C]31[/C][C]4554[/C][C]4611.75245850354[/C][C]-57.7524585035362[/C][/ROW]
[ROW][C]32[/C][C]4310[/C][C]4733.92985052952[/C][C]-423.929850529519[/C][/ROW]
[ROW][C]33[/C][C]3890[/C][C]4447.17192880867[/C][C]-557.171928808665[/C][/ROW]
[ROW][C]34[/C][C]4214[/C][C]4027.79125811258[/C][C]186.208741887419[/C][/ROW]
[ROW][C]35[/C][C]3720[/C][C]4014.07301997925[/C][C]-294.07301997925[/C][/ROW]
[ROW][C]36[/C][C]3606[/C][C]3414.98936830455[/C][C]191.010631695446[/C][/ROW]
[ROW][C]37[/C][C]4360[/C][C]3740.7841706013[/C][C]619.215829398698[/C][/ROW]
[ROW][C]38[/C][C]4262[/C][C]4194.40306480204[/C][C]67.5969351979611[/C][/ROW]
[ROW][C]39[/C][C]4788[/C][C]5052.73854012008[/C][C]-264.738540120085[/C][/ROW]
[ROW][C]40[/C][C]4780[/C][C]4653.02377826701[/C][C]126.97622173299[/C][/ROW]
[ROW][C]41[/C][C]4836[/C][C]4926.48025535313[/C][C]-90.4802553531263[/C][/ROW]
[ROW][C]42[/C][C]4492[/C][C]4621.36723789184[/C][C]-129.367237891839[/C][/ROW]
[ROW][C]43[/C][C]4514[/C][C]4172.11861573504[/C][C]341.881384264956[/C][/ROW]
[ROW][C]44[/C][C]4770[/C][C]4411.98386677154[/C][C]358.016133228462[/C][/ROW]
[ROW][C]45[/C][C]4664[/C][C]4570.23041273928[/C][C]93.7695872607183[/C][/ROW]
[ROW][C]46[/C][C]4906[/C][C]4835.82425110723[/C][C]70.1757488927733[/C][/ROW]
[ROW][C]47[/C][C]4684[/C][C]4571.96885330452[/C][C]112.031146695476[/C][/ROW]
[ROW][C]48[/C][C]4320[/C][C]4408.06696286477[/C][C]-88.0669628647738[/C][/ROW]
[ROW][C]49[/C][C]4588[/C][C]4715.18194697152[/C][C]-127.181946971524[/C][/ROW]
[ROW][C]50[/C][C]4372[/C][C]4494.1141093172[/C][C]-122.114109317198[/C][/ROW]
[ROW][C]51[/C][C]4674[/C][C]5110.2290134592[/C][C]-436.229013459205[/C][/ROW]
[ROW][C]52[/C][C]4794[/C][C]4746.37703567453[/C][C]47.6229643254719[/C][/ROW]
[ROW][C]53[/C][C]4558[/C][C]4889.63528682393[/C][C]-331.635286823934[/C][/ROW]
[ROW][C]54[/C][C]4260[/C][C]4417.83554215258[/C][C]-157.835542152578[/C][/ROW]
[ROW][C]55[/C][C]3994[/C][C]4124.09760953646[/C][C]-130.097609536459[/C][/ROW]
[ROW][C]56[/C][C]3394[/C][C]4071.69095794079[/C][C]-677.690957940787[/C][/ROW]
[ROW][C]57[/C][C]3334[/C][C]3478.25628290777[/C][C]-144.256282907771[/C][/ROW]
[ROW][C]58[/C][C]3412[/C][C]3584.770925442[/C][C]-172.770925441996[/C][/ROW]
[ROW][C]59[/C][C]3198[/C][C]3182.82341374547[/C][C]15.1765862545321[/C][/ROW]
[ROW][C]60[/C][C]3196[/C][C]2884.05615458652[/C][C]311.943845413482[/C][/ROW]
[ROW][C]61[/C][C]3536[/C][C]3429.51057431176[/C][C]106.489425688242[/C][/ROW]
[ROW][C]62[/C][C]3272[/C][C]3357.94996332506[/C][C]-85.9499633250612[/C][/ROW]
[ROW][C]63[/C][C]3562[/C][C]3881.26802817621[/C][C]-319.268028176212[/C][/ROW]
[ROW][C]64[/C][C]3900[/C][C]3769.45398037434[/C][C]130.546019625658[/C][/ROW]
[ROW][C]65[/C][C]3744[/C][C]3825.47564799799[/C][C]-81.4756479979892[/C][/ROW]
[ROW][C]66[/C][C]3886[/C][C]3575.72239298619[/C][C]310.277607013807[/C][/ROW]
[ROW][C]67[/C][C]3708[/C][C]3587.96624084973[/C][C]120.033759150266[/C][/ROW]
[ROW][C]68[/C][C]3700[/C][C]3491.99550152893[/C][C]208.004498471073[/C][/ROW]
[ROW][C]69[/C][C]3878[/C][C]3654.56569071913[/C][C]223.434309280874[/C][/ROW]
[ROW][C]70[/C][C]4152[/C][C]3982.90146101193[/C][C]169.098538988075[/C][/ROW]
[ROW][C]71[/C][C]3830[/C][C]3866.15451883554[/C][C]-36.1545188355426[/C][/ROW]
[ROW][C]72[/C][C]3864[/C][C]3644.21428454536[/C][C]219.785715454635[/C][/ROW]
[ROW][C]73[/C][C]3880[/C][C]4055.79868445826[/C][C]-175.798684458265[/C][/ROW]
[ROW][C]74[/C][C]4230[/C][C]3735.02924568385[/C][C]494.970754316153[/C][/ROW]
[ROW][C]75[/C][C]4394[/C][C]4539.49264736018[/C][C]-145.492647360179[/C][/ROW]
[ROW][C]76[/C][C]4076[/C][C]4703.08214927872[/C][C]-627.08214927872[/C][/ROW]
[ROW][C]77[/C][C]4224[/C][C]4202.34964247475[/C][C]21.6503575252518[/C][/ROW]
[ROW][C]78[/C][C]4026[/C][C]4161.98525529357[/C][C]-135.985255293574[/C][/ROW]
[ROW][C]79[/C][C]3950[/C][C]3822.2238458684[/C][C]127.776154131596[/C][/ROW]
[ROW][C]80[/C][C]4086[/C][C]3763.53288416623[/C][C]322.467115833773[/C][/ROW]
[ROW][C]81[/C][C]4166[/C][C]4004.10513647384[/C][C]161.894863526157[/C][/ROW]
[ROW][C]82[/C][C]4270[/C][C]4273.55361244625[/C][C]-3.55361244625146[/C][/ROW]
[ROW][C]83[/C][C]4162[/C][C]3972.15195971169[/C][C]189.848040288309[/C][/ROW]
[ROW][C]84[/C][C]4030[/C][C]3987.23633135363[/C][C]42.7636686463748[/C][/ROW]
[ROW][C]85[/C][C]4128[/C][C]4141.33136449908[/C][C]-13.3313644990785[/C][/ROW]
[ROW][C]86[/C][C]3958[/C][C]4170.1690190695[/C][C]-212.169019069501[/C][/ROW]
[ROW][C]87[/C][C]4216[/C][C]4292.04064869636[/C][C]-76.0406486963611[/C][/ROW]
[ROW][C]88[/C][C]4096[/C][C]4322.20717054475[/C][C]-226.207170544747[/C][/ROW]
[ROW][C]89[/C][C]4168[/C][C]4313.6024622408[/C][C]-145.602462240799[/C][/ROW]
[ROW][C]90[/C][C]3948[/C][C]4109.52598798401[/C][C]-161.52598798401[/C][/ROW]
[ROW][C]91[/C][C]3394[/C][C]3850.73518098086[/C][C]-456.735180980857[/C][/ROW]
[ROW][C]92[/C][C]3660[/C][C]3494.40900734146[/C][C]165.590992658538[/C][/ROW]
[ROW][C]93[/C][C]3808[/C][C]3576.74434582861[/C][C]231.255654171394[/C][/ROW]
[ROW][C]94[/C][C]3684[/C][C]3829.10472443827[/C][C]-145.104724438269[/C][/ROW]
[ROW][C]95[/C][C]3610[/C][C]3509.47032130328[/C][C]100.529678696715[/C][/ROW]
[ROW][C]96[/C][C]3598[/C][C]3413.9688260058[/C][C]184.0311739942[/C][/ROW]
[ROW][C]97[/C][C]3918[/C][C]3636.6691044744[/C][C]281.330895525603[/C][/ROW]
[ROW][C]98[/C][C]3764[/C][C]3778.47892027859[/C][C]-14.4789202785919[/C][/ROW]
[ROW][C]99[/C][C]3872[/C][C]4075.37568729076[/C][C]-203.375687290765[/C][/ROW]
[ROW][C]100[/C][C]3710[/C][C]3969.80138500097[/C][C]-259.80138500097[/C][/ROW]
[ROW][C]101[/C][C]4056[/C][C]3969.64667125578[/C][C]86.3533287442224[/C][/ROW]
[ROW][C]102[/C][C]4010[/C][C]3906.26514636557[/C][C]103.734853634426[/C][/ROW]
[ROW][C]103[/C][C]3656[/C][C]3706.38893258861[/C][C]-50.3889325886084[/C][/ROW]
[ROW][C]104[/C][C]3884[/C][C]3835.92556407117[/C][C]48.074435928831[/C][/ROW]
[ROW][C]105[/C][C]3886[/C][C]3868.18551988927[/C][C]17.8144801107319[/C][/ROW]
[ROW][C]106[/C][C]3880[/C][C]3847.1233435018[/C][C]32.8766564982006[/C][/ROW]
[ROW][C]107[/C][C]3642[/C][C]3730.37789255755[/C][C]-88.3778925575502[/C][/ROW]
[ROW][C]108[/C][C]3272[/C][C]3546.26069789788[/C][C]-274.260697897884[/C][/ROW]
[ROW][C]109[/C][C]3602[/C][C]3515.21927461847[/C][C]86.7807253815349[/C][/ROW]
[ROW][C]110[/C][C]3198[/C][C]3425.19851864242[/C][C]-227.198518642422[/C][/ROW]
[ROW][C]111[/C][C]3802[/C][C]3518.14645391858[/C][C]283.853546081417[/C][/ROW]
[ROW][C]112[/C][C]3402[/C][C]3699.64589314528[/C][C]-297.645893145281[/C][/ROW]
[ROW][C]113[/C][C]3344[/C][C]3803.02229158993[/C][C]-459.022291589934[/C][/ROW]
[ROW][C]114[/C][C]3508[/C][C]3401.45343209201[/C][C]106.546567907987[/C][/ROW]
[ROW][C]115[/C][C]3426[/C][C]3146.61055057527[/C][C]279.389449424732[/C][/ROW]
[ROW][C]116[/C][C]3394[/C][C]3520.7631427395[/C][C]-126.7631427395[/C][/ROW]
[ROW][C]117[/C][C]3448[/C][C]3431.41414628157[/C][C]16.5858537184345[/C][/ROW]
[ROW][C]118[/C][C]3554[/C][C]3415.12107010499[/C][C]138.87892989501[/C][/ROW]
[ROW][C]119[/C][C]3522[/C][C]3320.70956091014[/C][C]201.290439089864[/C][/ROW]
[ROW][C]120[/C][C]3472[/C][C]3251.17873637349[/C][C]220.821263626512[/C][/ROW]
[ROW][C]121[/C][C]3692[/C][C]3665.87004898446[/C][C]26.1299510155409[/C][/ROW]
[ROW][C]122[/C][C]3690[/C][C]3421.93148187613[/C][C]268.068518123873[/C][/ROW]
[ROW][C]123[/C][C]3802[/C][C]4015.95797121414[/C][C]-213.957971214136[/C][/ROW]
[ROW][C]124[/C][C]3814[/C][C]3668.83481019757[/C][C]145.165189802425[/C][/ROW]
[ROW][C]125[/C][C]3408[/C][C]3992.58074715223[/C][C]-584.580747152233[/C][/ROW]
[ROW][C]126[/C][C]3650[/C][C]3719.90330419262[/C][C]-69.9033041926245[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301439&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301439&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
1333243576.82371794872-252.823717948719
1434063473.87083117413-67.870831174132
1543464325.5273882455620.4726117544433
1640764004.4189654471371.5810345528712
1743104206.43589352351103.564106476491
1841484027.49413363883120.505866361172
1939583727.25674648616230.743253513842
2042964012.17104186926283.828958130739
2143704222.96000116933147.039998830667
2244764201.65443648812274.345563511882
2344064308.8681353200297.1318646799846
2440763944.19560243256131.804397567445
2544304194.34913585455235.650864145454
2645344468.1243340079865.8756659920236
2752005436.81150812914-236.811508129137
2849604971.95874506846-11.9587450684594
2951885132.9675286647855.0324713352165
3049584929.5992393513628.4007606486375
3145544611.75245850354-57.7524585035362
3243104733.92985052952-423.929850529519
3338904447.17192880867-557.171928808665
3442144027.79125811258186.208741887419
3537204014.07301997925-294.07301997925
3636063414.98936830455191.010631695446
3743603740.7841706013619.215829398698
3842624194.4030648020467.5969351979611
3947885052.73854012008-264.738540120085
4047804653.02377826701126.97622173299
4148364926.48025535313-90.4802553531263
4244924621.36723789184-129.367237891839
4345144172.11861573504341.881384264956
4447704411.98386677154358.016133228462
4546644570.2304127392893.7695872607183
4649064835.8242511072370.1757488927733
4746844571.96885330452112.031146695476
4843204408.06696286477-88.0669628647738
4945884715.18194697152-127.181946971524
5043724494.1141093172-122.114109317198
5146745110.2290134592-436.229013459205
5247944746.3770356745347.6229643254719
5345584889.63528682393-331.635286823934
5442604417.83554215258-157.835542152578
5539944124.09760953646-130.097609536459
5633944071.69095794079-677.690957940787
5733343478.25628290777-144.256282907771
5834123584.770925442-172.770925441996
5931983182.8234137454715.1765862545321
6031962884.05615458652311.943845413482
6135363429.51057431176106.489425688242
6232723357.94996332506-85.9499633250612
6335623881.26802817621-319.268028176212
6439003769.45398037434130.546019625658
6537443825.47564799799-81.4756479979892
6638863575.72239298619310.277607013807
6737083587.96624084973120.033759150266
6837003491.99550152893208.004498471073
6938783654.56569071913223.434309280874
7041523982.90146101193169.098538988075
7138303866.15451883554-36.1545188355426
7238643644.21428454536219.785715454635
7338804055.79868445826-175.798684458265
7442303735.02924568385494.970754316153
7543944539.49264736018-145.492647360179
7640764703.08214927872-627.08214927872
7742244202.3496424747521.6503575252518
7840264161.98525529357-135.985255293574
7939503822.2238458684127.776154131596
8040863763.53288416623322.467115833773
8141664004.10513647384161.894863526157
8242704273.55361244625-3.55361244625146
8341623972.15195971169189.848040288309
8440303987.2363313536342.7636686463748
8541284141.33136449908-13.3313644990785
8639584170.1690190695-212.169019069501
8742164292.04064869636-76.0406486963611
8840964322.20717054475-226.207170544747
8941684313.6024622408-145.602462240799
9039484109.52598798401-161.52598798401
9133943850.73518098086-456.735180980857
9236603494.40900734146165.590992658538
9338083576.74434582861231.255654171394
9436843829.10472443827-145.104724438269
9536103509.47032130328100.529678696715
9635983413.9688260058184.0311739942
9739183636.6691044744281.330895525603
9837643778.47892027859-14.4789202785919
9938724075.37568729076-203.375687290765
10037103969.80138500097-259.80138500097
10140563969.6466712557886.3533287442224
10240103906.26514636557103.734853634426
10336563706.38893258861-50.3889325886084
10438843835.9255640711748.074435928831
10538863868.1855198892717.8144801107319
10638803847.123343501832.8766564982006
10736423730.37789255755-88.3778925575502
10832723546.26069789788-274.260697897884
10936023515.2192746184786.7807253815349
11031983425.19851864242-227.198518642422
11138023518.14645391858283.853546081417
11234023699.64589314528-297.645893145281
11333443803.02229158993-459.022291589934
11435083401.45343209201106.546567907987
11534263146.61055057527279.389449424732
11633943520.7631427395-126.7631427395
11734483431.4141462815716.5858537184345
11835543415.12107010499138.87892989501
11935223320.70956091014201.290439089864
12034723251.17873637349220.821263626512
12136923665.8700489844626.1299510155409
12236903421.93148187613268.068518123873
12338024015.95797121414-213.957971214136
12438143668.83481019757145.165189802425
12534083992.58074715223-584.580747152233
12636503719.90330419262-69.9033041926245







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1273417.208414596692960.09024528343874.32658390999
1283465.301624381332924.584027695044006.01922106761
1293508.822125115062895.80171924264121.84253098753
1303527.073754205672849.421544981874204.72596342947
1313367.891696256882631.25676950164104.52662301216
1323178.369407598482387.136500063913969.60231513305
1333381.85962720712539.560385479174224.15886893504
1343210.484936782512320.043186152354100.92668741268
1353457.670766852732521.559122915334393.78241079012
1363377.950525866242398.295735358374357.60531637411
1373341.308269811882319.965033081514362.65150654226
1383627.475524475522566.07997810054688.87107085054

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 3417.20841459669 & 2960.0902452834 & 3874.32658390999 \tabularnewline
128 & 3465.30162438133 & 2924.58402769504 & 4006.01922106761 \tabularnewline
129 & 3508.82212511506 & 2895.8017192426 & 4121.84253098753 \tabularnewline
130 & 3527.07375420567 & 2849.42154498187 & 4204.72596342947 \tabularnewline
131 & 3367.89169625688 & 2631.2567695016 & 4104.52662301216 \tabularnewline
132 & 3178.36940759848 & 2387.13650006391 & 3969.60231513305 \tabularnewline
133 & 3381.8596272071 & 2539.56038547917 & 4224.15886893504 \tabularnewline
134 & 3210.48493678251 & 2320.04318615235 & 4100.92668741268 \tabularnewline
135 & 3457.67076685273 & 2521.55912291533 & 4393.78241079012 \tabularnewline
136 & 3377.95052586624 & 2398.29573535837 & 4357.60531637411 \tabularnewline
137 & 3341.30826981188 & 2319.96503308151 & 4362.65150654226 \tabularnewline
138 & 3627.47552447552 & 2566.0799781005 & 4688.87107085054 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301439&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]3417.20841459669[/C][C]2960.0902452834[/C][C]3874.32658390999[/C][/ROW]
[ROW][C]128[/C][C]3465.30162438133[/C][C]2924.58402769504[/C][C]4006.01922106761[/C][/ROW]
[ROW][C]129[/C][C]3508.82212511506[/C][C]2895.8017192426[/C][C]4121.84253098753[/C][/ROW]
[ROW][C]130[/C][C]3527.07375420567[/C][C]2849.42154498187[/C][C]4204.72596342947[/C][/ROW]
[ROW][C]131[/C][C]3367.89169625688[/C][C]2631.2567695016[/C][C]4104.52662301216[/C][/ROW]
[ROW][C]132[/C][C]3178.36940759848[/C][C]2387.13650006391[/C][C]3969.60231513305[/C][/ROW]
[ROW][C]133[/C][C]3381.8596272071[/C][C]2539.56038547917[/C][C]4224.15886893504[/C][/ROW]
[ROW][C]134[/C][C]3210.48493678251[/C][C]2320.04318615235[/C][C]4100.92668741268[/C][/ROW]
[ROW][C]135[/C][C]3457.67076685273[/C][C]2521.55912291533[/C][C]4393.78241079012[/C][/ROW]
[ROW][C]136[/C][C]3377.95052586624[/C][C]2398.29573535837[/C][C]4357.60531637411[/C][/ROW]
[ROW][C]137[/C][C]3341.30826981188[/C][C]2319.96503308151[/C][C]4362.65150654226[/C][/ROW]
[ROW][C]138[/C][C]3627.47552447552[/C][C]2566.0799781005[/C][C]4688.87107085054[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301439&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301439&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
1273417.208414596692960.09024528343874.32658390999
1283465.301624381332924.584027695044006.01922106761
1293508.822125115062895.80171924264121.84253098753
1303527.073754205672849.421544981874204.72596342947
1313367.891696256882631.25676950164104.52662301216
1323178.369407598482387.136500063913969.60231513305
1333381.85962720712539.560385479174224.15886893504
1343210.484936782512320.043186152354100.92668741268
1353457.670766852732521.559122915334393.78241079012
1363377.950525866242398.295735358374357.60531637411
1373341.308269811882319.965033081514362.65150654226
1383627.475524475522566.07997810054688.87107085054



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; 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')