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 computationFri, 23 Dec 2016 11:45:18 +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/23/t148249006789fxn4u0i1ahna4.htm/, Retrieved Tue, 07 May 2024 21:55:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302855, Retrieved Tue, 07 May 2024 21:55:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [ggg] [2016-12-23 10:45:18] [bb262dce3bb40077245e847c94886178] [Current]
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Dataseries X:
3710
3480
4024
4154
4142
4122
4228
4122
3938
3976
3952
4072
3756
3378
4250
3888
4116
4216
4214
4320
4056
4104
3976
4258
3892
3628
4056
4022
4294
4282
4250
4418
3966
4184
4094
4074
3950
3700
4148
4192
4394
4216
4366
4512
3996
4292
4074
4228
4044
3634
4330
4282
4428
4346
4632
4634
4156
4512
4142
4442
4064
3818
4334
4404
4644
4542
4718
4568
4338
4544
4302
4506
4164
4096
4556
4472
4548
4710
4660
4702
4460
4524
4440
4566
4196
3996
4616
4312
4592
4684
4542
4810
4360
4540
4428
4606
4130
4034
4564
4286
4578
4530
4666
4852
4164
4494
4356
4338
4130
3840
4362
4296
4626
4490
4708
4686
4266
4528
4216
4488
4268
4052
4438
4354
4558
4494




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=302855&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=302855&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302855&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
alpha0.159813145991518
beta0
gamma0.520902997312891

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.159813145991518 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.520902997312891 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302855&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]0.159813145991518[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.520902997312891[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302855&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302855&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
alpha0.159813145991518
beta0
gamma0.520902997312891







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1337563760.96688034188-4.96688034188082
1433783378.18417982975-0.184179829753703
1542504240.66581773289.3341822671955
1638883873.5852816939214.4147183060777
1741164101.233348769414.766651230595
1842164198.5209926860617.4790073139357
1942144258.32544009479-44.3254400947853
2043204151.25272432685168.747275673149
2140563992.7318295907563.2681704092511
2241044046.1873205393857.812679460616
2339764047.27095231659-71.2709523165895
2442584156.72532280347101.27467719653
2538923855.0809689292936.9190310707072
2636283481.08536455332146.914635446677
2740564371.24109375676-315.241093756765
2840223954.5126880668167.4873119331946
2942944190.79647879919103.203521200815
3042824303.40457563609-21.404575636092
3142504329.94583732734-79.9458373273446
3244184310.43303446588107.56696553412
3339664095.97117436358-129.971174363575
3441844116.156850163467.8431498365999
3540944062.3492763088731.650723691132
3640744263.76748787353-189.76748787353
3739503887.4451449400562.5548550599478
3837003565.68670203646134.313297963537
3941484251.5634130992-103.563413099205
4041924036.16720941546155.832790584537
4143944302.2011769708991.7988230291076
4242164358.45119050659-142.451190506586
4343664340.0266861856625.9733138143392
4445124419.5072313153692.492768684644
4539964098.67635973485-102.676359734846
4642924209.7987020397182.2012979602869
4740744142.44592195906-68.4459219590635
4842284230.96239796827-2.96239796826922
4940443994.9243137505949.07568624941
5036343702.41722483758-68.4172248375758
5143304251.7867989553678.2132010446394
5242824178.96715399981103.032846000186
5344284408.538155768119.4618442318997
5443464350.70688023399-4.70688023399362
5546324428.00769717319203.992302826806
5646344565.0506455829868.94935441702
5741564155.040316000290.959683999707522
5845124363.63784901984148.36215098016
5941424240.92680583409-98.9268058340931
6044424353.2312832882288.7687167117829
6140644154.62780910245-90.6278091024542
6238183788.3728051551829.6271948448175
6343344417.58483018618-83.5848301861797
6444044329.7701956679274.2298043320825
6546444518.16275487239125.837245127609
6645424466.7540831485675.2459168514351
6747184648.1708265936169.8291734063941
6845684704.67040676679-136.670406766785
6943384232.04325923579105.956740764214
7045444521.9322542770922.0677457229122
7143024270.8102461384331.1897538615731
7245064486.0551039084619.9448960915397
7341644197.93873933821-33.9387393382149
7440963893.37370000945202.626299990553
7545564500.685351179455.3146488205975
7644724504.13717747806-32.1371774780564
7745484698.11719308621-150.117193086209
7847104580.46578363365129.534216366351
7946604768.18784155502-108.187841555016
8047024705.86221312706-3.86221312706311
8144604360.6467514557199.3532485442893
8245244612.76591215373-88.7659121537345
8344404347.9235286987692.0764713012377
8445664567.9775065402-1.97750654020092
8541964252.77516554263-56.77516554263
8639964048.09463859815-52.0946385981542
8746164550.2267292327565.7732707672458
8843124517.07617738603-205.076177386033
8945924631.78362327468-39.7836232746786
9046844654.1560441852929.8439558147074
9145424721.90583848771-179.905838487711
9248104693.77745299015116.22254700985
9343604412.92596529021-52.925965290211
9445404558.37745447507-18.3774544750713
9544284383.9307990307644.0692009692384
9646064555.1493102996250.8506897003836
9741304224.40709348113-94.4070934811298
9840344015.7609497440118.2390502559888
9945644580.71886859014-16.7188685901419
10042864415.84614282902-129.846142829025
10145784614.91759057344-36.9175905734401
10245304668.22095853507-138.220958535067
10346664617.313545515148.6864544848977
10448524755.3195339355996.6804660644084
10541644397.31612877959-233.31612877959
10644944529.05925631753-35.0592563175287
10743564379.27677374282-23.2767737428203
10843384542.70047114174-204.700471141741
10941304107.5449006991222.4550993008806
11038403966.87511548707-126.875115487072
11143624493.3423452716-131.342345271602
11242964260.6404676694535.3595323305544
11346264526.7846786751199.2153213248866
11444904557.50786389077-67.5078638907735
11547084599.70245580917108.297544190834
11646864768.23993997096-82.2399399709648
11742664237.2177614473728.7822385526324
11845284497.6159337738530.3840662261537
11942164363.44882689187-147.448826891875
12044884427.627055236760.3729447633023
12142684134.24966569916133.750334300843
12240523946.0110799596105.988920040399
12344384507.73793459908-69.7379345990794
12443544357.83930370469-3.83930370469079
12545584645.66588504959-87.6658850495924
12644944573.55561931491-79.5556193149068

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3756 & 3760.96688034188 & -4.96688034188082 \tabularnewline
14 & 3378 & 3378.18417982975 & -0.184179829753703 \tabularnewline
15 & 4250 & 4240.6658177328 & 9.3341822671955 \tabularnewline
16 & 3888 & 3873.58528169392 & 14.4147183060777 \tabularnewline
17 & 4116 & 4101.2333487694 & 14.766651230595 \tabularnewline
18 & 4216 & 4198.52099268606 & 17.4790073139357 \tabularnewline
19 & 4214 & 4258.32544009479 & -44.3254400947853 \tabularnewline
20 & 4320 & 4151.25272432685 & 168.747275673149 \tabularnewline
21 & 4056 & 3992.73182959075 & 63.2681704092511 \tabularnewline
22 & 4104 & 4046.18732053938 & 57.812679460616 \tabularnewline
23 & 3976 & 4047.27095231659 & -71.2709523165895 \tabularnewline
24 & 4258 & 4156.72532280347 & 101.27467719653 \tabularnewline
25 & 3892 & 3855.08096892929 & 36.9190310707072 \tabularnewline
26 & 3628 & 3481.08536455332 & 146.914635446677 \tabularnewline
27 & 4056 & 4371.24109375676 & -315.241093756765 \tabularnewline
28 & 4022 & 3954.51268806681 & 67.4873119331946 \tabularnewline
29 & 4294 & 4190.79647879919 & 103.203521200815 \tabularnewline
30 & 4282 & 4303.40457563609 & -21.404575636092 \tabularnewline
31 & 4250 & 4329.94583732734 & -79.9458373273446 \tabularnewline
32 & 4418 & 4310.43303446588 & 107.56696553412 \tabularnewline
33 & 3966 & 4095.97117436358 & -129.971174363575 \tabularnewline
34 & 4184 & 4116.1568501634 & 67.8431498365999 \tabularnewline
35 & 4094 & 4062.34927630887 & 31.650723691132 \tabularnewline
36 & 4074 & 4263.76748787353 & -189.76748787353 \tabularnewline
37 & 3950 & 3887.44514494005 & 62.5548550599478 \tabularnewline
38 & 3700 & 3565.68670203646 & 134.313297963537 \tabularnewline
39 & 4148 & 4251.5634130992 & -103.563413099205 \tabularnewline
40 & 4192 & 4036.16720941546 & 155.832790584537 \tabularnewline
41 & 4394 & 4302.20117697089 & 91.7988230291076 \tabularnewline
42 & 4216 & 4358.45119050659 & -142.451190506586 \tabularnewline
43 & 4366 & 4340.02668618566 & 25.9733138143392 \tabularnewline
44 & 4512 & 4419.50723131536 & 92.492768684644 \tabularnewline
45 & 3996 & 4098.67635973485 & -102.676359734846 \tabularnewline
46 & 4292 & 4209.79870203971 & 82.2012979602869 \tabularnewline
47 & 4074 & 4142.44592195906 & -68.4459219590635 \tabularnewline
48 & 4228 & 4230.96239796827 & -2.96239796826922 \tabularnewline
49 & 4044 & 3994.92431375059 & 49.07568624941 \tabularnewline
50 & 3634 & 3702.41722483758 & -68.4172248375758 \tabularnewline
51 & 4330 & 4251.78679895536 & 78.2132010446394 \tabularnewline
52 & 4282 & 4178.96715399981 & 103.032846000186 \tabularnewline
53 & 4428 & 4408.5381557681 & 19.4618442318997 \tabularnewline
54 & 4346 & 4350.70688023399 & -4.70688023399362 \tabularnewline
55 & 4632 & 4428.00769717319 & 203.992302826806 \tabularnewline
56 & 4634 & 4565.05064558298 & 68.94935441702 \tabularnewline
57 & 4156 & 4155.04031600029 & 0.959683999707522 \tabularnewline
58 & 4512 & 4363.63784901984 & 148.36215098016 \tabularnewline
59 & 4142 & 4240.92680583409 & -98.9268058340931 \tabularnewline
60 & 4442 & 4353.23128328822 & 88.7687167117829 \tabularnewline
61 & 4064 & 4154.62780910245 & -90.6278091024542 \tabularnewline
62 & 3818 & 3788.37280515518 & 29.6271948448175 \tabularnewline
63 & 4334 & 4417.58483018618 & -83.5848301861797 \tabularnewline
64 & 4404 & 4329.77019566792 & 74.2298043320825 \tabularnewline
65 & 4644 & 4518.16275487239 & 125.837245127609 \tabularnewline
66 & 4542 & 4466.75408314856 & 75.2459168514351 \tabularnewline
67 & 4718 & 4648.17082659361 & 69.8291734063941 \tabularnewline
68 & 4568 & 4704.67040676679 & -136.670406766785 \tabularnewline
69 & 4338 & 4232.04325923579 & 105.956740764214 \tabularnewline
70 & 4544 & 4521.93225427709 & 22.0677457229122 \tabularnewline
71 & 4302 & 4270.81024613843 & 31.1897538615731 \tabularnewline
72 & 4506 & 4486.05510390846 & 19.9448960915397 \tabularnewline
73 & 4164 & 4197.93873933821 & -33.9387393382149 \tabularnewline
74 & 4096 & 3893.37370000945 & 202.626299990553 \tabularnewline
75 & 4556 & 4500.6853511794 & 55.3146488205975 \tabularnewline
76 & 4472 & 4504.13717747806 & -32.1371774780564 \tabularnewline
77 & 4548 & 4698.11719308621 & -150.117193086209 \tabularnewline
78 & 4710 & 4580.46578363365 & 129.534216366351 \tabularnewline
79 & 4660 & 4768.18784155502 & -108.187841555016 \tabularnewline
80 & 4702 & 4705.86221312706 & -3.86221312706311 \tabularnewline
81 & 4460 & 4360.64675145571 & 99.3532485442893 \tabularnewline
82 & 4524 & 4612.76591215373 & -88.7659121537345 \tabularnewline
83 & 4440 & 4347.92352869876 & 92.0764713012377 \tabularnewline
84 & 4566 & 4567.9775065402 & -1.97750654020092 \tabularnewline
85 & 4196 & 4252.77516554263 & -56.77516554263 \tabularnewline
86 & 3996 & 4048.09463859815 & -52.0946385981542 \tabularnewline
87 & 4616 & 4550.22672923275 & 65.7732707672458 \tabularnewline
88 & 4312 & 4517.07617738603 & -205.076177386033 \tabularnewline
89 & 4592 & 4631.78362327468 & -39.7836232746786 \tabularnewline
90 & 4684 & 4654.15604418529 & 29.8439558147074 \tabularnewline
91 & 4542 & 4721.90583848771 & -179.905838487711 \tabularnewline
92 & 4810 & 4693.77745299015 & 116.22254700985 \tabularnewline
93 & 4360 & 4412.92596529021 & -52.925965290211 \tabularnewline
94 & 4540 & 4558.37745447507 & -18.3774544750713 \tabularnewline
95 & 4428 & 4383.93079903076 & 44.0692009692384 \tabularnewline
96 & 4606 & 4555.14931029962 & 50.8506897003836 \tabularnewline
97 & 4130 & 4224.40709348113 & -94.4070934811298 \tabularnewline
98 & 4034 & 4015.76094974401 & 18.2390502559888 \tabularnewline
99 & 4564 & 4580.71886859014 & -16.7188685901419 \tabularnewline
100 & 4286 & 4415.84614282902 & -129.846142829025 \tabularnewline
101 & 4578 & 4614.91759057344 & -36.9175905734401 \tabularnewline
102 & 4530 & 4668.22095853507 & -138.220958535067 \tabularnewline
103 & 4666 & 4617.3135455151 & 48.6864544848977 \tabularnewline
104 & 4852 & 4755.31953393559 & 96.6804660644084 \tabularnewline
105 & 4164 & 4397.31612877959 & -233.31612877959 \tabularnewline
106 & 4494 & 4529.05925631753 & -35.0592563175287 \tabularnewline
107 & 4356 & 4379.27677374282 & -23.2767737428203 \tabularnewline
108 & 4338 & 4542.70047114174 & -204.700471141741 \tabularnewline
109 & 4130 & 4107.54490069912 & 22.4550993008806 \tabularnewline
110 & 3840 & 3966.87511548707 & -126.875115487072 \tabularnewline
111 & 4362 & 4493.3423452716 & -131.342345271602 \tabularnewline
112 & 4296 & 4260.64046766945 & 35.3595323305544 \tabularnewline
113 & 4626 & 4526.78467867511 & 99.2153213248866 \tabularnewline
114 & 4490 & 4557.50786389077 & -67.5078638907735 \tabularnewline
115 & 4708 & 4599.70245580917 & 108.297544190834 \tabularnewline
116 & 4686 & 4768.23993997096 & -82.2399399709648 \tabularnewline
117 & 4266 & 4237.21776144737 & 28.7822385526324 \tabularnewline
118 & 4528 & 4497.61593377385 & 30.3840662261537 \tabularnewline
119 & 4216 & 4363.44882689187 & -147.448826891875 \tabularnewline
120 & 4488 & 4427.6270552367 & 60.3729447633023 \tabularnewline
121 & 4268 & 4134.24966569916 & 133.750334300843 \tabularnewline
122 & 4052 & 3946.0110799596 & 105.988920040399 \tabularnewline
123 & 4438 & 4507.73793459908 & -69.7379345990794 \tabularnewline
124 & 4354 & 4357.83930370469 & -3.83930370469079 \tabularnewline
125 & 4558 & 4645.66588504959 & -87.6658850495924 \tabularnewline
126 & 4494 & 4573.55561931491 & -79.5556193149068 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302855&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]3756[/C][C]3760.96688034188[/C][C]-4.96688034188082[/C][/ROW]
[ROW][C]14[/C][C]3378[/C][C]3378.18417982975[/C][C]-0.184179829753703[/C][/ROW]
[ROW][C]15[/C][C]4250[/C][C]4240.6658177328[/C][C]9.3341822671955[/C][/ROW]
[ROW][C]16[/C][C]3888[/C][C]3873.58528169392[/C][C]14.4147183060777[/C][/ROW]
[ROW][C]17[/C][C]4116[/C][C]4101.2333487694[/C][C]14.766651230595[/C][/ROW]
[ROW][C]18[/C][C]4216[/C][C]4198.52099268606[/C][C]17.4790073139357[/C][/ROW]
[ROW][C]19[/C][C]4214[/C][C]4258.32544009479[/C][C]-44.3254400947853[/C][/ROW]
[ROW][C]20[/C][C]4320[/C][C]4151.25272432685[/C][C]168.747275673149[/C][/ROW]
[ROW][C]21[/C][C]4056[/C][C]3992.73182959075[/C][C]63.2681704092511[/C][/ROW]
[ROW][C]22[/C][C]4104[/C][C]4046.18732053938[/C][C]57.812679460616[/C][/ROW]
[ROW][C]23[/C][C]3976[/C][C]4047.27095231659[/C][C]-71.2709523165895[/C][/ROW]
[ROW][C]24[/C][C]4258[/C][C]4156.72532280347[/C][C]101.27467719653[/C][/ROW]
[ROW][C]25[/C][C]3892[/C][C]3855.08096892929[/C][C]36.9190310707072[/C][/ROW]
[ROW][C]26[/C][C]3628[/C][C]3481.08536455332[/C][C]146.914635446677[/C][/ROW]
[ROW][C]27[/C][C]4056[/C][C]4371.24109375676[/C][C]-315.241093756765[/C][/ROW]
[ROW][C]28[/C][C]4022[/C][C]3954.51268806681[/C][C]67.4873119331946[/C][/ROW]
[ROW][C]29[/C][C]4294[/C][C]4190.79647879919[/C][C]103.203521200815[/C][/ROW]
[ROW][C]30[/C][C]4282[/C][C]4303.40457563609[/C][C]-21.404575636092[/C][/ROW]
[ROW][C]31[/C][C]4250[/C][C]4329.94583732734[/C][C]-79.9458373273446[/C][/ROW]
[ROW][C]32[/C][C]4418[/C][C]4310.43303446588[/C][C]107.56696553412[/C][/ROW]
[ROW][C]33[/C][C]3966[/C][C]4095.97117436358[/C][C]-129.971174363575[/C][/ROW]
[ROW][C]34[/C][C]4184[/C][C]4116.1568501634[/C][C]67.8431498365999[/C][/ROW]
[ROW][C]35[/C][C]4094[/C][C]4062.34927630887[/C][C]31.650723691132[/C][/ROW]
[ROW][C]36[/C][C]4074[/C][C]4263.76748787353[/C][C]-189.76748787353[/C][/ROW]
[ROW][C]37[/C][C]3950[/C][C]3887.44514494005[/C][C]62.5548550599478[/C][/ROW]
[ROW][C]38[/C][C]3700[/C][C]3565.68670203646[/C][C]134.313297963537[/C][/ROW]
[ROW][C]39[/C][C]4148[/C][C]4251.5634130992[/C][C]-103.563413099205[/C][/ROW]
[ROW][C]40[/C][C]4192[/C][C]4036.16720941546[/C][C]155.832790584537[/C][/ROW]
[ROW][C]41[/C][C]4394[/C][C]4302.20117697089[/C][C]91.7988230291076[/C][/ROW]
[ROW][C]42[/C][C]4216[/C][C]4358.45119050659[/C][C]-142.451190506586[/C][/ROW]
[ROW][C]43[/C][C]4366[/C][C]4340.02668618566[/C][C]25.9733138143392[/C][/ROW]
[ROW][C]44[/C][C]4512[/C][C]4419.50723131536[/C][C]92.492768684644[/C][/ROW]
[ROW][C]45[/C][C]3996[/C][C]4098.67635973485[/C][C]-102.676359734846[/C][/ROW]
[ROW][C]46[/C][C]4292[/C][C]4209.79870203971[/C][C]82.2012979602869[/C][/ROW]
[ROW][C]47[/C][C]4074[/C][C]4142.44592195906[/C][C]-68.4459219590635[/C][/ROW]
[ROW][C]48[/C][C]4228[/C][C]4230.96239796827[/C][C]-2.96239796826922[/C][/ROW]
[ROW][C]49[/C][C]4044[/C][C]3994.92431375059[/C][C]49.07568624941[/C][/ROW]
[ROW][C]50[/C][C]3634[/C][C]3702.41722483758[/C][C]-68.4172248375758[/C][/ROW]
[ROW][C]51[/C][C]4330[/C][C]4251.78679895536[/C][C]78.2132010446394[/C][/ROW]
[ROW][C]52[/C][C]4282[/C][C]4178.96715399981[/C][C]103.032846000186[/C][/ROW]
[ROW][C]53[/C][C]4428[/C][C]4408.5381557681[/C][C]19.4618442318997[/C][/ROW]
[ROW][C]54[/C][C]4346[/C][C]4350.70688023399[/C][C]-4.70688023399362[/C][/ROW]
[ROW][C]55[/C][C]4632[/C][C]4428.00769717319[/C][C]203.992302826806[/C][/ROW]
[ROW][C]56[/C][C]4634[/C][C]4565.05064558298[/C][C]68.94935441702[/C][/ROW]
[ROW][C]57[/C][C]4156[/C][C]4155.04031600029[/C][C]0.959683999707522[/C][/ROW]
[ROW][C]58[/C][C]4512[/C][C]4363.63784901984[/C][C]148.36215098016[/C][/ROW]
[ROW][C]59[/C][C]4142[/C][C]4240.92680583409[/C][C]-98.9268058340931[/C][/ROW]
[ROW][C]60[/C][C]4442[/C][C]4353.23128328822[/C][C]88.7687167117829[/C][/ROW]
[ROW][C]61[/C][C]4064[/C][C]4154.62780910245[/C][C]-90.6278091024542[/C][/ROW]
[ROW][C]62[/C][C]3818[/C][C]3788.37280515518[/C][C]29.6271948448175[/C][/ROW]
[ROW][C]63[/C][C]4334[/C][C]4417.58483018618[/C][C]-83.5848301861797[/C][/ROW]
[ROW][C]64[/C][C]4404[/C][C]4329.77019566792[/C][C]74.2298043320825[/C][/ROW]
[ROW][C]65[/C][C]4644[/C][C]4518.16275487239[/C][C]125.837245127609[/C][/ROW]
[ROW][C]66[/C][C]4542[/C][C]4466.75408314856[/C][C]75.2459168514351[/C][/ROW]
[ROW][C]67[/C][C]4718[/C][C]4648.17082659361[/C][C]69.8291734063941[/C][/ROW]
[ROW][C]68[/C][C]4568[/C][C]4704.67040676679[/C][C]-136.670406766785[/C][/ROW]
[ROW][C]69[/C][C]4338[/C][C]4232.04325923579[/C][C]105.956740764214[/C][/ROW]
[ROW][C]70[/C][C]4544[/C][C]4521.93225427709[/C][C]22.0677457229122[/C][/ROW]
[ROW][C]71[/C][C]4302[/C][C]4270.81024613843[/C][C]31.1897538615731[/C][/ROW]
[ROW][C]72[/C][C]4506[/C][C]4486.05510390846[/C][C]19.9448960915397[/C][/ROW]
[ROW][C]73[/C][C]4164[/C][C]4197.93873933821[/C][C]-33.9387393382149[/C][/ROW]
[ROW][C]74[/C][C]4096[/C][C]3893.37370000945[/C][C]202.626299990553[/C][/ROW]
[ROW][C]75[/C][C]4556[/C][C]4500.6853511794[/C][C]55.3146488205975[/C][/ROW]
[ROW][C]76[/C][C]4472[/C][C]4504.13717747806[/C][C]-32.1371774780564[/C][/ROW]
[ROW][C]77[/C][C]4548[/C][C]4698.11719308621[/C][C]-150.117193086209[/C][/ROW]
[ROW][C]78[/C][C]4710[/C][C]4580.46578363365[/C][C]129.534216366351[/C][/ROW]
[ROW][C]79[/C][C]4660[/C][C]4768.18784155502[/C][C]-108.187841555016[/C][/ROW]
[ROW][C]80[/C][C]4702[/C][C]4705.86221312706[/C][C]-3.86221312706311[/C][/ROW]
[ROW][C]81[/C][C]4460[/C][C]4360.64675145571[/C][C]99.3532485442893[/C][/ROW]
[ROW][C]82[/C][C]4524[/C][C]4612.76591215373[/C][C]-88.7659121537345[/C][/ROW]
[ROW][C]83[/C][C]4440[/C][C]4347.92352869876[/C][C]92.0764713012377[/C][/ROW]
[ROW][C]84[/C][C]4566[/C][C]4567.9775065402[/C][C]-1.97750654020092[/C][/ROW]
[ROW][C]85[/C][C]4196[/C][C]4252.77516554263[/C][C]-56.77516554263[/C][/ROW]
[ROW][C]86[/C][C]3996[/C][C]4048.09463859815[/C][C]-52.0946385981542[/C][/ROW]
[ROW][C]87[/C][C]4616[/C][C]4550.22672923275[/C][C]65.7732707672458[/C][/ROW]
[ROW][C]88[/C][C]4312[/C][C]4517.07617738603[/C][C]-205.076177386033[/C][/ROW]
[ROW][C]89[/C][C]4592[/C][C]4631.78362327468[/C][C]-39.7836232746786[/C][/ROW]
[ROW][C]90[/C][C]4684[/C][C]4654.15604418529[/C][C]29.8439558147074[/C][/ROW]
[ROW][C]91[/C][C]4542[/C][C]4721.90583848771[/C][C]-179.905838487711[/C][/ROW]
[ROW][C]92[/C][C]4810[/C][C]4693.77745299015[/C][C]116.22254700985[/C][/ROW]
[ROW][C]93[/C][C]4360[/C][C]4412.92596529021[/C][C]-52.925965290211[/C][/ROW]
[ROW][C]94[/C][C]4540[/C][C]4558.37745447507[/C][C]-18.3774544750713[/C][/ROW]
[ROW][C]95[/C][C]4428[/C][C]4383.93079903076[/C][C]44.0692009692384[/C][/ROW]
[ROW][C]96[/C][C]4606[/C][C]4555.14931029962[/C][C]50.8506897003836[/C][/ROW]
[ROW][C]97[/C][C]4130[/C][C]4224.40709348113[/C][C]-94.4070934811298[/C][/ROW]
[ROW][C]98[/C][C]4034[/C][C]4015.76094974401[/C][C]18.2390502559888[/C][/ROW]
[ROW][C]99[/C][C]4564[/C][C]4580.71886859014[/C][C]-16.7188685901419[/C][/ROW]
[ROW][C]100[/C][C]4286[/C][C]4415.84614282902[/C][C]-129.846142829025[/C][/ROW]
[ROW][C]101[/C][C]4578[/C][C]4614.91759057344[/C][C]-36.9175905734401[/C][/ROW]
[ROW][C]102[/C][C]4530[/C][C]4668.22095853507[/C][C]-138.220958535067[/C][/ROW]
[ROW][C]103[/C][C]4666[/C][C]4617.3135455151[/C][C]48.6864544848977[/C][/ROW]
[ROW][C]104[/C][C]4852[/C][C]4755.31953393559[/C][C]96.6804660644084[/C][/ROW]
[ROW][C]105[/C][C]4164[/C][C]4397.31612877959[/C][C]-233.31612877959[/C][/ROW]
[ROW][C]106[/C][C]4494[/C][C]4529.05925631753[/C][C]-35.0592563175287[/C][/ROW]
[ROW][C]107[/C][C]4356[/C][C]4379.27677374282[/C][C]-23.2767737428203[/C][/ROW]
[ROW][C]108[/C][C]4338[/C][C]4542.70047114174[/C][C]-204.700471141741[/C][/ROW]
[ROW][C]109[/C][C]4130[/C][C]4107.54490069912[/C][C]22.4550993008806[/C][/ROW]
[ROW][C]110[/C][C]3840[/C][C]3966.87511548707[/C][C]-126.875115487072[/C][/ROW]
[ROW][C]111[/C][C]4362[/C][C]4493.3423452716[/C][C]-131.342345271602[/C][/ROW]
[ROW][C]112[/C][C]4296[/C][C]4260.64046766945[/C][C]35.3595323305544[/C][/ROW]
[ROW][C]113[/C][C]4626[/C][C]4526.78467867511[/C][C]99.2153213248866[/C][/ROW]
[ROW][C]114[/C][C]4490[/C][C]4557.50786389077[/C][C]-67.5078638907735[/C][/ROW]
[ROW][C]115[/C][C]4708[/C][C]4599.70245580917[/C][C]108.297544190834[/C][/ROW]
[ROW][C]116[/C][C]4686[/C][C]4768.23993997096[/C][C]-82.2399399709648[/C][/ROW]
[ROW][C]117[/C][C]4266[/C][C]4237.21776144737[/C][C]28.7822385526324[/C][/ROW]
[ROW][C]118[/C][C]4528[/C][C]4497.61593377385[/C][C]30.3840662261537[/C][/ROW]
[ROW][C]119[/C][C]4216[/C][C]4363.44882689187[/C][C]-147.448826891875[/C][/ROW]
[ROW][C]120[/C][C]4488[/C][C]4427.6270552367[/C][C]60.3729447633023[/C][/ROW]
[ROW][C]121[/C][C]4268[/C][C]4134.24966569916[/C][C]133.750334300843[/C][/ROW]
[ROW][C]122[/C][C]4052[/C][C]3946.0110799596[/C][C]105.988920040399[/C][/ROW]
[ROW][C]123[/C][C]4438[/C][C]4507.73793459908[/C][C]-69.7379345990794[/C][/ROW]
[ROW][C]124[/C][C]4354[/C][C]4357.83930370469[/C][C]-3.83930370469079[/C][/ROW]
[ROW][C]125[/C][C]4558[/C][C]4645.66588504959[/C][C]-87.6658850495924[/C][/ROW]
[ROW][C]126[/C][C]4494[/C][C]4573.55561931491[/C][C]-79.5556193149068[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302855&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302855&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
1337563760.96688034188-4.96688034188082
1433783378.18417982975-0.184179829753703
1542504240.66581773289.3341822671955
1638883873.5852816939214.4147183060777
1741164101.233348769414.766651230595
1842164198.5209926860617.4790073139357
1942144258.32544009479-44.3254400947853
2043204151.25272432685168.747275673149
2140563992.7318295907563.2681704092511
2241044046.1873205393857.812679460616
2339764047.27095231659-71.2709523165895
2442584156.72532280347101.27467719653
2538923855.0809689292936.9190310707072
2636283481.08536455332146.914635446677
2740564371.24109375676-315.241093756765
2840223954.5126880668167.4873119331946
2942944190.79647879919103.203521200815
3042824303.40457563609-21.404575636092
3142504329.94583732734-79.9458373273446
3244184310.43303446588107.56696553412
3339664095.97117436358-129.971174363575
3441844116.156850163467.8431498365999
3540944062.3492763088731.650723691132
3640744263.76748787353-189.76748787353
3739503887.4451449400562.5548550599478
3837003565.68670203646134.313297963537
3941484251.5634130992-103.563413099205
4041924036.16720941546155.832790584537
4143944302.2011769708991.7988230291076
4242164358.45119050659-142.451190506586
4343664340.0266861856625.9733138143392
4445124419.5072313153692.492768684644
4539964098.67635973485-102.676359734846
4642924209.7987020397182.2012979602869
4740744142.44592195906-68.4459219590635
4842284230.96239796827-2.96239796826922
4940443994.9243137505949.07568624941
5036343702.41722483758-68.4172248375758
5143304251.7867989553678.2132010446394
5242824178.96715399981103.032846000186
5344284408.538155768119.4618442318997
5443464350.70688023399-4.70688023399362
5546324428.00769717319203.992302826806
5646344565.0506455829868.94935441702
5741564155.040316000290.959683999707522
5845124363.63784901984148.36215098016
5941424240.92680583409-98.9268058340931
6044424353.2312832882288.7687167117829
6140644154.62780910245-90.6278091024542
6238183788.3728051551829.6271948448175
6343344417.58483018618-83.5848301861797
6444044329.7701956679274.2298043320825
6546444518.16275487239125.837245127609
6645424466.7540831485675.2459168514351
6747184648.1708265936169.8291734063941
6845684704.67040676679-136.670406766785
6943384232.04325923579105.956740764214
7045444521.9322542770922.0677457229122
7143024270.8102461384331.1897538615731
7245064486.0551039084619.9448960915397
7341644197.93873933821-33.9387393382149
7440963893.37370000945202.626299990553
7545564500.685351179455.3146488205975
7644724504.13717747806-32.1371774780564
7745484698.11719308621-150.117193086209
7847104580.46578363365129.534216366351
7946604768.18784155502-108.187841555016
8047024705.86221312706-3.86221312706311
8144604360.6467514557199.3532485442893
8245244612.76591215373-88.7659121537345
8344404347.9235286987692.0764713012377
8445664567.9775065402-1.97750654020092
8541964252.77516554263-56.77516554263
8639964048.09463859815-52.0946385981542
8746164550.2267292327565.7732707672458
8843124517.07617738603-205.076177386033
8945924631.78362327468-39.7836232746786
9046844654.1560441852929.8439558147074
9145424721.90583848771-179.905838487711
9248104693.77745299015116.22254700985
9343604412.92596529021-52.925965290211
9445404558.37745447507-18.3774544750713
9544284383.9307990307644.0692009692384
9646064555.1493102996250.8506897003836
9741304224.40709348113-94.4070934811298
9840344015.7609497440118.2390502559888
9945644580.71886859014-16.7188685901419
10042864415.84614282902-129.846142829025
10145784614.91759057344-36.9175905734401
10245304668.22095853507-138.220958535067
10346664617.313545515148.6864544848977
10448524755.3195339355996.6804660644084
10541644397.31612877959-233.31612877959
10644944529.05925631753-35.0592563175287
10743564379.27677374282-23.2767737428203
10843384542.70047114174-204.700471141741
10941304107.5449006991222.4550993008806
11038403966.87511548707-126.875115487072
11143624493.3423452716-131.342345271602
11242964260.6404676694535.3595323305544
11346264526.7846786751199.2153213248866
11444904557.50786389077-67.5078638907735
11547084599.70245580917108.297544190834
11646864768.23993997096-82.2399399709648
11742664237.2177614473728.7822385526324
11845284497.6159337738530.3840662261537
11942164363.44882689187-147.448826891875
12044884427.627055236760.3729447633023
12142684134.24966569916133.750334300843
12240523946.0110799596105.988920040399
12344384507.73793459908-69.7379345990794
12443544357.83930370469-3.83930370469079
12545584645.66588504959-87.6658850495924
12644944573.55561931491-79.5556193149068







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1274690.767086943124496.788434167274884.74573971896
1284758.607355171014562.167189380834955.04752096119
1294289.317706152644090.446492200954488.18892010433
1304545.817147640244344.544246479754747.09004880074
1314328.964661452274125.318395234334532.6109276702
1324507.661564933224301.669276855614713.65385301083
1334236.749828989914028.43793842584445.06171955402
1344014.986236177533804.380289553664225.5921828014
1354482.866782032354269.991499868644695.74206419607
1364372.954111215754157.833431690924588.07479074057
1374624.707070006424407.364189372694842.04995064014
1384570.156470405994350.61388053994789.69906027208

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 4690.76708694312 & 4496.78843416727 & 4884.74573971896 \tabularnewline
128 & 4758.60735517101 & 4562.16718938083 & 4955.04752096119 \tabularnewline
129 & 4289.31770615264 & 4090.44649220095 & 4488.18892010433 \tabularnewline
130 & 4545.81714764024 & 4344.54424647975 & 4747.09004880074 \tabularnewline
131 & 4328.96466145227 & 4125.31839523433 & 4532.6109276702 \tabularnewline
132 & 4507.66156493322 & 4301.66927685561 & 4713.65385301083 \tabularnewline
133 & 4236.74982898991 & 4028.4379384258 & 4445.06171955402 \tabularnewline
134 & 4014.98623617753 & 3804.38028955366 & 4225.5921828014 \tabularnewline
135 & 4482.86678203235 & 4269.99149986864 & 4695.74206419607 \tabularnewline
136 & 4372.95411121575 & 4157.83343169092 & 4588.07479074057 \tabularnewline
137 & 4624.70707000642 & 4407.36418937269 & 4842.04995064014 \tabularnewline
138 & 4570.15647040599 & 4350.6138805399 & 4789.69906027208 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302855&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]4690.76708694312[/C][C]4496.78843416727[/C][C]4884.74573971896[/C][/ROW]
[ROW][C]128[/C][C]4758.60735517101[/C][C]4562.16718938083[/C][C]4955.04752096119[/C][/ROW]
[ROW][C]129[/C][C]4289.31770615264[/C][C]4090.44649220095[/C][C]4488.18892010433[/C][/ROW]
[ROW][C]130[/C][C]4545.81714764024[/C][C]4344.54424647975[/C][C]4747.09004880074[/C][/ROW]
[ROW][C]131[/C][C]4328.96466145227[/C][C]4125.31839523433[/C][C]4532.6109276702[/C][/ROW]
[ROW][C]132[/C][C]4507.66156493322[/C][C]4301.66927685561[/C][C]4713.65385301083[/C][/ROW]
[ROW][C]133[/C][C]4236.74982898991[/C][C]4028.4379384258[/C][C]4445.06171955402[/C][/ROW]
[ROW][C]134[/C][C]4014.98623617753[/C][C]3804.38028955366[/C][C]4225.5921828014[/C][/ROW]
[ROW][C]135[/C][C]4482.86678203235[/C][C]4269.99149986864[/C][C]4695.74206419607[/C][/ROW]
[ROW][C]136[/C][C]4372.95411121575[/C][C]4157.83343169092[/C][C]4588.07479074057[/C][/ROW]
[ROW][C]137[/C][C]4624.70707000642[/C][C]4407.36418937269[/C][C]4842.04995064014[/C][/ROW]
[ROW][C]138[/C][C]4570.15647040599[/C][C]4350.6138805399[/C][C]4789.69906027208[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302855&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302855&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
1274690.767086943124496.788434167274884.74573971896
1284758.607355171014562.167189380834955.04752096119
1294289.317706152644090.446492200954488.18892010433
1304545.817147640244344.544246479754747.09004880074
1314328.964661452274125.318395234334532.6109276702
1324507.661564933224301.669276855614713.65385301083
1334236.749828989914028.43793842584445.06171955402
1344014.986236177533804.380289553664225.5921828014
1354482.866782032354269.991499868644695.74206419607
1364372.954111215754157.833431690924588.07479074057
1374624.707070006424407.364189372694842.04995064014
1384570.156470405994350.61388053994789.69906027208



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')