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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 09:56:07 +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/07/t1481101048agpclvegmpouuzl.htm/, Retrieved Fri, 01 Nov 2024 03:41:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297936, Retrieved Fri, 01 Nov 2024 03:41:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2016-12-07 08:56:07] [bd7223969ac5b08f41438741a34686d6] [Current]
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Dataseries X:
5350
6100
4820
5130
4060
6710
4510
5630
5200
4510
4810
4930
4720
4400
4090
4160
5020
5930
4390
4490
5760
5040
4800
4820
4620
4380
4250
4230
3800
6360
4280
4680
5070
4560
4690
4820
4370
3850
5050
4010
4570
4240
3850
4830
5400
4680
4390
4140
4300
4180
4120
3910
4300
4240
3610
3600
3970
3790
3750
3680
3970
4290
3670
3760
4160
3620
4280
4410
4500
4690
3650
3720
3770
3970
3390
3400
3130
3930
3740
3400
3620
3980
3440
3420
3740
3630
3650
3940
3540
3590
3740
3910
3670
3510
3430
3420
3630
3690
3350
3470
3380
3990
3790
3440
3580
3600
3990
3640




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297936&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=297936&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297936&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00622827685189025
beta0.402898575563397
gamma0.327726473737551

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00622827685189025 \tabularnewline
beta & 0.402898575563397 \tabularnewline
gamma & 0.327726473737551 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297936&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]0.00622827685189025[/C][/ROW]
[ROW][C]beta[/C][C]0.402898575563397[/C][/ROW]
[ROW][C]gamma[/C][C]0.327726473737551[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297936&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297936&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
alpha0.00622827685189025
beta0.402898575563397
gamma0.327726473737551







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1347204935.67744320357-215.677443203571
1444004626.80390602621-226.803906026214
1540904298.79161458566-208.791614585664
1641604306.2762041811-146.2762041811
1750205143.56677930318-123.566779303183
1859306047.36457457384-117.364574573839
1943904292.0567858132897.9432141867192
2044905431.40842790985-941.408427909845
2157605082.93518130298677.064818697017
2250404450.4929224453589.507077554701
2348004724.6458473515775.3541526484278
2448204808.8895489261811.1104510738169
2546204548.5737030394971.4262969605115
2643804256.12063524281123.879364757194
2742503955.92757837764294.072421622365
2842303985.28305976009244.716940239915
2938004780.07506048829-980.075060488287
3063605621.33008178991738.669918210086
3142804049.64742943758230.352570562423
3246804801.95879800439-121.95879800439
3350704977.5934860317192.4065139682907
3445604355.97199597593204.028004024074
3546904454.78354582844235.21645417156
3648204516.58561204197303.414387958032
3743704294.4706531904675.5293468095415
3838504037.79447434636-187.794474346356
3950503807.056785152951242.94321484705
4040103829.13863242529180.861367574709
4145704205.17261060795364.82738939205
4242405545.49464128068-1305.49464128068
4338503896.13538010358-46.1353801035812
4448304499.07694580472330.923054195285
4554004737.84418170841662.15581829159
4646804192.08904038714487.910959612865
4743904303.0048836664886.9951163335227
4841404387.44915227954-247.449152279539
4943004106.59513255746193.404867442542
5041803785.66007571671394.339924283287
5141204018.39311187415101.606888125854
5239103705.75912515372204.240874846284
5343004124.37443457562175.625565424377
5442404885.03528185082-645.035281850825
5536103708.86033495999-98.8603349599948
5636004405.67054186484-805.670541864838
5739704730.43527754814-760.435277548141
5837904145.0026608449-355.002660844899
5937504116.73002763754-366.730027637543
6036804085.04232456102-405.042324561018
6139703947.8840179255222.1159820744788
6242903698.97390226938591.026097730625
6336703824.52403154087-154.524031540875
6437603553.54806183552206.451938164477
6541603932.59836623821227.401633761793
6636204389.62217263867-769.622172638667
6742803445.31804989941834.681950100586
6844103884.49032835626525.509671643744
6945004209.89608085635290.103919143647
7046903790.71939048155899.280609518447
7136503772.23828596921-122.238285969209
7237203736.55059631379-16.5505963137925
7337703746.3398702226723.6601297773336
7439703691.53898783224278.461012167764
7533903583.32776156001-193.32776156001
7634003441.85480556071-41.8548055607112
7731303811.32035617764-681.320356177639
7839303933.28050220286-3.28050220285922
7937403539.6442432551200.355756744896
8034003859.83610780396-459.836107803959
8136204089.72254530637-469.722545306367
8239803872.88347616721107.116523832791
8334403531.61747025927-91.6174702592684
8434203526.63002899176-106.630028991755
8537403543.46214894913196.537851050871
8636303567.2698646720762.7301353279258
8736503315.01134976554334.988650234464
8839403228.63231625755711.367683742447
8935403384.20938406855155.790615931448
9035903713.98107486608-123.981074866081
9137403404.88211231843335.117887681569
9239103506.21818594095403.781814059054
9336703729.34575514888-59.3457551488764
9435103708.7033898964-198.7033898964
9534303325.02704416277104.972955837226
9634203320.6609855718699.339014428137
9736303436.35624326489193.643756735111
9836903422.11138491217267.888615087826
9933503272.1393966740777.8606033259252
10034703309.24877950112160.751220498878
10133803284.6764085954195.3235914045881
10239903515.50924072083474.490759279171
10337903370.59295754894419.407042451064
10434403494.52548007579-54.525480075793
10535803564.8504757127515.1495242872484
10636003505.6558056755394.3441943244666
10739903237.54891646384752.451083536163
10836403241.51448134535398.485518654649

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4720 & 4935.67744320357 & -215.677443203571 \tabularnewline
14 & 4400 & 4626.80390602621 & -226.803906026214 \tabularnewline
15 & 4090 & 4298.79161458566 & -208.791614585664 \tabularnewline
16 & 4160 & 4306.2762041811 & -146.2762041811 \tabularnewline
17 & 5020 & 5143.56677930318 & -123.566779303183 \tabularnewline
18 & 5930 & 6047.36457457384 & -117.364574573839 \tabularnewline
19 & 4390 & 4292.05678581328 & 97.9432141867192 \tabularnewline
20 & 4490 & 5431.40842790985 & -941.408427909845 \tabularnewline
21 & 5760 & 5082.93518130298 & 677.064818697017 \tabularnewline
22 & 5040 & 4450.4929224453 & 589.507077554701 \tabularnewline
23 & 4800 & 4724.64584735157 & 75.3541526484278 \tabularnewline
24 & 4820 & 4808.88954892618 & 11.1104510738169 \tabularnewline
25 & 4620 & 4548.57370303949 & 71.4262969605115 \tabularnewline
26 & 4380 & 4256.12063524281 & 123.879364757194 \tabularnewline
27 & 4250 & 3955.92757837764 & 294.072421622365 \tabularnewline
28 & 4230 & 3985.28305976009 & 244.716940239915 \tabularnewline
29 & 3800 & 4780.07506048829 & -980.075060488287 \tabularnewline
30 & 6360 & 5621.33008178991 & 738.669918210086 \tabularnewline
31 & 4280 & 4049.64742943758 & 230.352570562423 \tabularnewline
32 & 4680 & 4801.95879800439 & -121.95879800439 \tabularnewline
33 & 5070 & 4977.59348603171 & 92.4065139682907 \tabularnewline
34 & 4560 & 4355.97199597593 & 204.028004024074 \tabularnewline
35 & 4690 & 4454.78354582844 & 235.21645417156 \tabularnewline
36 & 4820 & 4516.58561204197 & 303.414387958032 \tabularnewline
37 & 4370 & 4294.47065319046 & 75.5293468095415 \tabularnewline
38 & 3850 & 4037.79447434636 & -187.794474346356 \tabularnewline
39 & 5050 & 3807.05678515295 & 1242.94321484705 \tabularnewline
40 & 4010 & 3829.13863242529 & 180.861367574709 \tabularnewline
41 & 4570 & 4205.17261060795 & 364.82738939205 \tabularnewline
42 & 4240 & 5545.49464128068 & -1305.49464128068 \tabularnewline
43 & 3850 & 3896.13538010358 & -46.1353801035812 \tabularnewline
44 & 4830 & 4499.07694580472 & 330.923054195285 \tabularnewline
45 & 5400 & 4737.84418170841 & 662.15581829159 \tabularnewline
46 & 4680 & 4192.08904038714 & 487.910959612865 \tabularnewline
47 & 4390 & 4303.00488366648 & 86.9951163335227 \tabularnewline
48 & 4140 & 4387.44915227954 & -247.449152279539 \tabularnewline
49 & 4300 & 4106.59513255746 & 193.404867442542 \tabularnewline
50 & 4180 & 3785.66007571671 & 394.339924283287 \tabularnewline
51 & 4120 & 4018.39311187415 & 101.606888125854 \tabularnewline
52 & 3910 & 3705.75912515372 & 204.240874846284 \tabularnewline
53 & 4300 & 4124.37443457562 & 175.625565424377 \tabularnewline
54 & 4240 & 4885.03528185082 & -645.035281850825 \tabularnewline
55 & 3610 & 3708.86033495999 & -98.8603349599948 \tabularnewline
56 & 3600 & 4405.67054186484 & -805.670541864838 \tabularnewline
57 & 3970 & 4730.43527754814 & -760.435277548141 \tabularnewline
58 & 3790 & 4145.0026608449 & -355.002660844899 \tabularnewline
59 & 3750 & 4116.73002763754 & -366.730027637543 \tabularnewline
60 & 3680 & 4085.04232456102 & -405.042324561018 \tabularnewline
61 & 3970 & 3947.88401792552 & 22.1159820744788 \tabularnewline
62 & 4290 & 3698.97390226938 & 591.026097730625 \tabularnewline
63 & 3670 & 3824.52403154087 & -154.524031540875 \tabularnewline
64 & 3760 & 3553.54806183552 & 206.451938164477 \tabularnewline
65 & 4160 & 3932.59836623821 & 227.401633761793 \tabularnewline
66 & 3620 & 4389.62217263867 & -769.622172638667 \tabularnewline
67 & 4280 & 3445.31804989941 & 834.681950100586 \tabularnewline
68 & 4410 & 3884.49032835626 & 525.509671643744 \tabularnewline
69 & 4500 & 4209.89608085635 & 290.103919143647 \tabularnewline
70 & 4690 & 3790.71939048155 & 899.280609518447 \tabularnewline
71 & 3650 & 3772.23828596921 & -122.238285969209 \tabularnewline
72 & 3720 & 3736.55059631379 & -16.5505963137925 \tabularnewline
73 & 3770 & 3746.33987022267 & 23.6601297773336 \tabularnewline
74 & 3970 & 3691.53898783224 & 278.461012167764 \tabularnewline
75 & 3390 & 3583.32776156001 & -193.32776156001 \tabularnewline
76 & 3400 & 3441.85480556071 & -41.8548055607112 \tabularnewline
77 & 3130 & 3811.32035617764 & -681.320356177639 \tabularnewline
78 & 3930 & 3933.28050220286 & -3.28050220285922 \tabularnewline
79 & 3740 & 3539.6442432551 & 200.355756744896 \tabularnewline
80 & 3400 & 3859.83610780396 & -459.836107803959 \tabularnewline
81 & 3620 & 4089.72254530637 & -469.722545306367 \tabularnewline
82 & 3980 & 3872.88347616721 & 107.116523832791 \tabularnewline
83 & 3440 & 3531.61747025927 & -91.6174702592684 \tabularnewline
84 & 3420 & 3526.63002899176 & -106.630028991755 \tabularnewline
85 & 3740 & 3543.46214894913 & 196.537851050871 \tabularnewline
86 & 3630 & 3567.26986467207 & 62.7301353279258 \tabularnewline
87 & 3650 & 3315.01134976554 & 334.988650234464 \tabularnewline
88 & 3940 & 3228.63231625755 & 711.367683742447 \tabularnewline
89 & 3540 & 3384.20938406855 & 155.790615931448 \tabularnewline
90 & 3590 & 3713.98107486608 & -123.981074866081 \tabularnewline
91 & 3740 & 3404.88211231843 & 335.117887681569 \tabularnewline
92 & 3910 & 3506.21818594095 & 403.781814059054 \tabularnewline
93 & 3670 & 3729.34575514888 & -59.3457551488764 \tabularnewline
94 & 3510 & 3708.7033898964 & -198.7033898964 \tabularnewline
95 & 3430 & 3325.02704416277 & 104.972955837226 \tabularnewline
96 & 3420 & 3320.66098557186 & 99.339014428137 \tabularnewline
97 & 3630 & 3436.35624326489 & 193.643756735111 \tabularnewline
98 & 3690 & 3422.11138491217 & 267.888615087826 \tabularnewline
99 & 3350 & 3272.13939667407 & 77.8606033259252 \tabularnewline
100 & 3470 & 3309.24877950112 & 160.751220498878 \tabularnewline
101 & 3380 & 3284.67640859541 & 95.3235914045881 \tabularnewline
102 & 3990 & 3515.50924072083 & 474.490759279171 \tabularnewline
103 & 3790 & 3370.59295754894 & 419.407042451064 \tabularnewline
104 & 3440 & 3494.52548007579 & -54.525480075793 \tabularnewline
105 & 3580 & 3564.85047571275 & 15.1495242872484 \tabularnewline
106 & 3600 & 3505.65580567553 & 94.3441943244666 \tabularnewline
107 & 3990 & 3237.54891646384 & 752.451083536163 \tabularnewline
108 & 3640 & 3241.51448134535 & 398.485518654649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297936&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]4720[/C][C]4935.67744320357[/C][C]-215.677443203571[/C][/ROW]
[ROW][C]14[/C][C]4400[/C][C]4626.80390602621[/C][C]-226.803906026214[/C][/ROW]
[ROW][C]15[/C][C]4090[/C][C]4298.79161458566[/C][C]-208.791614585664[/C][/ROW]
[ROW][C]16[/C][C]4160[/C][C]4306.2762041811[/C][C]-146.2762041811[/C][/ROW]
[ROW][C]17[/C][C]5020[/C][C]5143.56677930318[/C][C]-123.566779303183[/C][/ROW]
[ROW][C]18[/C][C]5930[/C][C]6047.36457457384[/C][C]-117.364574573839[/C][/ROW]
[ROW][C]19[/C][C]4390[/C][C]4292.05678581328[/C][C]97.9432141867192[/C][/ROW]
[ROW][C]20[/C][C]4490[/C][C]5431.40842790985[/C][C]-941.408427909845[/C][/ROW]
[ROW][C]21[/C][C]5760[/C][C]5082.93518130298[/C][C]677.064818697017[/C][/ROW]
[ROW][C]22[/C][C]5040[/C][C]4450.4929224453[/C][C]589.507077554701[/C][/ROW]
[ROW][C]23[/C][C]4800[/C][C]4724.64584735157[/C][C]75.3541526484278[/C][/ROW]
[ROW][C]24[/C][C]4820[/C][C]4808.88954892618[/C][C]11.1104510738169[/C][/ROW]
[ROW][C]25[/C][C]4620[/C][C]4548.57370303949[/C][C]71.4262969605115[/C][/ROW]
[ROW][C]26[/C][C]4380[/C][C]4256.12063524281[/C][C]123.879364757194[/C][/ROW]
[ROW][C]27[/C][C]4250[/C][C]3955.92757837764[/C][C]294.072421622365[/C][/ROW]
[ROW][C]28[/C][C]4230[/C][C]3985.28305976009[/C][C]244.716940239915[/C][/ROW]
[ROW][C]29[/C][C]3800[/C][C]4780.07506048829[/C][C]-980.075060488287[/C][/ROW]
[ROW][C]30[/C][C]6360[/C][C]5621.33008178991[/C][C]738.669918210086[/C][/ROW]
[ROW][C]31[/C][C]4280[/C][C]4049.64742943758[/C][C]230.352570562423[/C][/ROW]
[ROW][C]32[/C][C]4680[/C][C]4801.95879800439[/C][C]-121.95879800439[/C][/ROW]
[ROW][C]33[/C][C]5070[/C][C]4977.59348603171[/C][C]92.4065139682907[/C][/ROW]
[ROW][C]34[/C][C]4560[/C][C]4355.97199597593[/C][C]204.028004024074[/C][/ROW]
[ROW][C]35[/C][C]4690[/C][C]4454.78354582844[/C][C]235.21645417156[/C][/ROW]
[ROW][C]36[/C][C]4820[/C][C]4516.58561204197[/C][C]303.414387958032[/C][/ROW]
[ROW][C]37[/C][C]4370[/C][C]4294.47065319046[/C][C]75.5293468095415[/C][/ROW]
[ROW][C]38[/C][C]3850[/C][C]4037.79447434636[/C][C]-187.794474346356[/C][/ROW]
[ROW][C]39[/C][C]5050[/C][C]3807.05678515295[/C][C]1242.94321484705[/C][/ROW]
[ROW][C]40[/C][C]4010[/C][C]3829.13863242529[/C][C]180.861367574709[/C][/ROW]
[ROW][C]41[/C][C]4570[/C][C]4205.17261060795[/C][C]364.82738939205[/C][/ROW]
[ROW][C]42[/C][C]4240[/C][C]5545.49464128068[/C][C]-1305.49464128068[/C][/ROW]
[ROW][C]43[/C][C]3850[/C][C]3896.13538010358[/C][C]-46.1353801035812[/C][/ROW]
[ROW][C]44[/C][C]4830[/C][C]4499.07694580472[/C][C]330.923054195285[/C][/ROW]
[ROW][C]45[/C][C]5400[/C][C]4737.84418170841[/C][C]662.15581829159[/C][/ROW]
[ROW][C]46[/C][C]4680[/C][C]4192.08904038714[/C][C]487.910959612865[/C][/ROW]
[ROW][C]47[/C][C]4390[/C][C]4303.00488366648[/C][C]86.9951163335227[/C][/ROW]
[ROW][C]48[/C][C]4140[/C][C]4387.44915227954[/C][C]-247.449152279539[/C][/ROW]
[ROW][C]49[/C][C]4300[/C][C]4106.59513255746[/C][C]193.404867442542[/C][/ROW]
[ROW][C]50[/C][C]4180[/C][C]3785.66007571671[/C][C]394.339924283287[/C][/ROW]
[ROW][C]51[/C][C]4120[/C][C]4018.39311187415[/C][C]101.606888125854[/C][/ROW]
[ROW][C]52[/C][C]3910[/C][C]3705.75912515372[/C][C]204.240874846284[/C][/ROW]
[ROW][C]53[/C][C]4300[/C][C]4124.37443457562[/C][C]175.625565424377[/C][/ROW]
[ROW][C]54[/C][C]4240[/C][C]4885.03528185082[/C][C]-645.035281850825[/C][/ROW]
[ROW][C]55[/C][C]3610[/C][C]3708.86033495999[/C][C]-98.8603349599948[/C][/ROW]
[ROW][C]56[/C][C]3600[/C][C]4405.67054186484[/C][C]-805.670541864838[/C][/ROW]
[ROW][C]57[/C][C]3970[/C][C]4730.43527754814[/C][C]-760.435277548141[/C][/ROW]
[ROW][C]58[/C][C]3790[/C][C]4145.0026608449[/C][C]-355.002660844899[/C][/ROW]
[ROW][C]59[/C][C]3750[/C][C]4116.73002763754[/C][C]-366.730027637543[/C][/ROW]
[ROW][C]60[/C][C]3680[/C][C]4085.04232456102[/C][C]-405.042324561018[/C][/ROW]
[ROW][C]61[/C][C]3970[/C][C]3947.88401792552[/C][C]22.1159820744788[/C][/ROW]
[ROW][C]62[/C][C]4290[/C][C]3698.97390226938[/C][C]591.026097730625[/C][/ROW]
[ROW][C]63[/C][C]3670[/C][C]3824.52403154087[/C][C]-154.524031540875[/C][/ROW]
[ROW][C]64[/C][C]3760[/C][C]3553.54806183552[/C][C]206.451938164477[/C][/ROW]
[ROW][C]65[/C][C]4160[/C][C]3932.59836623821[/C][C]227.401633761793[/C][/ROW]
[ROW][C]66[/C][C]3620[/C][C]4389.62217263867[/C][C]-769.622172638667[/C][/ROW]
[ROW][C]67[/C][C]4280[/C][C]3445.31804989941[/C][C]834.681950100586[/C][/ROW]
[ROW][C]68[/C][C]4410[/C][C]3884.49032835626[/C][C]525.509671643744[/C][/ROW]
[ROW][C]69[/C][C]4500[/C][C]4209.89608085635[/C][C]290.103919143647[/C][/ROW]
[ROW][C]70[/C][C]4690[/C][C]3790.71939048155[/C][C]899.280609518447[/C][/ROW]
[ROW][C]71[/C][C]3650[/C][C]3772.23828596921[/C][C]-122.238285969209[/C][/ROW]
[ROW][C]72[/C][C]3720[/C][C]3736.55059631379[/C][C]-16.5505963137925[/C][/ROW]
[ROW][C]73[/C][C]3770[/C][C]3746.33987022267[/C][C]23.6601297773336[/C][/ROW]
[ROW][C]74[/C][C]3970[/C][C]3691.53898783224[/C][C]278.461012167764[/C][/ROW]
[ROW][C]75[/C][C]3390[/C][C]3583.32776156001[/C][C]-193.32776156001[/C][/ROW]
[ROW][C]76[/C][C]3400[/C][C]3441.85480556071[/C][C]-41.8548055607112[/C][/ROW]
[ROW][C]77[/C][C]3130[/C][C]3811.32035617764[/C][C]-681.320356177639[/C][/ROW]
[ROW][C]78[/C][C]3930[/C][C]3933.28050220286[/C][C]-3.28050220285922[/C][/ROW]
[ROW][C]79[/C][C]3740[/C][C]3539.6442432551[/C][C]200.355756744896[/C][/ROW]
[ROW][C]80[/C][C]3400[/C][C]3859.83610780396[/C][C]-459.836107803959[/C][/ROW]
[ROW][C]81[/C][C]3620[/C][C]4089.72254530637[/C][C]-469.722545306367[/C][/ROW]
[ROW][C]82[/C][C]3980[/C][C]3872.88347616721[/C][C]107.116523832791[/C][/ROW]
[ROW][C]83[/C][C]3440[/C][C]3531.61747025927[/C][C]-91.6174702592684[/C][/ROW]
[ROW][C]84[/C][C]3420[/C][C]3526.63002899176[/C][C]-106.630028991755[/C][/ROW]
[ROW][C]85[/C][C]3740[/C][C]3543.46214894913[/C][C]196.537851050871[/C][/ROW]
[ROW][C]86[/C][C]3630[/C][C]3567.26986467207[/C][C]62.7301353279258[/C][/ROW]
[ROW][C]87[/C][C]3650[/C][C]3315.01134976554[/C][C]334.988650234464[/C][/ROW]
[ROW][C]88[/C][C]3940[/C][C]3228.63231625755[/C][C]711.367683742447[/C][/ROW]
[ROW][C]89[/C][C]3540[/C][C]3384.20938406855[/C][C]155.790615931448[/C][/ROW]
[ROW][C]90[/C][C]3590[/C][C]3713.98107486608[/C][C]-123.981074866081[/C][/ROW]
[ROW][C]91[/C][C]3740[/C][C]3404.88211231843[/C][C]335.117887681569[/C][/ROW]
[ROW][C]92[/C][C]3910[/C][C]3506.21818594095[/C][C]403.781814059054[/C][/ROW]
[ROW][C]93[/C][C]3670[/C][C]3729.34575514888[/C][C]-59.3457551488764[/C][/ROW]
[ROW][C]94[/C][C]3510[/C][C]3708.7033898964[/C][C]-198.7033898964[/C][/ROW]
[ROW][C]95[/C][C]3430[/C][C]3325.02704416277[/C][C]104.972955837226[/C][/ROW]
[ROW][C]96[/C][C]3420[/C][C]3320.66098557186[/C][C]99.339014428137[/C][/ROW]
[ROW][C]97[/C][C]3630[/C][C]3436.35624326489[/C][C]193.643756735111[/C][/ROW]
[ROW][C]98[/C][C]3690[/C][C]3422.11138491217[/C][C]267.888615087826[/C][/ROW]
[ROW][C]99[/C][C]3350[/C][C]3272.13939667407[/C][C]77.8606033259252[/C][/ROW]
[ROW][C]100[/C][C]3470[/C][C]3309.24877950112[/C][C]160.751220498878[/C][/ROW]
[ROW][C]101[/C][C]3380[/C][C]3284.67640859541[/C][C]95.3235914045881[/C][/ROW]
[ROW][C]102[/C][C]3990[/C][C]3515.50924072083[/C][C]474.490759279171[/C][/ROW]
[ROW][C]103[/C][C]3790[/C][C]3370.59295754894[/C][C]419.407042451064[/C][/ROW]
[ROW][C]104[/C][C]3440[/C][C]3494.52548007579[/C][C]-54.525480075793[/C][/ROW]
[ROW][C]105[/C][C]3580[/C][C]3564.85047571275[/C][C]15.1495242872484[/C][/ROW]
[ROW][C]106[/C][C]3600[/C][C]3505.65580567553[/C][C]94.3441943244666[/C][/ROW]
[ROW][C]107[/C][C]3990[/C][C]3237.54891646384[/C][C]752.451083536163[/C][/ROW]
[ROW][C]108[/C][C]3640[/C][C]3241.51448134535[/C][C]398.485518654649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297936&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297936&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
1347204935.67744320357-215.677443203571
1444004626.80390602621-226.803906026214
1540904298.79161458566-208.791614585664
1641604306.2762041811-146.2762041811
1750205143.56677930318-123.566779303183
1859306047.36457457384-117.364574573839
1943904292.0567858132897.9432141867192
2044905431.40842790985-941.408427909845
2157605082.93518130298677.064818697017
2250404450.4929224453589.507077554701
2348004724.6458473515775.3541526484278
2448204808.8895489261811.1104510738169
2546204548.5737030394971.4262969605115
2643804256.12063524281123.879364757194
2742503955.92757837764294.072421622365
2842303985.28305976009244.716940239915
2938004780.07506048829-980.075060488287
3063605621.33008178991738.669918210086
3142804049.64742943758230.352570562423
3246804801.95879800439-121.95879800439
3350704977.5934860317192.4065139682907
3445604355.97199597593204.028004024074
3546904454.78354582844235.21645417156
3648204516.58561204197303.414387958032
3743704294.4706531904675.5293468095415
3838504037.79447434636-187.794474346356
3950503807.056785152951242.94321484705
4040103829.13863242529180.861367574709
4145704205.17261060795364.82738939205
4242405545.49464128068-1305.49464128068
4338503896.13538010358-46.1353801035812
4448304499.07694580472330.923054195285
4554004737.84418170841662.15581829159
4646804192.08904038714487.910959612865
4743904303.0048836664886.9951163335227
4841404387.44915227954-247.449152279539
4943004106.59513255746193.404867442542
5041803785.66007571671394.339924283287
5141204018.39311187415101.606888125854
5239103705.75912515372204.240874846284
5343004124.37443457562175.625565424377
5442404885.03528185082-645.035281850825
5536103708.86033495999-98.8603349599948
5636004405.67054186484-805.670541864838
5739704730.43527754814-760.435277548141
5837904145.0026608449-355.002660844899
5937504116.73002763754-366.730027637543
6036804085.04232456102-405.042324561018
6139703947.8840179255222.1159820744788
6242903698.97390226938591.026097730625
6336703824.52403154087-154.524031540875
6437603553.54806183552206.451938164477
6541603932.59836623821227.401633761793
6636204389.62217263867-769.622172638667
6742803445.31804989941834.681950100586
6844103884.49032835626525.509671643744
6945004209.89608085635290.103919143647
7046903790.71939048155899.280609518447
7136503772.23828596921-122.238285969209
7237203736.55059631379-16.5505963137925
7337703746.3398702226723.6601297773336
7439703691.53898783224278.461012167764
7533903583.32776156001-193.32776156001
7634003441.85480556071-41.8548055607112
7731303811.32035617764-681.320356177639
7839303933.28050220286-3.28050220285922
7937403539.6442432551200.355756744896
8034003859.83610780396-459.836107803959
8136204089.72254530637-469.722545306367
8239803872.88347616721107.116523832791
8334403531.61747025927-91.6174702592684
8434203526.63002899176-106.630028991755
8537403543.46214894913196.537851050871
8636303567.2698646720762.7301353279258
8736503315.01134976554334.988650234464
8839403228.63231625755711.367683742447
8935403384.20938406855155.790615931448
9035903713.98107486608-123.981074866081
9137403404.88211231843335.117887681569
9239103506.21818594095403.781814059054
9336703729.34575514888-59.3457551488764
9435103708.7033898964-198.7033898964
9534303325.02704416277104.972955837226
9634203320.6609855718699.339014428137
9736303436.35624326489193.643756735111
9836903422.11138491217267.888615087826
9933503272.1393966740777.8606033259252
10034703309.24877950112160.751220498878
10133803284.6764085954195.3235914045881
10239903515.50924072083474.490759279171
10337903370.59295754894419.407042451064
10434403494.52548007579-54.525480075793
10535803564.8504757127515.1495242872484
10636003505.6558056755394.3441943244666
10739903237.54891646384752.451083536163
10836403241.51448134535398.485518654649







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1093392.004987994853121.230394972543662.77958101716
1103407.013605423993136.14401089983677.88319994817
1113205.406267087812934.408514768073476.40401940755
1123272.77814698433001.542221461243544.01407250737
1133232.258591206252960.722396240323503.79478617218
1143582.331827894523310.106378997833854.55727679121
1153424.564849745393151.873842511193697.25585697959
1163395.30356752173121.915957794163668.69117724924
1173489.68730486083215.212505335053764.16210438655
1183460.094735016023184.579059289043735.61041074301
1193409.463889308893132.821935908333686.10584270945
1203296.827220428883220.757854795843372.89658606192

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 3392.00498799485 & 3121.23039497254 & 3662.77958101716 \tabularnewline
110 & 3407.01360542399 & 3136.1440108998 & 3677.88319994817 \tabularnewline
111 & 3205.40626708781 & 2934.40851476807 & 3476.40401940755 \tabularnewline
112 & 3272.7781469843 & 3001.54222146124 & 3544.01407250737 \tabularnewline
113 & 3232.25859120625 & 2960.72239624032 & 3503.79478617218 \tabularnewline
114 & 3582.33182789452 & 3310.10637899783 & 3854.55727679121 \tabularnewline
115 & 3424.56484974539 & 3151.87384251119 & 3697.25585697959 \tabularnewline
116 & 3395.3035675217 & 3121.91595779416 & 3668.69117724924 \tabularnewline
117 & 3489.6873048608 & 3215.21250533505 & 3764.16210438655 \tabularnewline
118 & 3460.09473501602 & 3184.57905928904 & 3735.61041074301 \tabularnewline
119 & 3409.46388930889 & 3132.82193590833 & 3686.10584270945 \tabularnewline
120 & 3296.82722042888 & 3220.75785479584 & 3372.89658606192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297936&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]109[/C][C]3392.00498799485[/C][C]3121.23039497254[/C][C]3662.77958101716[/C][/ROW]
[ROW][C]110[/C][C]3407.01360542399[/C][C]3136.1440108998[/C][C]3677.88319994817[/C][/ROW]
[ROW][C]111[/C][C]3205.40626708781[/C][C]2934.40851476807[/C][C]3476.40401940755[/C][/ROW]
[ROW][C]112[/C][C]3272.7781469843[/C][C]3001.54222146124[/C][C]3544.01407250737[/C][/ROW]
[ROW][C]113[/C][C]3232.25859120625[/C][C]2960.72239624032[/C][C]3503.79478617218[/C][/ROW]
[ROW][C]114[/C][C]3582.33182789452[/C][C]3310.10637899783[/C][C]3854.55727679121[/C][/ROW]
[ROW][C]115[/C][C]3424.56484974539[/C][C]3151.87384251119[/C][C]3697.25585697959[/C][/ROW]
[ROW][C]116[/C][C]3395.3035675217[/C][C]3121.91595779416[/C][C]3668.69117724924[/C][/ROW]
[ROW][C]117[/C][C]3489.6873048608[/C][C]3215.21250533505[/C][C]3764.16210438655[/C][/ROW]
[ROW][C]118[/C][C]3460.09473501602[/C][C]3184.57905928904[/C][C]3735.61041074301[/C][/ROW]
[ROW][C]119[/C][C]3409.46388930889[/C][C]3132.82193590833[/C][C]3686.10584270945[/C][/ROW]
[ROW][C]120[/C][C]3296.82722042888[/C][C]3220.75785479584[/C][C]3372.89658606192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297936&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297936&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
1093392.004987994853121.230394972543662.77958101716
1103407.013605423993136.14401089983677.88319994817
1113205.406267087812934.408514768073476.40401940755
1123272.77814698433001.542221461243544.01407250737
1133232.258591206252960.722396240323503.79478617218
1143582.331827894523310.106378997833854.55727679121
1153424.564849745393151.873842511193697.25585697959
1163395.30356752173121.915957794163668.69117724924
1173489.68730486083215.212505335053764.16210438655
1183460.094735016023184.579059289043735.61041074301
1193409.463889308893132.821935908333686.10584270945
1203296.827220428883220.757854795843372.89658606192



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')