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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, 14 Dec 2016 22:33:43 +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/14/t1481751576bkf6k6p6hxq7o33.htm/, Retrieved Fri, 03 May 2024 18:51:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299734, Retrieved Fri, 03 May 2024 18:51:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-14 21:33:43] [6deb082de88ded72ec069288c69f9f98] [Current]
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Dataseries X:
5410.4
5432.2
5452.9
5477.6
5472.5
5454.9
5446
5010.6
5395.9
5360
5336.9
5333.9
5329.6
5345.7
5353.8
5377.2
5334.1
5351.1
5001
5246.4
5230
5115.8
4972.6
5077.6
5056.9
5070.7
4799.3
5076
5021.5
5026.4
4981.9
4936.6
4901.8
4853.8
4839.2
4821.3
4840.5
4847.6
4832.3
4814.7
4806.4
4803.4
4770.3
4723.4
4667.1
4636.8
4613.2
4605.3
4590.4
4595.4
4600.1
4543.3
4596.4
4575.4
4547.9
4503.7
4446.3
4401.4
4354.3
4336.3
4300.9
4304.1
4273.2
4279.9
4243.1
4199.1
4177.6
4141.7
4088.3
4021.4
3981.2
3937.2
3893.1
3864.7
3847.8
3840.8
3828.4
3798.6
3773
3737.8
3699
3674
3648.8
3645.6
3331
3674.7
3714.5
3739.7
3759.7
3708.6
3717.3
3705.3
3612.8
3665
3670.8
3687.6
3708.2
3737.2
3748.7
3785.3
3787.1
3785.8
3749.7
3716.3
3650
3096.9
3703.2
3716
3736.9
3771.9
3704
3824.2
3733.5
3827.5
3827.6
3696.5
3675.8
3757.5
3753.3
3418.7
3772.9




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=299734&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=299734&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299734&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
alpha0.221394872467023
beta0.121706789645633
gamma0.409824035408748

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.221394872467023 \tabularnewline
beta & 0.121706789645633 \tabularnewline
gamma & 0.409824035408748 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299734&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]0.221394872467023[/C][/ROW]
[ROW][C]beta[/C][C]0.121706789645633[/C][/ROW]
[ROW][C]gamma[/C][C]0.409824035408748[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299734&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299734&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
alpha0.221394872467023
beta0.121706789645633
gamma0.409824035408748







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135329.65395.91685363248-66.3168536324774
145345.75392.3225572151-46.6225572150952
155353.85372.20305348728-18.4030534872791
165377.25393.13532814259-15.9353281425947
175334.15355.95122965576-21.8512296557547
185351.15377.47276052825-26.3727605282475
1950015309.29512678235-308.295126782354
205246.44787.09423462143459.305765378573
2152305268.67485697334-38.6748569733445
225115.85218.34218557069-102.542185570693
234972.65165.54408933216-192.944089332161
245077.65107.77421331349-30.1742133134921
255056.95075.54158377329-18.641583773293
265070.75079.0553090554-8.35530905540327
274799.35067.71237792104-268.412377921035
2850765018.6445409313457.3554590686608
295021.54982.3370163649139.1629836350858
305026.45004.1061256857422.2938743142631
314981.94846.23757850673135.662421493265
324936.64668.71723160797267.882768392033
334901.84945.31467044284-43.5146704428389
344853.84869.69865202664-15.8986520266426
354839.24805.7388385324933.4611614675077
364821.34854.63518150962-33.335181509623
374840.54829.9003554432710.5996445567343
384847.64848.47577611719-0.875776117186433
394832.34761.3139969260670.9860030739374
404814.74905.98913114891-91.2891311489075
414806.44841.61442656711-35.2144265671068
424803.44850.17688446858-46.7768844685797
434770.34719.973098256950.326901743103
444723.44570.23263137114153.167368628856
454667.14723.45987408388-56.3598740838843
464636.84654.85725669748-18.0572566974843
474613.24607.156889675556.04311032445094
484605.34628.91718549984-23.6171854998438
494590.44620.86322664518-30.4632266451827
504595.44626.08952487754-30.6895248775436
514600.14553.8579404747446.2420595252624
524543.34639.2079622279-95.907962227896
534596.44589.51277551946.88722448060162
544575.44602.65045011173-27.2504501117346
554547.94507.2244190674140.6755809325869
564503.74387.37236834427116.327631655729
574446.34463.80224042068-17.5022404206784
584401.44415.28859264677-13.8885926467656
594354.34375.57774934189-21.2777493418862
604336.34380.4652333567-44.1652333566999
614300.94363.76408153961-62.8640815396066
624304.14358.95828769163-54.858287691628
634273.24302.48631389222-29.286313892223
644279.94320.28307053216-40.3830705321643
654243.14311.70510709393-68.6051070939257
664199.14291.2252463772-92.1252463772007
674177.64195.35189932802-17.7518993280237
684141.74077.3708957883464.3291042116589
694088.34088.8502222353-0.550222235296133
704021.44034.96510591014-13.5651059101424
713981.23982.69914195856-1.49914195856127
723937.23974.92633074247-37.726330742466
733893.13944.12159575373-51.0215957537339
743864.73935.24885666672-70.54885666672
753847.83873.79668563517-25.9966856351698
763840.83879.20333791336-38.4033379133552
773828.43852.53408601557-24.1340860155692
783798.63826.0689069702-27.4689069701972
7937733761.6582891738711.3417108261265
803737.83670.5099883975667.2900116024398
8136993656.2224209601642.7775790398437
8236743603.2243947629370.7756052370737
833648.83571.2012263520777.5987736479301
843645.63569.2318814580376.3681185419678
8533313562.37034308305-231.370343083045
863674.73505.40446851004169.295531489964
873714.53515.79761296369198.702387036305
883739.73577.57600696554162.123993034462
893759.73615.84230150175143.857698498245
903708.63646.0187450202862.5812549797247
913717.33636.8685333679480.4314666320638
923705.33603.67023570076101.629764299237
933612.83614.89018886802-2.09018886801778
9436653585.410190521379.5898094787021
953670.83582.270755791488.5292442086002
963687.63607.3782960844880.2217039155212
973708.23528.3267809426179.873219057404
983737.23726.4915615100410.7084384899626
993748.73743.119158517485.58084148251783
1003785.33777.227238701978.07276129802858
1013787.13798.16546407752-11.0654640775228
1023785.83786.54037519378-0.740375193780892
1033749.73785.79295596434-36.0929559643437
1043716.33747.14718894381-30.8471889438074
10536503705.95793694156-55.9579369415637
1063096.93699.18040155318-602.28040155318
1073703.23538.12286890682165.077131093185
10837163569.78143584785146.218564152154
1093736.93531.1720799107205.727920089303
1103771.93675.8115268380196.0884731619917
11137043706.73578559868-2.73578559867792
1123824.23736.6037933539387.5962066460716
1133733.53767.99008105664-34.4900810566414
1143827.53752.7911802147174.7088197852927
1153827.63757.8177644856469.7822355143612
1163696.53747.48956632075-50.9895663207508
1173675.83696.48900438163-20.6890043816297
1183757.53526.80425191518230.69574808482
1193753.33821.0761372895-67.7761372895025
1203418.73814.94610610784-396.246106107842
1213772.93680.3914304351892.5085695648195

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5329.6 & 5395.91685363248 & -66.3168536324774 \tabularnewline
14 & 5345.7 & 5392.3225572151 & -46.6225572150952 \tabularnewline
15 & 5353.8 & 5372.20305348728 & -18.4030534872791 \tabularnewline
16 & 5377.2 & 5393.13532814259 & -15.9353281425947 \tabularnewline
17 & 5334.1 & 5355.95122965576 & -21.8512296557547 \tabularnewline
18 & 5351.1 & 5377.47276052825 & -26.3727605282475 \tabularnewline
19 & 5001 & 5309.29512678235 & -308.295126782354 \tabularnewline
20 & 5246.4 & 4787.09423462143 & 459.305765378573 \tabularnewline
21 & 5230 & 5268.67485697334 & -38.6748569733445 \tabularnewline
22 & 5115.8 & 5218.34218557069 & -102.542185570693 \tabularnewline
23 & 4972.6 & 5165.54408933216 & -192.944089332161 \tabularnewline
24 & 5077.6 & 5107.77421331349 & -30.1742133134921 \tabularnewline
25 & 5056.9 & 5075.54158377329 & -18.641583773293 \tabularnewline
26 & 5070.7 & 5079.0553090554 & -8.35530905540327 \tabularnewline
27 & 4799.3 & 5067.71237792104 & -268.412377921035 \tabularnewline
28 & 5076 & 5018.64454093134 & 57.3554590686608 \tabularnewline
29 & 5021.5 & 4982.33701636491 & 39.1629836350858 \tabularnewline
30 & 5026.4 & 5004.10612568574 & 22.2938743142631 \tabularnewline
31 & 4981.9 & 4846.23757850673 & 135.662421493265 \tabularnewline
32 & 4936.6 & 4668.71723160797 & 267.882768392033 \tabularnewline
33 & 4901.8 & 4945.31467044284 & -43.5146704428389 \tabularnewline
34 & 4853.8 & 4869.69865202664 & -15.8986520266426 \tabularnewline
35 & 4839.2 & 4805.73883853249 & 33.4611614675077 \tabularnewline
36 & 4821.3 & 4854.63518150962 & -33.335181509623 \tabularnewline
37 & 4840.5 & 4829.90035544327 & 10.5996445567343 \tabularnewline
38 & 4847.6 & 4848.47577611719 & -0.875776117186433 \tabularnewline
39 & 4832.3 & 4761.31399692606 & 70.9860030739374 \tabularnewline
40 & 4814.7 & 4905.98913114891 & -91.2891311489075 \tabularnewline
41 & 4806.4 & 4841.61442656711 & -35.2144265671068 \tabularnewline
42 & 4803.4 & 4850.17688446858 & -46.7768844685797 \tabularnewline
43 & 4770.3 & 4719.9730982569 & 50.326901743103 \tabularnewline
44 & 4723.4 & 4570.23263137114 & 153.167368628856 \tabularnewline
45 & 4667.1 & 4723.45987408388 & -56.3598740838843 \tabularnewline
46 & 4636.8 & 4654.85725669748 & -18.0572566974843 \tabularnewline
47 & 4613.2 & 4607.15688967555 & 6.04311032445094 \tabularnewline
48 & 4605.3 & 4628.91718549984 & -23.6171854998438 \tabularnewline
49 & 4590.4 & 4620.86322664518 & -30.4632266451827 \tabularnewline
50 & 4595.4 & 4626.08952487754 & -30.6895248775436 \tabularnewline
51 & 4600.1 & 4553.85794047474 & 46.2420595252624 \tabularnewline
52 & 4543.3 & 4639.2079622279 & -95.907962227896 \tabularnewline
53 & 4596.4 & 4589.5127755194 & 6.88722448060162 \tabularnewline
54 & 4575.4 & 4602.65045011173 & -27.2504501117346 \tabularnewline
55 & 4547.9 & 4507.22441906741 & 40.6755809325869 \tabularnewline
56 & 4503.7 & 4387.37236834427 & 116.327631655729 \tabularnewline
57 & 4446.3 & 4463.80224042068 & -17.5022404206784 \tabularnewline
58 & 4401.4 & 4415.28859264677 & -13.8885926467656 \tabularnewline
59 & 4354.3 & 4375.57774934189 & -21.2777493418862 \tabularnewline
60 & 4336.3 & 4380.4652333567 & -44.1652333566999 \tabularnewline
61 & 4300.9 & 4363.76408153961 & -62.8640815396066 \tabularnewline
62 & 4304.1 & 4358.95828769163 & -54.858287691628 \tabularnewline
63 & 4273.2 & 4302.48631389222 & -29.286313892223 \tabularnewline
64 & 4279.9 & 4320.28307053216 & -40.3830705321643 \tabularnewline
65 & 4243.1 & 4311.70510709393 & -68.6051070939257 \tabularnewline
66 & 4199.1 & 4291.2252463772 & -92.1252463772007 \tabularnewline
67 & 4177.6 & 4195.35189932802 & -17.7518993280237 \tabularnewline
68 & 4141.7 & 4077.37089578834 & 64.3291042116589 \tabularnewline
69 & 4088.3 & 4088.8502222353 & -0.550222235296133 \tabularnewline
70 & 4021.4 & 4034.96510591014 & -13.5651059101424 \tabularnewline
71 & 3981.2 & 3982.69914195856 & -1.49914195856127 \tabularnewline
72 & 3937.2 & 3974.92633074247 & -37.726330742466 \tabularnewline
73 & 3893.1 & 3944.12159575373 & -51.0215957537339 \tabularnewline
74 & 3864.7 & 3935.24885666672 & -70.54885666672 \tabularnewline
75 & 3847.8 & 3873.79668563517 & -25.9966856351698 \tabularnewline
76 & 3840.8 & 3879.20333791336 & -38.4033379133552 \tabularnewline
77 & 3828.4 & 3852.53408601557 & -24.1340860155692 \tabularnewline
78 & 3798.6 & 3826.0689069702 & -27.4689069701972 \tabularnewline
79 & 3773 & 3761.65828917387 & 11.3417108261265 \tabularnewline
80 & 3737.8 & 3670.50998839756 & 67.2900116024398 \tabularnewline
81 & 3699 & 3656.22242096016 & 42.7775790398437 \tabularnewline
82 & 3674 & 3603.22439476293 & 70.7756052370737 \tabularnewline
83 & 3648.8 & 3571.20122635207 & 77.5987736479301 \tabularnewline
84 & 3645.6 & 3569.23188145803 & 76.3681185419678 \tabularnewline
85 & 3331 & 3562.37034308305 & -231.370343083045 \tabularnewline
86 & 3674.7 & 3505.40446851004 & 169.295531489964 \tabularnewline
87 & 3714.5 & 3515.79761296369 & 198.702387036305 \tabularnewline
88 & 3739.7 & 3577.57600696554 & 162.123993034462 \tabularnewline
89 & 3759.7 & 3615.84230150175 & 143.857698498245 \tabularnewline
90 & 3708.6 & 3646.01874502028 & 62.5812549797247 \tabularnewline
91 & 3717.3 & 3636.86853336794 & 80.4314666320638 \tabularnewline
92 & 3705.3 & 3603.67023570076 & 101.629764299237 \tabularnewline
93 & 3612.8 & 3614.89018886802 & -2.09018886801778 \tabularnewline
94 & 3665 & 3585.4101905213 & 79.5898094787021 \tabularnewline
95 & 3670.8 & 3582.2707557914 & 88.5292442086002 \tabularnewline
96 & 3687.6 & 3607.37829608448 & 80.2217039155212 \tabularnewline
97 & 3708.2 & 3528.3267809426 & 179.873219057404 \tabularnewline
98 & 3737.2 & 3726.49156151004 & 10.7084384899626 \tabularnewline
99 & 3748.7 & 3743.11915851748 & 5.58084148251783 \tabularnewline
100 & 3785.3 & 3777.22723870197 & 8.07276129802858 \tabularnewline
101 & 3787.1 & 3798.16546407752 & -11.0654640775228 \tabularnewline
102 & 3785.8 & 3786.54037519378 & -0.740375193780892 \tabularnewline
103 & 3749.7 & 3785.79295596434 & -36.0929559643437 \tabularnewline
104 & 3716.3 & 3747.14718894381 & -30.8471889438074 \tabularnewline
105 & 3650 & 3705.95793694156 & -55.9579369415637 \tabularnewline
106 & 3096.9 & 3699.18040155318 & -602.28040155318 \tabularnewline
107 & 3703.2 & 3538.12286890682 & 165.077131093185 \tabularnewline
108 & 3716 & 3569.78143584785 & 146.218564152154 \tabularnewline
109 & 3736.9 & 3531.1720799107 & 205.727920089303 \tabularnewline
110 & 3771.9 & 3675.81152683801 & 96.0884731619917 \tabularnewline
111 & 3704 & 3706.73578559868 & -2.73578559867792 \tabularnewline
112 & 3824.2 & 3736.60379335393 & 87.5962066460716 \tabularnewline
113 & 3733.5 & 3767.99008105664 & -34.4900810566414 \tabularnewline
114 & 3827.5 & 3752.79118021471 & 74.7088197852927 \tabularnewline
115 & 3827.6 & 3757.81776448564 & 69.7822355143612 \tabularnewline
116 & 3696.5 & 3747.48956632075 & -50.9895663207508 \tabularnewline
117 & 3675.8 & 3696.48900438163 & -20.6890043816297 \tabularnewline
118 & 3757.5 & 3526.80425191518 & 230.69574808482 \tabularnewline
119 & 3753.3 & 3821.0761372895 & -67.7761372895025 \tabularnewline
120 & 3418.7 & 3814.94610610784 & -396.246106107842 \tabularnewline
121 & 3772.9 & 3680.39143043518 & 92.5085695648195 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299734&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]5329.6[/C][C]5395.91685363248[/C][C]-66.3168536324774[/C][/ROW]
[ROW][C]14[/C][C]5345.7[/C][C]5392.3225572151[/C][C]-46.6225572150952[/C][/ROW]
[ROW][C]15[/C][C]5353.8[/C][C]5372.20305348728[/C][C]-18.4030534872791[/C][/ROW]
[ROW][C]16[/C][C]5377.2[/C][C]5393.13532814259[/C][C]-15.9353281425947[/C][/ROW]
[ROW][C]17[/C][C]5334.1[/C][C]5355.95122965576[/C][C]-21.8512296557547[/C][/ROW]
[ROW][C]18[/C][C]5351.1[/C][C]5377.47276052825[/C][C]-26.3727605282475[/C][/ROW]
[ROW][C]19[/C][C]5001[/C][C]5309.29512678235[/C][C]-308.295126782354[/C][/ROW]
[ROW][C]20[/C][C]5246.4[/C][C]4787.09423462143[/C][C]459.305765378573[/C][/ROW]
[ROW][C]21[/C][C]5230[/C][C]5268.67485697334[/C][C]-38.6748569733445[/C][/ROW]
[ROW][C]22[/C][C]5115.8[/C][C]5218.34218557069[/C][C]-102.542185570693[/C][/ROW]
[ROW][C]23[/C][C]4972.6[/C][C]5165.54408933216[/C][C]-192.944089332161[/C][/ROW]
[ROW][C]24[/C][C]5077.6[/C][C]5107.77421331349[/C][C]-30.1742133134921[/C][/ROW]
[ROW][C]25[/C][C]5056.9[/C][C]5075.54158377329[/C][C]-18.641583773293[/C][/ROW]
[ROW][C]26[/C][C]5070.7[/C][C]5079.0553090554[/C][C]-8.35530905540327[/C][/ROW]
[ROW][C]27[/C][C]4799.3[/C][C]5067.71237792104[/C][C]-268.412377921035[/C][/ROW]
[ROW][C]28[/C][C]5076[/C][C]5018.64454093134[/C][C]57.3554590686608[/C][/ROW]
[ROW][C]29[/C][C]5021.5[/C][C]4982.33701636491[/C][C]39.1629836350858[/C][/ROW]
[ROW][C]30[/C][C]5026.4[/C][C]5004.10612568574[/C][C]22.2938743142631[/C][/ROW]
[ROW][C]31[/C][C]4981.9[/C][C]4846.23757850673[/C][C]135.662421493265[/C][/ROW]
[ROW][C]32[/C][C]4936.6[/C][C]4668.71723160797[/C][C]267.882768392033[/C][/ROW]
[ROW][C]33[/C][C]4901.8[/C][C]4945.31467044284[/C][C]-43.5146704428389[/C][/ROW]
[ROW][C]34[/C][C]4853.8[/C][C]4869.69865202664[/C][C]-15.8986520266426[/C][/ROW]
[ROW][C]35[/C][C]4839.2[/C][C]4805.73883853249[/C][C]33.4611614675077[/C][/ROW]
[ROW][C]36[/C][C]4821.3[/C][C]4854.63518150962[/C][C]-33.335181509623[/C][/ROW]
[ROW][C]37[/C][C]4840.5[/C][C]4829.90035544327[/C][C]10.5996445567343[/C][/ROW]
[ROW][C]38[/C][C]4847.6[/C][C]4848.47577611719[/C][C]-0.875776117186433[/C][/ROW]
[ROW][C]39[/C][C]4832.3[/C][C]4761.31399692606[/C][C]70.9860030739374[/C][/ROW]
[ROW][C]40[/C][C]4814.7[/C][C]4905.98913114891[/C][C]-91.2891311489075[/C][/ROW]
[ROW][C]41[/C][C]4806.4[/C][C]4841.61442656711[/C][C]-35.2144265671068[/C][/ROW]
[ROW][C]42[/C][C]4803.4[/C][C]4850.17688446858[/C][C]-46.7768844685797[/C][/ROW]
[ROW][C]43[/C][C]4770.3[/C][C]4719.9730982569[/C][C]50.326901743103[/C][/ROW]
[ROW][C]44[/C][C]4723.4[/C][C]4570.23263137114[/C][C]153.167368628856[/C][/ROW]
[ROW][C]45[/C][C]4667.1[/C][C]4723.45987408388[/C][C]-56.3598740838843[/C][/ROW]
[ROW][C]46[/C][C]4636.8[/C][C]4654.85725669748[/C][C]-18.0572566974843[/C][/ROW]
[ROW][C]47[/C][C]4613.2[/C][C]4607.15688967555[/C][C]6.04311032445094[/C][/ROW]
[ROW][C]48[/C][C]4605.3[/C][C]4628.91718549984[/C][C]-23.6171854998438[/C][/ROW]
[ROW][C]49[/C][C]4590.4[/C][C]4620.86322664518[/C][C]-30.4632266451827[/C][/ROW]
[ROW][C]50[/C][C]4595.4[/C][C]4626.08952487754[/C][C]-30.6895248775436[/C][/ROW]
[ROW][C]51[/C][C]4600.1[/C][C]4553.85794047474[/C][C]46.2420595252624[/C][/ROW]
[ROW][C]52[/C][C]4543.3[/C][C]4639.2079622279[/C][C]-95.907962227896[/C][/ROW]
[ROW][C]53[/C][C]4596.4[/C][C]4589.5127755194[/C][C]6.88722448060162[/C][/ROW]
[ROW][C]54[/C][C]4575.4[/C][C]4602.65045011173[/C][C]-27.2504501117346[/C][/ROW]
[ROW][C]55[/C][C]4547.9[/C][C]4507.22441906741[/C][C]40.6755809325869[/C][/ROW]
[ROW][C]56[/C][C]4503.7[/C][C]4387.37236834427[/C][C]116.327631655729[/C][/ROW]
[ROW][C]57[/C][C]4446.3[/C][C]4463.80224042068[/C][C]-17.5022404206784[/C][/ROW]
[ROW][C]58[/C][C]4401.4[/C][C]4415.28859264677[/C][C]-13.8885926467656[/C][/ROW]
[ROW][C]59[/C][C]4354.3[/C][C]4375.57774934189[/C][C]-21.2777493418862[/C][/ROW]
[ROW][C]60[/C][C]4336.3[/C][C]4380.4652333567[/C][C]-44.1652333566999[/C][/ROW]
[ROW][C]61[/C][C]4300.9[/C][C]4363.76408153961[/C][C]-62.8640815396066[/C][/ROW]
[ROW][C]62[/C][C]4304.1[/C][C]4358.95828769163[/C][C]-54.858287691628[/C][/ROW]
[ROW][C]63[/C][C]4273.2[/C][C]4302.48631389222[/C][C]-29.286313892223[/C][/ROW]
[ROW][C]64[/C][C]4279.9[/C][C]4320.28307053216[/C][C]-40.3830705321643[/C][/ROW]
[ROW][C]65[/C][C]4243.1[/C][C]4311.70510709393[/C][C]-68.6051070939257[/C][/ROW]
[ROW][C]66[/C][C]4199.1[/C][C]4291.2252463772[/C][C]-92.1252463772007[/C][/ROW]
[ROW][C]67[/C][C]4177.6[/C][C]4195.35189932802[/C][C]-17.7518993280237[/C][/ROW]
[ROW][C]68[/C][C]4141.7[/C][C]4077.37089578834[/C][C]64.3291042116589[/C][/ROW]
[ROW][C]69[/C][C]4088.3[/C][C]4088.8502222353[/C][C]-0.550222235296133[/C][/ROW]
[ROW][C]70[/C][C]4021.4[/C][C]4034.96510591014[/C][C]-13.5651059101424[/C][/ROW]
[ROW][C]71[/C][C]3981.2[/C][C]3982.69914195856[/C][C]-1.49914195856127[/C][/ROW]
[ROW][C]72[/C][C]3937.2[/C][C]3974.92633074247[/C][C]-37.726330742466[/C][/ROW]
[ROW][C]73[/C][C]3893.1[/C][C]3944.12159575373[/C][C]-51.0215957537339[/C][/ROW]
[ROW][C]74[/C][C]3864.7[/C][C]3935.24885666672[/C][C]-70.54885666672[/C][/ROW]
[ROW][C]75[/C][C]3847.8[/C][C]3873.79668563517[/C][C]-25.9966856351698[/C][/ROW]
[ROW][C]76[/C][C]3840.8[/C][C]3879.20333791336[/C][C]-38.4033379133552[/C][/ROW]
[ROW][C]77[/C][C]3828.4[/C][C]3852.53408601557[/C][C]-24.1340860155692[/C][/ROW]
[ROW][C]78[/C][C]3798.6[/C][C]3826.0689069702[/C][C]-27.4689069701972[/C][/ROW]
[ROW][C]79[/C][C]3773[/C][C]3761.65828917387[/C][C]11.3417108261265[/C][/ROW]
[ROW][C]80[/C][C]3737.8[/C][C]3670.50998839756[/C][C]67.2900116024398[/C][/ROW]
[ROW][C]81[/C][C]3699[/C][C]3656.22242096016[/C][C]42.7775790398437[/C][/ROW]
[ROW][C]82[/C][C]3674[/C][C]3603.22439476293[/C][C]70.7756052370737[/C][/ROW]
[ROW][C]83[/C][C]3648.8[/C][C]3571.20122635207[/C][C]77.5987736479301[/C][/ROW]
[ROW][C]84[/C][C]3645.6[/C][C]3569.23188145803[/C][C]76.3681185419678[/C][/ROW]
[ROW][C]85[/C][C]3331[/C][C]3562.37034308305[/C][C]-231.370343083045[/C][/ROW]
[ROW][C]86[/C][C]3674.7[/C][C]3505.40446851004[/C][C]169.295531489964[/C][/ROW]
[ROW][C]87[/C][C]3714.5[/C][C]3515.79761296369[/C][C]198.702387036305[/C][/ROW]
[ROW][C]88[/C][C]3739.7[/C][C]3577.57600696554[/C][C]162.123993034462[/C][/ROW]
[ROW][C]89[/C][C]3759.7[/C][C]3615.84230150175[/C][C]143.857698498245[/C][/ROW]
[ROW][C]90[/C][C]3708.6[/C][C]3646.01874502028[/C][C]62.5812549797247[/C][/ROW]
[ROW][C]91[/C][C]3717.3[/C][C]3636.86853336794[/C][C]80.4314666320638[/C][/ROW]
[ROW][C]92[/C][C]3705.3[/C][C]3603.67023570076[/C][C]101.629764299237[/C][/ROW]
[ROW][C]93[/C][C]3612.8[/C][C]3614.89018886802[/C][C]-2.09018886801778[/C][/ROW]
[ROW][C]94[/C][C]3665[/C][C]3585.4101905213[/C][C]79.5898094787021[/C][/ROW]
[ROW][C]95[/C][C]3670.8[/C][C]3582.2707557914[/C][C]88.5292442086002[/C][/ROW]
[ROW][C]96[/C][C]3687.6[/C][C]3607.37829608448[/C][C]80.2217039155212[/C][/ROW]
[ROW][C]97[/C][C]3708.2[/C][C]3528.3267809426[/C][C]179.873219057404[/C][/ROW]
[ROW][C]98[/C][C]3737.2[/C][C]3726.49156151004[/C][C]10.7084384899626[/C][/ROW]
[ROW][C]99[/C][C]3748.7[/C][C]3743.11915851748[/C][C]5.58084148251783[/C][/ROW]
[ROW][C]100[/C][C]3785.3[/C][C]3777.22723870197[/C][C]8.07276129802858[/C][/ROW]
[ROW][C]101[/C][C]3787.1[/C][C]3798.16546407752[/C][C]-11.0654640775228[/C][/ROW]
[ROW][C]102[/C][C]3785.8[/C][C]3786.54037519378[/C][C]-0.740375193780892[/C][/ROW]
[ROW][C]103[/C][C]3749.7[/C][C]3785.79295596434[/C][C]-36.0929559643437[/C][/ROW]
[ROW][C]104[/C][C]3716.3[/C][C]3747.14718894381[/C][C]-30.8471889438074[/C][/ROW]
[ROW][C]105[/C][C]3650[/C][C]3705.95793694156[/C][C]-55.9579369415637[/C][/ROW]
[ROW][C]106[/C][C]3096.9[/C][C]3699.18040155318[/C][C]-602.28040155318[/C][/ROW]
[ROW][C]107[/C][C]3703.2[/C][C]3538.12286890682[/C][C]165.077131093185[/C][/ROW]
[ROW][C]108[/C][C]3716[/C][C]3569.78143584785[/C][C]146.218564152154[/C][/ROW]
[ROW][C]109[/C][C]3736.9[/C][C]3531.1720799107[/C][C]205.727920089303[/C][/ROW]
[ROW][C]110[/C][C]3771.9[/C][C]3675.81152683801[/C][C]96.0884731619917[/C][/ROW]
[ROW][C]111[/C][C]3704[/C][C]3706.73578559868[/C][C]-2.73578559867792[/C][/ROW]
[ROW][C]112[/C][C]3824.2[/C][C]3736.60379335393[/C][C]87.5962066460716[/C][/ROW]
[ROW][C]113[/C][C]3733.5[/C][C]3767.99008105664[/C][C]-34.4900810566414[/C][/ROW]
[ROW][C]114[/C][C]3827.5[/C][C]3752.79118021471[/C][C]74.7088197852927[/C][/ROW]
[ROW][C]115[/C][C]3827.6[/C][C]3757.81776448564[/C][C]69.7822355143612[/C][/ROW]
[ROW][C]116[/C][C]3696.5[/C][C]3747.48956632075[/C][C]-50.9895663207508[/C][/ROW]
[ROW][C]117[/C][C]3675.8[/C][C]3696.48900438163[/C][C]-20.6890043816297[/C][/ROW]
[ROW][C]118[/C][C]3757.5[/C][C]3526.80425191518[/C][C]230.69574808482[/C][/ROW]
[ROW][C]119[/C][C]3753.3[/C][C]3821.0761372895[/C][C]-67.7761372895025[/C][/ROW]
[ROW][C]120[/C][C]3418.7[/C][C]3814.94610610784[/C][C]-396.246106107842[/C][/ROW]
[ROW][C]121[/C][C]3772.9[/C][C]3680.39143043518[/C][C]92.5085695648195[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299734&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299734&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
135329.65395.91685363248-66.3168536324774
145345.75392.3225572151-46.6225572150952
155353.85372.20305348728-18.4030534872791
165377.25393.13532814259-15.9353281425947
175334.15355.95122965576-21.8512296557547
185351.15377.47276052825-26.3727605282475
1950015309.29512678235-308.295126782354
205246.44787.09423462143459.305765378573
2152305268.67485697334-38.6748569733445
225115.85218.34218557069-102.542185570693
234972.65165.54408933216-192.944089332161
245077.65107.77421331349-30.1742133134921
255056.95075.54158377329-18.641583773293
265070.75079.0553090554-8.35530905540327
274799.35067.71237792104-268.412377921035
2850765018.6445409313457.3554590686608
295021.54982.3370163649139.1629836350858
305026.45004.1061256857422.2938743142631
314981.94846.23757850673135.662421493265
324936.64668.71723160797267.882768392033
334901.84945.31467044284-43.5146704428389
344853.84869.69865202664-15.8986520266426
354839.24805.7388385324933.4611614675077
364821.34854.63518150962-33.335181509623
374840.54829.9003554432710.5996445567343
384847.64848.47577611719-0.875776117186433
394832.34761.3139969260670.9860030739374
404814.74905.98913114891-91.2891311489075
414806.44841.61442656711-35.2144265671068
424803.44850.17688446858-46.7768844685797
434770.34719.973098256950.326901743103
444723.44570.23263137114153.167368628856
454667.14723.45987408388-56.3598740838843
464636.84654.85725669748-18.0572566974843
474613.24607.156889675556.04311032445094
484605.34628.91718549984-23.6171854998438
494590.44620.86322664518-30.4632266451827
504595.44626.08952487754-30.6895248775436
514600.14553.8579404747446.2420595252624
524543.34639.2079622279-95.907962227896
534596.44589.51277551946.88722448060162
544575.44602.65045011173-27.2504501117346
554547.94507.2244190674140.6755809325869
564503.74387.37236834427116.327631655729
574446.34463.80224042068-17.5022404206784
584401.44415.28859264677-13.8885926467656
594354.34375.57774934189-21.2777493418862
604336.34380.4652333567-44.1652333566999
614300.94363.76408153961-62.8640815396066
624304.14358.95828769163-54.858287691628
634273.24302.48631389222-29.286313892223
644279.94320.28307053216-40.3830705321643
654243.14311.70510709393-68.6051070939257
664199.14291.2252463772-92.1252463772007
674177.64195.35189932802-17.7518993280237
684141.74077.3708957883464.3291042116589
694088.34088.8502222353-0.550222235296133
704021.44034.96510591014-13.5651059101424
713981.23982.69914195856-1.49914195856127
723937.23974.92633074247-37.726330742466
733893.13944.12159575373-51.0215957537339
743864.73935.24885666672-70.54885666672
753847.83873.79668563517-25.9966856351698
763840.83879.20333791336-38.4033379133552
773828.43852.53408601557-24.1340860155692
783798.63826.0689069702-27.4689069701972
7937733761.6582891738711.3417108261265
803737.83670.5099883975667.2900116024398
8136993656.2224209601642.7775790398437
8236743603.2243947629370.7756052370737
833648.83571.2012263520777.5987736479301
843645.63569.2318814580376.3681185419678
8533313562.37034308305-231.370343083045
863674.73505.40446851004169.295531489964
873714.53515.79761296369198.702387036305
883739.73577.57600696554162.123993034462
893759.73615.84230150175143.857698498245
903708.63646.0187450202862.5812549797247
913717.33636.8685333679480.4314666320638
923705.33603.67023570076101.629764299237
933612.83614.89018886802-2.09018886801778
9436653585.410190521379.5898094787021
953670.83582.270755791488.5292442086002
963687.63607.3782960844880.2217039155212
973708.23528.3267809426179.873219057404
983737.23726.4915615100410.7084384899626
993748.73743.119158517485.58084148251783
1003785.33777.227238701978.07276129802858
1013787.13798.16546407752-11.0654640775228
1023785.83786.54037519378-0.740375193780892
1033749.73785.79295596434-36.0929559643437
1043716.33747.14718894381-30.8471889438074
10536503705.95793694156-55.9579369415637
1063096.93699.18040155318-602.28040155318
1073703.23538.12286890682165.077131093185
10837163569.78143584785146.218564152154
1093736.93531.1720799107205.727920089303
1103771.93675.8115268380196.0884731619917
11137043706.73578559868-2.73578559867792
1123824.23736.6037933539387.5962066460716
1133733.53767.99008105664-34.4900810566414
1143827.53752.7911802147174.7088197852927
1153827.63757.8177644856469.7822355143612
1163696.53747.48956632075-50.9895663207508
1173675.83696.48900438163-20.6890043816297
1183757.53526.80425191518230.69574808482
1193753.33821.0761372895-67.7761372895025
1203418.73814.94610610784-396.246106107842
1213772.93680.3914304351892.5085695648195







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1223767.093668919633526.025233656144008.16210418313
1233744.735309072143496.344398989143993.12621915515
1243803.631674162863546.528501614194060.73484671152
1253773.906195185793506.679009397174041.1333809744
1263799.355194085133520.594698932844078.11568923743
1273782.424126807723490.743543275514074.10471033992
1283712.383519805063406.433845419144018.33319419097
1293677.98857980733356.469183852753999.50797576186
1303589.304527342263250.969625299873927.63942938464
1313727.251303926393370.913062745444083.58954510735
1323623.130433232213247.659505576483998.60136088794
1333734.752545889923339.076770694984130.42832108486

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
122 & 3767.09366891963 & 3526.02523365614 & 4008.16210418313 \tabularnewline
123 & 3744.73530907214 & 3496.34439898914 & 3993.12621915515 \tabularnewline
124 & 3803.63167416286 & 3546.52850161419 & 4060.73484671152 \tabularnewline
125 & 3773.90619518579 & 3506.67900939717 & 4041.1333809744 \tabularnewline
126 & 3799.35519408513 & 3520.59469893284 & 4078.11568923743 \tabularnewline
127 & 3782.42412680772 & 3490.74354327551 & 4074.10471033992 \tabularnewline
128 & 3712.38351980506 & 3406.43384541914 & 4018.33319419097 \tabularnewline
129 & 3677.9885798073 & 3356.46918385275 & 3999.50797576186 \tabularnewline
130 & 3589.30452734226 & 3250.96962529987 & 3927.63942938464 \tabularnewline
131 & 3727.25130392639 & 3370.91306274544 & 4083.58954510735 \tabularnewline
132 & 3623.13043323221 & 3247.65950557648 & 3998.60136088794 \tabularnewline
133 & 3734.75254588992 & 3339.07677069498 & 4130.42832108486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299734&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]122[/C][C]3767.09366891963[/C][C]3526.02523365614[/C][C]4008.16210418313[/C][/ROW]
[ROW][C]123[/C][C]3744.73530907214[/C][C]3496.34439898914[/C][C]3993.12621915515[/C][/ROW]
[ROW][C]124[/C][C]3803.63167416286[/C][C]3546.52850161419[/C][C]4060.73484671152[/C][/ROW]
[ROW][C]125[/C][C]3773.90619518579[/C][C]3506.67900939717[/C][C]4041.1333809744[/C][/ROW]
[ROW][C]126[/C][C]3799.35519408513[/C][C]3520.59469893284[/C][C]4078.11568923743[/C][/ROW]
[ROW][C]127[/C][C]3782.42412680772[/C][C]3490.74354327551[/C][C]4074.10471033992[/C][/ROW]
[ROW][C]128[/C][C]3712.38351980506[/C][C]3406.43384541914[/C][C]4018.33319419097[/C][/ROW]
[ROW][C]129[/C][C]3677.9885798073[/C][C]3356.46918385275[/C][C]3999.50797576186[/C][/ROW]
[ROW][C]130[/C][C]3589.30452734226[/C][C]3250.96962529987[/C][C]3927.63942938464[/C][/ROW]
[ROW][C]131[/C][C]3727.25130392639[/C][C]3370.91306274544[/C][C]4083.58954510735[/C][/ROW]
[ROW][C]132[/C][C]3623.13043323221[/C][C]3247.65950557648[/C][C]3998.60136088794[/C][/ROW]
[ROW][C]133[/C][C]3734.75254588992[/C][C]3339.07677069498[/C][C]4130.42832108486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299734&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299734&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
1223767.093668919633526.025233656144008.16210418313
1233744.735309072143496.344398989143993.12621915515
1243803.631674162863546.528501614194060.73484671152
1253773.906195185793506.679009397174041.1333809744
1263799.355194085133520.594698932844078.11568923743
1273782.424126807723490.743543275514074.10471033992
1283712.383519805063406.433845419144018.33319419097
1293677.98857980733356.469183852753999.50797576186
1303589.304527342263250.969625299873927.63942938464
1313727.251303926393370.913062745444083.58954510735
1323623.130433232213247.659505576483998.60136088794
1333734.752545889923339.076770694984130.42832108486



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):
par4 <- '12'
par3 <- 'multiplicative'
par2 <- 'Triple'
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')