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 computationThu, 15 Dec 2016 00:17:12 +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/15/t1481758825cj88mf5una23c1h.htm/, Retrieved Fri, 03 May 2024 06:46:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299753, Retrieved Fri, 03 May 2024 06:46:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-14 23:17:12] [31f526a885cd288e1bc58dc4a6a7fb1f] [Current]
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Dataseries X:
4926
5242
5650
5042
4738
4178
3688
3870
3822
3872
3216
3366
4034
4514
5286
4940
5112
5188
4588
4754
4898
5422
5458
5088
5676
6518
6768
6306
6296
5728
5604
4956
4744
5160
3782
4114
5488
5874
6812
6658
6236
5542
5468
5738
5828
6168
5324
5038
5662
5868
6008
6206
5880
5594
5216
5522
5748
5966
5600
5546
5798
6218
7020
6684
6386
6680
6332
7128
7592
8468
7892
7866
8270
7536
7990
7638
8040
7564
7234
7718
7722
7966
7412
6792
7316
7424
7910
7574
7414
7292
6432
6630
6594
7318
6634
6032
6460
6446
6890
6638
6872
7516
6474
6812
6532
6908
6502
5656
5948
5608
7062
6074
5998
5944
5914
6286
6340
6666
6090
6264
7052
6666
5060
6818
6830
6986




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=299753&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=299753&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299753&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
alpha0.788213429577142
beta0
gamma0.421842734073014

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.788213429577142 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.421842734073014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299753&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]0.788213429577142[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.421842734073014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299753&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299753&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
alpha0.788213429577142
beta0
gamma0.421842734073014







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1340343911.88888888889122.111111111109
1445144470.5021429308943.4978570691101
1552865251.8180410608934.1819589391089
1649404880.0410231762559.9589768237456
1751124997.9984636294114.001536370595
1851885055.38630861944132.613691380564
1945884321.36117080836266.638829191636
2047544837.72644652091-83.7264465209064
2148984825.9291066593372.070893340675
2254225008.8499890357413.150010964298
2354584723.86401247134734.135987528659
2450885451.55016000761-363.550160007609
2556765821.01816102521-145.018161025209
2665186162.05317801549355.946821984513
2767687188.81325817946-420.813258179464
2863066460.70583468043-154.705834680433
2962966414.28978394388-118.289783943883
3057286290.24531226591-562.245312265908
3156045020.49686581742583.503134182576
3249565755.31698904917-799.316989049172
3347445193.40060534632-449.400605346318
3451604995.76287116823164.237128831766
3537824543.25750616593-761.257506165929
3641143994.18645199937119.813548000629
3754884764.17200460909723.827995390908
3858745834.7997554626839.2002445373228
3968126542.49969776866269.500302231336
4066586382.28089697857275.719103021427
4162366678.3849953294-442.384995329402
4255426259.2210608005-717.221060800501
4354684969.68053143611498.319468563895
4457385513.81573012011224.184269879894
4558285789.8985326294238.1014673705758
4661686031.33925836519136.660741634812
4753245474.41354467064-150.413544670644
4850385485.53334377866-447.533343778662
4956625862.29148584589-200.291485845891
5058686143.35077928012-275.350779280123
5160086623.69253162679-615.692531626791
5262065766.30844297926439.691557020745
5358806127.50196203993-247.501962039932
5455945837.39342543548-243.393425435481
5552165029.92735327947186.072646720531
5655225303.45400341015218.545996589854
5757485558.4678891459189.532110854105
5859665928.073628976637.9263710233963
5956005267.67676198492332.323238015076
6055465632.75130733498-86.7513073349792
6157986315.97143801546-517.971438015463
6262186339.92528258665-121.925282586652
6370206910.79272668968109.207273310322
6466846719.07307444362-35.0730744436169
6563866644.65643598364-258.65643598364
6666806346.12285244869333.877147551307
6763326032.03796611285299.962033887148
6871286398.23495009719729.765049902807
6975927053.60644039829538.393559601705
7084687684.64490750601783.355092493989
7178927638.10656993211253.893430067894
7278667903.92130519572-37.9213051957195
7382708587.1044229499-317.1044229499
7475368804.76735776896-1268.76735776896
7579908492.32800382052-502.328003820523
7676387805.69793690532-167.697936905316
7780407606.7695232948433.230476705197
7875647906.52781731387-342.527817313869
7972347056.26145635617177.738543643826
8077187364.51911438855353.480885611451
8177227706.2011243337115.7988756662871
8279667947.2084600096818.7915399903231
8374127250.7284262722161.271573727801
8467927417.46645939881-625.466459398812
8573167612.59620164428-296.596201644283
8674247761.40182966382-337.401829663824
8779108251.55146441467-341.551464414668
8875747721.54368464564-147.543684645642
8974147592.18844392663-178.188443926628
9072927340.71140206582-48.7114020658228
9164326768.51600776323-336.516007763234
9266306687.13225298517-57.1322529851668
9365946674.99475060158-80.9947506015787
9473186839.97541665958478.024583340421
9566346518.1982903896115.801709610396
9660326578.80869767336-546.808697673358
9764606865.31901872134-405.319018721338
9864466924.78226187149-478.782261871486
9968907303.1232103109-413.123210310903
10066386734.0343957236-96.0343957235991
10168726642.54164630597229.458353694028
10275166723.94484481433792.05515518567
10364746788.74029846475-314.740298464747
10468126749.4807697144762.5192302855303
10565326829.52228284091-297.522282840911
10669086873.7761773032434.2238226967638
10765026169.82811318046332.171886819539
10856566341.78637138114-685.786371381141
10959486531.39340007823-583.393400078228
11056086443.93277225503-835.932772255033
11170626546.6289127927515.371087207301
11260746737.72068595841-663.720685958415
11359986227.84970475208-229.84970475208
11459445997.48287365882-53.4828736588233
11559145296.93209917554617.067900824463
11662866025.84090932309260.159090676913
11763406229.4984804945110.501519505496
11866666625.0006202643840.9993797356165
11960905953.01200772904136.987992270956
12062645880.17867107439383.821328925614
12170526922.01270567707129.987294322927
12266667374.28629600547-708.286296005466
12350607698.32143595632-2638.32143595632
12468185298.289612590881519.71038740912
12568306548.19063099278281.809369007218
12669866736.87707628073249.122923719267

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4034 & 3911.88888888889 & 122.111111111109 \tabularnewline
14 & 4514 & 4470.50214293089 & 43.4978570691101 \tabularnewline
15 & 5286 & 5251.81804106089 & 34.1819589391089 \tabularnewline
16 & 4940 & 4880.04102317625 & 59.9589768237456 \tabularnewline
17 & 5112 & 4997.9984636294 & 114.001536370595 \tabularnewline
18 & 5188 & 5055.38630861944 & 132.613691380564 \tabularnewline
19 & 4588 & 4321.36117080836 & 266.638829191636 \tabularnewline
20 & 4754 & 4837.72644652091 & -83.7264465209064 \tabularnewline
21 & 4898 & 4825.92910665933 & 72.070893340675 \tabularnewline
22 & 5422 & 5008.8499890357 & 413.150010964298 \tabularnewline
23 & 5458 & 4723.86401247134 & 734.135987528659 \tabularnewline
24 & 5088 & 5451.55016000761 & -363.550160007609 \tabularnewline
25 & 5676 & 5821.01816102521 & -145.018161025209 \tabularnewline
26 & 6518 & 6162.05317801549 & 355.946821984513 \tabularnewline
27 & 6768 & 7188.81325817946 & -420.813258179464 \tabularnewline
28 & 6306 & 6460.70583468043 & -154.705834680433 \tabularnewline
29 & 6296 & 6414.28978394388 & -118.289783943883 \tabularnewline
30 & 5728 & 6290.24531226591 & -562.245312265908 \tabularnewline
31 & 5604 & 5020.49686581742 & 583.503134182576 \tabularnewline
32 & 4956 & 5755.31698904917 & -799.316989049172 \tabularnewline
33 & 4744 & 5193.40060534632 & -449.400605346318 \tabularnewline
34 & 5160 & 4995.76287116823 & 164.237128831766 \tabularnewline
35 & 3782 & 4543.25750616593 & -761.257506165929 \tabularnewline
36 & 4114 & 3994.18645199937 & 119.813548000629 \tabularnewline
37 & 5488 & 4764.17200460909 & 723.827995390908 \tabularnewline
38 & 5874 & 5834.79975546268 & 39.2002445373228 \tabularnewline
39 & 6812 & 6542.49969776866 & 269.500302231336 \tabularnewline
40 & 6658 & 6382.28089697857 & 275.719103021427 \tabularnewline
41 & 6236 & 6678.3849953294 & -442.384995329402 \tabularnewline
42 & 5542 & 6259.2210608005 & -717.221060800501 \tabularnewline
43 & 5468 & 4969.68053143611 & 498.319468563895 \tabularnewline
44 & 5738 & 5513.81573012011 & 224.184269879894 \tabularnewline
45 & 5828 & 5789.89853262942 & 38.1014673705758 \tabularnewline
46 & 6168 & 6031.33925836519 & 136.660741634812 \tabularnewline
47 & 5324 & 5474.41354467064 & -150.413544670644 \tabularnewline
48 & 5038 & 5485.53334377866 & -447.533343778662 \tabularnewline
49 & 5662 & 5862.29148584589 & -200.291485845891 \tabularnewline
50 & 5868 & 6143.35077928012 & -275.350779280123 \tabularnewline
51 & 6008 & 6623.69253162679 & -615.692531626791 \tabularnewline
52 & 6206 & 5766.30844297926 & 439.691557020745 \tabularnewline
53 & 5880 & 6127.50196203993 & -247.501962039932 \tabularnewline
54 & 5594 & 5837.39342543548 & -243.393425435481 \tabularnewline
55 & 5216 & 5029.92735327947 & 186.072646720531 \tabularnewline
56 & 5522 & 5303.45400341015 & 218.545996589854 \tabularnewline
57 & 5748 & 5558.4678891459 & 189.532110854105 \tabularnewline
58 & 5966 & 5928.0736289766 & 37.9263710233963 \tabularnewline
59 & 5600 & 5267.67676198492 & 332.323238015076 \tabularnewline
60 & 5546 & 5632.75130733498 & -86.7513073349792 \tabularnewline
61 & 5798 & 6315.97143801546 & -517.971438015463 \tabularnewline
62 & 6218 & 6339.92528258665 & -121.925282586652 \tabularnewline
63 & 7020 & 6910.79272668968 & 109.207273310322 \tabularnewline
64 & 6684 & 6719.07307444362 & -35.0730744436169 \tabularnewline
65 & 6386 & 6644.65643598364 & -258.65643598364 \tabularnewline
66 & 6680 & 6346.12285244869 & 333.877147551307 \tabularnewline
67 & 6332 & 6032.03796611285 & 299.962033887148 \tabularnewline
68 & 7128 & 6398.23495009719 & 729.765049902807 \tabularnewline
69 & 7592 & 7053.60644039829 & 538.393559601705 \tabularnewline
70 & 8468 & 7684.64490750601 & 783.355092493989 \tabularnewline
71 & 7892 & 7638.10656993211 & 253.893430067894 \tabularnewline
72 & 7866 & 7903.92130519572 & -37.9213051957195 \tabularnewline
73 & 8270 & 8587.1044229499 & -317.1044229499 \tabularnewline
74 & 7536 & 8804.76735776896 & -1268.76735776896 \tabularnewline
75 & 7990 & 8492.32800382052 & -502.328003820523 \tabularnewline
76 & 7638 & 7805.69793690532 & -167.697936905316 \tabularnewline
77 & 8040 & 7606.7695232948 & 433.230476705197 \tabularnewline
78 & 7564 & 7906.52781731387 & -342.527817313869 \tabularnewline
79 & 7234 & 7056.26145635617 & 177.738543643826 \tabularnewline
80 & 7718 & 7364.51911438855 & 353.480885611451 \tabularnewline
81 & 7722 & 7706.20112433371 & 15.7988756662871 \tabularnewline
82 & 7966 & 7947.20846000968 & 18.7915399903231 \tabularnewline
83 & 7412 & 7250.7284262722 & 161.271573727801 \tabularnewline
84 & 6792 & 7417.46645939881 & -625.466459398812 \tabularnewline
85 & 7316 & 7612.59620164428 & -296.596201644283 \tabularnewline
86 & 7424 & 7761.40182966382 & -337.401829663824 \tabularnewline
87 & 7910 & 8251.55146441467 & -341.551464414668 \tabularnewline
88 & 7574 & 7721.54368464564 & -147.543684645642 \tabularnewline
89 & 7414 & 7592.18844392663 & -178.188443926628 \tabularnewline
90 & 7292 & 7340.71140206582 & -48.7114020658228 \tabularnewline
91 & 6432 & 6768.51600776323 & -336.516007763234 \tabularnewline
92 & 6630 & 6687.13225298517 & -57.1322529851668 \tabularnewline
93 & 6594 & 6674.99475060158 & -80.9947506015787 \tabularnewline
94 & 7318 & 6839.97541665958 & 478.024583340421 \tabularnewline
95 & 6634 & 6518.1982903896 & 115.801709610396 \tabularnewline
96 & 6032 & 6578.80869767336 & -546.808697673358 \tabularnewline
97 & 6460 & 6865.31901872134 & -405.319018721338 \tabularnewline
98 & 6446 & 6924.78226187149 & -478.782261871486 \tabularnewline
99 & 6890 & 7303.1232103109 & -413.123210310903 \tabularnewline
100 & 6638 & 6734.0343957236 & -96.0343957235991 \tabularnewline
101 & 6872 & 6642.54164630597 & 229.458353694028 \tabularnewline
102 & 7516 & 6723.94484481433 & 792.05515518567 \tabularnewline
103 & 6474 & 6788.74029846475 & -314.740298464747 \tabularnewline
104 & 6812 & 6749.48076971447 & 62.5192302855303 \tabularnewline
105 & 6532 & 6829.52228284091 & -297.522282840911 \tabularnewline
106 & 6908 & 6873.77617730324 & 34.2238226967638 \tabularnewline
107 & 6502 & 6169.82811318046 & 332.171886819539 \tabularnewline
108 & 5656 & 6341.78637138114 & -685.786371381141 \tabularnewline
109 & 5948 & 6531.39340007823 & -583.393400078228 \tabularnewline
110 & 5608 & 6443.93277225503 & -835.932772255033 \tabularnewline
111 & 7062 & 6546.6289127927 & 515.371087207301 \tabularnewline
112 & 6074 & 6737.72068595841 & -663.720685958415 \tabularnewline
113 & 5998 & 6227.84970475208 & -229.84970475208 \tabularnewline
114 & 5944 & 5997.48287365882 & -53.4828736588233 \tabularnewline
115 & 5914 & 5296.93209917554 & 617.067900824463 \tabularnewline
116 & 6286 & 6025.84090932309 & 260.159090676913 \tabularnewline
117 & 6340 & 6229.4984804945 & 110.501519505496 \tabularnewline
118 & 6666 & 6625.00062026438 & 40.9993797356165 \tabularnewline
119 & 6090 & 5953.01200772904 & 136.987992270956 \tabularnewline
120 & 6264 & 5880.17867107439 & 383.821328925614 \tabularnewline
121 & 7052 & 6922.01270567707 & 129.987294322927 \tabularnewline
122 & 6666 & 7374.28629600547 & -708.286296005466 \tabularnewline
123 & 5060 & 7698.32143595632 & -2638.32143595632 \tabularnewline
124 & 6818 & 5298.28961259088 & 1519.71038740912 \tabularnewline
125 & 6830 & 6548.19063099278 & 281.809369007218 \tabularnewline
126 & 6986 & 6736.87707628073 & 249.122923719267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299753&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]4034[/C][C]3911.88888888889[/C][C]122.111111111109[/C][/ROW]
[ROW][C]14[/C][C]4514[/C][C]4470.50214293089[/C][C]43.4978570691101[/C][/ROW]
[ROW][C]15[/C][C]5286[/C][C]5251.81804106089[/C][C]34.1819589391089[/C][/ROW]
[ROW][C]16[/C][C]4940[/C][C]4880.04102317625[/C][C]59.9589768237456[/C][/ROW]
[ROW][C]17[/C][C]5112[/C][C]4997.9984636294[/C][C]114.001536370595[/C][/ROW]
[ROW][C]18[/C][C]5188[/C][C]5055.38630861944[/C][C]132.613691380564[/C][/ROW]
[ROW][C]19[/C][C]4588[/C][C]4321.36117080836[/C][C]266.638829191636[/C][/ROW]
[ROW][C]20[/C][C]4754[/C][C]4837.72644652091[/C][C]-83.7264465209064[/C][/ROW]
[ROW][C]21[/C][C]4898[/C][C]4825.92910665933[/C][C]72.070893340675[/C][/ROW]
[ROW][C]22[/C][C]5422[/C][C]5008.8499890357[/C][C]413.150010964298[/C][/ROW]
[ROW][C]23[/C][C]5458[/C][C]4723.86401247134[/C][C]734.135987528659[/C][/ROW]
[ROW][C]24[/C][C]5088[/C][C]5451.55016000761[/C][C]-363.550160007609[/C][/ROW]
[ROW][C]25[/C][C]5676[/C][C]5821.01816102521[/C][C]-145.018161025209[/C][/ROW]
[ROW][C]26[/C][C]6518[/C][C]6162.05317801549[/C][C]355.946821984513[/C][/ROW]
[ROW][C]27[/C][C]6768[/C][C]7188.81325817946[/C][C]-420.813258179464[/C][/ROW]
[ROW][C]28[/C][C]6306[/C][C]6460.70583468043[/C][C]-154.705834680433[/C][/ROW]
[ROW][C]29[/C][C]6296[/C][C]6414.28978394388[/C][C]-118.289783943883[/C][/ROW]
[ROW][C]30[/C][C]5728[/C][C]6290.24531226591[/C][C]-562.245312265908[/C][/ROW]
[ROW][C]31[/C][C]5604[/C][C]5020.49686581742[/C][C]583.503134182576[/C][/ROW]
[ROW][C]32[/C][C]4956[/C][C]5755.31698904917[/C][C]-799.316989049172[/C][/ROW]
[ROW][C]33[/C][C]4744[/C][C]5193.40060534632[/C][C]-449.400605346318[/C][/ROW]
[ROW][C]34[/C][C]5160[/C][C]4995.76287116823[/C][C]164.237128831766[/C][/ROW]
[ROW][C]35[/C][C]3782[/C][C]4543.25750616593[/C][C]-761.257506165929[/C][/ROW]
[ROW][C]36[/C][C]4114[/C][C]3994.18645199937[/C][C]119.813548000629[/C][/ROW]
[ROW][C]37[/C][C]5488[/C][C]4764.17200460909[/C][C]723.827995390908[/C][/ROW]
[ROW][C]38[/C][C]5874[/C][C]5834.79975546268[/C][C]39.2002445373228[/C][/ROW]
[ROW][C]39[/C][C]6812[/C][C]6542.49969776866[/C][C]269.500302231336[/C][/ROW]
[ROW][C]40[/C][C]6658[/C][C]6382.28089697857[/C][C]275.719103021427[/C][/ROW]
[ROW][C]41[/C][C]6236[/C][C]6678.3849953294[/C][C]-442.384995329402[/C][/ROW]
[ROW][C]42[/C][C]5542[/C][C]6259.2210608005[/C][C]-717.221060800501[/C][/ROW]
[ROW][C]43[/C][C]5468[/C][C]4969.68053143611[/C][C]498.319468563895[/C][/ROW]
[ROW][C]44[/C][C]5738[/C][C]5513.81573012011[/C][C]224.184269879894[/C][/ROW]
[ROW][C]45[/C][C]5828[/C][C]5789.89853262942[/C][C]38.1014673705758[/C][/ROW]
[ROW][C]46[/C][C]6168[/C][C]6031.33925836519[/C][C]136.660741634812[/C][/ROW]
[ROW][C]47[/C][C]5324[/C][C]5474.41354467064[/C][C]-150.413544670644[/C][/ROW]
[ROW][C]48[/C][C]5038[/C][C]5485.53334377866[/C][C]-447.533343778662[/C][/ROW]
[ROW][C]49[/C][C]5662[/C][C]5862.29148584589[/C][C]-200.291485845891[/C][/ROW]
[ROW][C]50[/C][C]5868[/C][C]6143.35077928012[/C][C]-275.350779280123[/C][/ROW]
[ROW][C]51[/C][C]6008[/C][C]6623.69253162679[/C][C]-615.692531626791[/C][/ROW]
[ROW][C]52[/C][C]6206[/C][C]5766.30844297926[/C][C]439.691557020745[/C][/ROW]
[ROW][C]53[/C][C]5880[/C][C]6127.50196203993[/C][C]-247.501962039932[/C][/ROW]
[ROW][C]54[/C][C]5594[/C][C]5837.39342543548[/C][C]-243.393425435481[/C][/ROW]
[ROW][C]55[/C][C]5216[/C][C]5029.92735327947[/C][C]186.072646720531[/C][/ROW]
[ROW][C]56[/C][C]5522[/C][C]5303.45400341015[/C][C]218.545996589854[/C][/ROW]
[ROW][C]57[/C][C]5748[/C][C]5558.4678891459[/C][C]189.532110854105[/C][/ROW]
[ROW][C]58[/C][C]5966[/C][C]5928.0736289766[/C][C]37.9263710233963[/C][/ROW]
[ROW][C]59[/C][C]5600[/C][C]5267.67676198492[/C][C]332.323238015076[/C][/ROW]
[ROW][C]60[/C][C]5546[/C][C]5632.75130733498[/C][C]-86.7513073349792[/C][/ROW]
[ROW][C]61[/C][C]5798[/C][C]6315.97143801546[/C][C]-517.971438015463[/C][/ROW]
[ROW][C]62[/C][C]6218[/C][C]6339.92528258665[/C][C]-121.925282586652[/C][/ROW]
[ROW][C]63[/C][C]7020[/C][C]6910.79272668968[/C][C]109.207273310322[/C][/ROW]
[ROW][C]64[/C][C]6684[/C][C]6719.07307444362[/C][C]-35.0730744436169[/C][/ROW]
[ROW][C]65[/C][C]6386[/C][C]6644.65643598364[/C][C]-258.65643598364[/C][/ROW]
[ROW][C]66[/C][C]6680[/C][C]6346.12285244869[/C][C]333.877147551307[/C][/ROW]
[ROW][C]67[/C][C]6332[/C][C]6032.03796611285[/C][C]299.962033887148[/C][/ROW]
[ROW][C]68[/C][C]7128[/C][C]6398.23495009719[/C][C]729.765049902807[/C][/ROW]
[ROW][C]69[/C][C]7592[/C][C]7053.60644039829[/C][C]538.393559601705[/C][/ROW]
[ROW][C]70[/C][C]8468[/C][C]7684.64490750601[/C][C]783.355092493989[/C][/ROW]
[ROW][C]71[/C][C]7892[/C][C]7638.10656993211[/C][C]253.893430067894[/C][/ROW]
[ROW][C]72[/C][C]7866[/C][C]7903.92130519572[/C][C]-37.9213051957195[/C][/ROW]
[ROW][C]73[/C][C]8270[/C][C]8587.1044229499[/C][C]-317.1044229499[/C][/ROW]
[ROW][C]74[/C][C]7536[/C][C]8804.76735776896[/C][C]-1268.76735776896[/C][/ROW]
[ROW][C]75[/C][C]7990[/C][C]8492.32800382052[/C][C]-502.328003820523[/C][/ROW]
[ROW][C]76[/C][C]7638[/C][C]7805.69793690532[/C][C]-167.697936905316[/C][/ROW]
[ROW][C]77[/C][C]8040[/C][C]7606.7695232948[/C][C]433.230476705197[/C][/ROW]
[ROW][C]78[/C][C]7564[/C][C]7906.52781731387[/C][C]-342.527817313869[/C][/ROW]
[ROW][C]79[/C][C]7234[/C][C]7056.26145635617[/C][C]177.738543643826[/C][/ROW]
[ROW][C]80[/C][C]7718[/C][C]7364.51911438855[/C][C]353.480885611451[/C][/ROW]
[ROW][C]81[/C][C]7722[/C][C]7706.20112433371[/C][C]15.7988756662871[/C][/ROW]
[ROW][C]82[/C][C]7966[/C][C]7947.20846000968[/C][C]18.7915399903231[/C][/ROW]
[ROW][C]83[/C][C]7412[/C][C]7250.7284262722[/C][C]161.271573727801[/C][/ROW]
[ROW][C]84[/C][C]6792[/C][C]7417.46645939881[/C][C]-625.466459398812[/C][/ROW]
[ROW][C]85[/C][C]7316[/C][C]7612.59620164428[/C][C]-296.596201644283[/C][/ROW]
[ROW][C]86[/C][C]7424[/C][C]7761.40182966382[/C][C]-337.401829663824[/C][/ROW]
[ROW][C]87[/C][C]7910[/C][C]8251.55146441467[/C][C]-341.551464414668[/C][/ROW]
[ROW][C]88[/C][C]7574[/C][C]7721.54368464564[/C][C]-147.543684645642[/C][/ROW]
[ROW][C]89[/C][C]7414[/C][C]7592.18844392663[/C][C]-178.188443926628[/C][/ROW]
[ROW][C]90[/C][C]7292[/C][C]7340.71140206582[/C][C]-48.7114020658228[/C][/ROW]
[ROW][C]91[/C][C]6432[/C][C]6768.51600776323[/C][C]-336.516007763234[/C][/ROW]
[ROW][C]92[/C][C]6630[/C][C]6687.13225298517[/C][C]-57.1322529851668[/C][/ROW]
[ROW][C]93[/C][C]6594[/C][C]6674.99475060158[/C][C]-80.9947506015787[/C][/ROW]
[ROW][C]94[/C][C]7318[/C][C]6839.97541665958[/C][C]478.024583340421[/C][/ROW]
[ROW][C]95[/C][C]6634[/C][C]6518.1982903896[/C][C]115.801709610396[/C][/ROW]
[ROW][C]96[/C][C]6032[/C][C]6578.80869767336[/C][C]-546.808697673358[/C][/ROW]
[ROW][C]97[/C][C]6460[/C][C]6865.31901872134[/C][C]-405.319018721338[/C][/ROW]
[ROW][C]98[/C][C]6446[/C][C]6924.78226187149[/C][C]-478.782261871486[/C][/ROW]
[ROW][C]99[/C][C]6890[/C][C]7303.1232103109[/C][C]-413.123210310903[/C][/ROW]
[ROW][C]100[/C][C]6638[/C][C]6734.0343957236[/C][C]-96.0343957235991[/C][/ROW]
[ROW][C]101[/C][C]6872[/C][C]6642.54164630597[/C][C]229.458353694028[/C][/ROW]
[ROW][C]102[/C][C]7516[/C][C]6723.94484481433[/C][C]792.05515518567[/C][/ROW]
[ROW][C]103[/C][C]6474[/C][C]6788.74029846475[/C][C]-314.740298464747[/C][/ROW]
[ROW][C]104[/C][C]6812[/C][C]6749.48076971447[/C][C]62.5192302855303[/C][/ROW]
[ROW][C]105[/C][C]6532[/C][C]6829.52228284091[/C][C]-297.522282840911[/C][/ROW]
[ROW][C]106[/C][C]6908[/C][C]6873.77617730324[/C][C]34.2238226967638[/C][/ROW]
[ROW][C]107[/C][C]6502[/C][C]6169.82811318046[/C][C]332.171886819539[/C][/ROW]
[ROW][C]108[/C][C]5656[/C][C]6341.78637138114[/C][C]-685.786371381141[/C][/ROW]
[ROW][C]109[/C][C]5948[/C][C]6531.39340007823[/C][C]-583.393400078228[/C][/ROW]
[ROW][C]110[/C][C]5608[/C][C]6443.93277225503[/C][C]-835.932772255033[/C][/ROW]
[ROW][C]111[/C][C]7062[/C][C]6546.6289127927[/C][C]515.371087207301[/C][/ROW]
[ROW][C]112[/C][C]6074[/C][C]6737.72068595841[/C][C]-663.720685958415[/C][/ROW]
[ROW][C]113[/C][C]5998[/C][C]6227.84970475208[/C][C]-229.84970475208[/C][/ROW]
[ROW][C]114[/C][C]5944[/C][C]5997.48287365882[/C][C]-53.4828736588233[/C][/ROW]
[ROW][C]115[/C][C]5914[/C][C]5296.93209917554[/C][C]617.067900824463[/C][/ROW]
[ROW][C]116[/C][C]6286[/C][C]6025.84090932309[/C][C]260.159090676913[/C][/ROW]
[ROW][C]117[/C][C]6340[/C][C]6229.4984804945[/C][C]110.501519505496[/C][/ROW]
[ROW][C]118[/C][C]6666[/C][C]6625.00062026438[/C][C]40.9993797356165[/C][/ROW]
[ROW][C]119[/C][C]6090[/C][C]5953.01200772904[/C][C]136.987992270956[/C][/ROW]
[ROW][C]120[/C][C]6264[/C][C]5880.17867107439[/C][C]383.821328925614[/C][/ROW]
[ROW][C]121[/C][C]7052[/C][C]6922.01270567707[/C][C]129.987294322927[/C][/ROW]
[ROW][C]122[/C][C]6666[/C][C]7374.28629600547[/C][C]-708.286296005466[/C][/ROW]
[ROW][C]123[/C][C]5060[/C][C]7698.32143595632[/C][C]-2638.32143595632[/C][/ROW]
[ROW][C]124[/C][C]6818[/C][C]5298.28961259088[/C][C]1519.71038740912[/C][/ROW]
[ROW][C]125[/C][C]6830[/C][C]6548.19063099278[/C][C]281.809369007218[/C][/ROW]
[ROW][C]126[/C][C]6986[/C][C]6736.87707628073[/C][C]249.122923719267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299753&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299753&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
1340343911.88888888889122.111111111109
1445144470.5021429308943.4978570691101
1552865251.8180410608934.1819589391089
1649404880.0410231762559.9589768237456
1751124997.9984636294114.001536370595
1851885055.38630861944132.613691380564
1945884321.36117080836266.638829191636
2047544837.72644652091-83.7264465209064
2148984825.9291066593372.070893340675
2254225008.8499890357413.150010964298
2354584723.86401247134734.135987528659
2450885451.55016000761-363.550160007609
2556765821.01816102521-145.018161025209
2665186162.05317801549355.946821984513
2767687188.81325817946-420.813258179464
2863066460.70583468043-154.705834680433
2962966414.28978394388-118.289783943883
3057286290.24531226591-562.245312265908
3156045020.49686581742583.503134182576
3249565755.31698904917-799.316989049172
3347445193.40060534632-449.400605346318
3451604995.76287116823164.237128831766
3537824543.25750616593-761.257506165929
3641143994.18645199937119.813548000629
3754884764.17200460909723.827995390908
3858745834.7997554626839.2002445373228
3968126542.49969776866269.500302231336
4066586382.28089697857275.719103021427
4162366678.3849953294-442.384995329402
4255426259.2210608005-717.221060800501
4354684969.68053143611498.319468563895
4457385513.81573012011224.184269879894
4558285789.8985326294238.1014673705758
4661686031.33925836519136.660741634812
4753245474.41354467064-150.413544670644
4850385485.53334377866-447.533343778662
4956625862.29148584589-200.291485845891
5058686143.35077928012-275.350779280123
5160086623.69253162679-615.692531626791
5262065766.30844297926439.691557020745
5358806127.50196203993-247.501962039932
5455945837.39342543548-243.393425435481
5552165029.92735327947186.072646720531
5655225303.45400341015218.545996589854
5757485558.4678891459189.532110854105
5859665928.073628976637.9263710233963
5956005267.67676198492332.323238015076
6055465632.75130733498-86.7513073349792
6157986315.97143801546-517.971438015463
6262186339.92528258665-121.925282586652
6370206910.79272668968109.207273310322
6466846719.07307444362-35.0730744436169
6563866644.65643598364-258.65643598364
6666806346.12285244869333.877147551307
6763326032.03796611285299.962033887148
6871286398.23495009719729.765049902807
6975927053.60644039829538.393559601705
7084687684.64490750601783.355092493989
7178927638.10656993211253.893430067894
7278667903.92130519572-37.9213051957195
7382708587.1044229499-317.1044229499
7475368804.76735776896-1268.76735776896
7579908492.32800382052-502.328003820523
7676387805.69793690532-167.697936905316
7780407606.7695232948433.230476705197
7875647906.52781731387-342.527817313869
7972347056.26145635617177.738543643826
8077187364.51911438855353.480885611451
8177227706.2011243337115.7988756662871
8279667947.2084600096818.7915399903231
8374127250.7284262722161.271573727801
8467927417.46645939881-625.466459398812
8573167612.59620164428-296.596201644283
8674247761.40182966382-337.401829663824
8779108251.55146441467-341.551464414668
8875747721.54368464564-147.543684645642
8974147592.18844392663-178.188443926628
9072927340.71140206582-48.7114020658228
9164326768.51600776323-336.516007763234
9266306687.13225298517-57.1322529851668
9365946674.99475060158-80.9947506015787
9473186839.97541665958478.024583340421
9566346518.1982903896115.801709610396
9660326578.80869767336-546.808697673358
9764606865.31901872134-405.319018721338
9864466924.78226187149-478.782261871486
9968907303.1232103109-413.123210310903
10066386734.0343957236-96.0343957235991
10168726642.54164630597229.458353694028
10275166723.94484481433792.05515518567
10364746788.74029846475-314.740298464747
10468126749.4807697144762.5192302855303
10565326829.52228284091-297.522282840911
10669086873.7761773032434.2238226967638
10765026169.82811318046332.171886819539
10856566341.78637138114-685.786371381141
10959486531.39340007823-583.393400078228
11056086443.93277225503-835.932772255033
11170626546.6289127927515.371087207301
11260746737.72068595841-663.720685958415
11359986227.84970475208-229.84970475208
11459445997.48287365882-53.4828736588233
11559145296.93209917554617.067900824463
11662866025.84090932309260.159090676913
11763406229.4984804945110.501519505496
11866666625.0006202643840.9993797356165
11960905953.01200772904136.987992270956
12062645880.17867107439383.821328925614
12170526922.01270567707129.987294322927
12266667374.28629600547-708.286296005466
12350607698.32143595632-2638.32143595632
12468185298.289612590881519.71038740912
12568306548.19063099278281.809369007218
12669866736.87707628073249.122923719267







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1276334.75168105365384.196841765767285.30652034144
1286545.392828319985335.056009590897755.72964704907
1296530.619009313095107.14581776757954.09220085867
1306832.813002751135224.19973682098441.42626868135
1316137.083811227714362.54236296447911.62525949101
1325978.326944165744052.097969229967904.55591910152
1336694.950161223184628.136484047648761.76383839872
1346969.87413325054771.447539425369168.30072707563
1357679.759496272355357.1660749617410002.352917583
1367730.769225910155290.3182608233610171.2201909969
1377672.219256093215119.3460463017910225.0924658846
1387635.859544668314975.3102898059810296.4087995306

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 6334.7516810536 & 5384.19684176576 & 7285.30652034144 \tabularnewline
128 & 6545.39282831998 & 5335.05600959089 & 7755.72964704907 \tabularnewline
129 & 6530.61900931309 & 5107.1458177675 & 7954.09220085867 \tabularnewline
130 & 6832.81300275113 & 5224.1997368209 & 8441.42626868135 \tabularnewline
131 & 6137.08381122771 & 4362.5423629644 & 7911.62525949101 \tabularnewline
132 & 5978.32694416574 & 4052.09796922996 & 7904.55591910152 \tabularnewline
133 & 6694.95016122318 & 4628.13648404764 & 8761.76383839872 \tabularnewline
134 & 6969.8741332505 & 4771.44753942536 & 9168.30072707563 \tabularnewline
135 & 7679.75949627235 & 5357.16607496174 & 10002.352917583 \tabularnewline
136 & 7730.76922591015 & 5290.31826082336 & 10171.2201909969 \tabularnewline
137 & 7672.21925609321 & 5119.34604630179 & 10225.0924658846 \tabularnewline
138 & 7635.85954466831 & 4975.31028980598 & 10296.4087995306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299753&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]6334.7516810536[/C][C]5384.19684176576[/C][C]7285.30652034144[/C][/ROW]
[ROW][C]128[/C][C]6545.39282831998[/C][C]5335.05600959089[/C][C]7755.72964704907[/C][/ROW]
[ROW][C]129[/C][C]6530.61900931309[/C][C]5107.1458177675[/C][C]7954.09220085867[/C][/ROW]
[ROW][C]130[/C][C]6832.81300275113[/C][C]5224.1997368209[/C][C]8441.42626868135[/C][/ROW]
[ROW][C]131[/C][C]6137.08381122771[/C][C]4362.5423629644[/C][C]7911.62525949101[/C][/ROW]
[ROW][C]132[/C][C]5978.32694416574[/C][C]4052.09796922996[/C][C]7904.55591910152[/C][/ROW]
[ROW][C]133[/C][C]6694.95016122318[/C][C]4628.13648404764[/C][C]8761.76383839872[/C][/ROW]
[ROW][C]134[/C][C]6969.8741332505[/C][C]4771.44753942536[/C][C]9168.30072707563[/C][/ROW]
[ROW][C]135[/C][C]7679.75949627235[/C][C]5357.16607496174[/C][C]10002.352917583[/C][/ROW]
[ROW][C]136[/C][C]7730.76922591015[/C][C]5290.31826082336[/C][C]10171.2201909969[/C][/ROW]
[ROW][C]137[/C][C]7672.21925609321[/C][C]5119.34604630179[/C][C]10225.0924658846[/C][/ROW]
[ROW][C]138[/C][C]7635.85954466831[/C][C]4975.31028980598[/C][C]10296.4087995306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299753&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299753&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
1276334.75168105365384.196841765767285.30652034144
1286545.392828319985335.056009590897755.72964704907
1296530.619009313095107.14581776757954.09220085867
1306832.813002751135224.19973682098441.42626868135
1316137.083811227714362.54236296447911.62525949101
1325978.326944165744052.097969229967904.55591910152
1336694.950161223184628.136484047648761.76383839872
1346969.87413325054771.447539425369168.30072707563
1357679.759496272355357.1660749617410002.352917583
1367730.769225910155290.3182608233610171.2201909969
1377672.219256093215119.3460463017910225.0924658846
1387635.859544668314975.3102898059810296.4087995306



Parameters (Session):
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')