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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 computationFri, 16 Dec 2016 19:31:08 +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/16/t1481913335txbrrueb3o3np3o.htm/, Retrieved Fri, 01 Nov 2024 03:47:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300473, Retrieved Fri, 01 Nov 2024 03:47:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [autocorrelatie co...] [2016-12-16 18:31:08] [2d1dd91c3b5ba64567b1d6b2c9fe9017] [Current]
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Dataseries X:
5797.8
5784.3
5714.8
5748.8
5793.8
5783.2
5765
5846.1
5879.4
5922.7
5992.7
6032.5
6028.3
6096.3
6184.8
6206.1
6324
6380.6
6504.6
6591
6637.9
6653.8
6611.3
6603.1
6562.8
6554.9
6529.8
6543.4
6481.5
6489.6
6452.3
6444.5
6409.6
6427.5
6374.2
6400.5
6268.2
6239.5
6220.1
6226.6
6207.1
6217.4
6196.9
6132.9
6151.2
6115.2
6122.6
6140.9
6146.5
6126
6131.9
6190.8
6209.2
6230.8
6196.5
6168.2
6213.4
6243
6298.1
6361.4
6388.7
6416.3
6505.7
6538.7
6605.5
6668.9
6741.7
6813.2
6864.3
6870
6889.8
6938.8
7033.3
7104
7168.7
7156
7156.6
7171.8
7251.2
7258.8
7231.5
7261.7
7252.8
7194.2
7211.9
7177.8
7145.9
7170.6
7189.6
7161
7219.9
7155.3
7155.8
7232.1
7254.9
7278.8
7291.2
7298.6
7256.3
7187.7
7126.3
7034.6
7018.6
7024.4
7028.2
7042.2
7022.2
6998.7
6982.7
6936.6
6887.2
6881.1
6890.9
6947.7
6887.5
6937.1




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300473&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300473&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300473&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.796020371440619
beta0.291583709111859
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.796020371440619 \tabularnewline
beta & 0.291583709111859 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300473&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]0.796020371440619[/C][/ROW]
[ROW][C]beta[/C][C]0.291583709111859[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300473&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300473&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
alpha0.796020371440619
beta0.291583709111859
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136028.35776.81503739316251.484962606835
146096.36091.956880467994.34311953200631
156184.86231.08934840812-46.2893484081196
166206.16252.54827841241-46.4482784124129
1763246365.52891286459-41.5289128645927
186380.66418.17382888552-37.5738288855191
196504.66372.60843968874131.991560311265
2065916636.73999657115-45.7399965711475
216637.96690.9978930334-53.0978930333968
226653.86731.02021739867-77.2202173986698
236611.36758.1090268464-146.809026846398
246603.16659.69088632586-56.5908863258574
256562.86618.52591613792-55.7259161379152
266554.96529.4595845037625.4404154962394
276529.86570.70460331602-40.9046033160212
286543.46493.3139818579150.0860181420849
296481.56603.44407819539-121.944078195394
306489.66493.52149753266-3.92149753266312
316452.36417.7807185602634.5192814397396
326444.56453.89356611407-9.39356611406583
336409.66429.84417331555-20.2441733155538
346427.56392.9849020188134.5150979811942
356374.26422.64373721677-48.4437372167713
366400.56371.5814021006728.9185978993337
376268.26369.15984112295-100.95984112295
386239.56220.6432521307218.8567478692839
396220.16201.5869828040718.5130171959327
406226.66162.3179288076264.2820711923832
416207.16224.21643257502-17.1164325750169
426217.46221.70287616245-4.30287616244823
436196.96153.3010080422543.5989919577505
446132.96189.59298448361-56.6929844836077
456151.26116.6093030846534.5906969153548
466115.26138.22732996102-23.0273299610153
476122.66095.4611807709927.1388192290078
486140.96128.189521670712.7104783293025
496146.56090.456481481856.0435185181977
5061266131.88249003219-5.8824900321888
516131.96127.845611158824.05438884118212
526190.86117.8296482649472.9703517350599
536209.26203.483669972775.71633002722865
546230.86260.50190267164-29.701902671638
556196.56214.50035678185-18.000356781854
566168.26199.85032243698-31.6503224369808
576213.46189.7835338397423.6164661602625
5862436212.7281669001530.2718330998496
596298.16256.8084169635241.2915830364818
606361.46335.3308152446926.069184755308
616388.76357.6425352057431.0574647942631
626416.36401.3199647358614.9800352641423
636505.76455.5318040666950.1681959333055
646538.76546.59894344874-7.89894344873846
656605.56585.7087333919319.7912666080683
666668.96681.52101466553-12.6210146655303
676741.76690.2823772240851.4176227759217
686813.26782.9978197766630.2021802233348
696864.36902.68822066966-38.3882206696617
7068706932.48976216834-62.4897621683413
716889.86938.30346428207-48.5034642820683
726938.86954.72586291371-15.9258629137094
737033.36947.3625967841585.9374032158485
7471047046.9205214239657.0794785760418
757168.77167.068014935271.631985064726
7671567221.63522638205-65.6352263820463
777156.67221.01342515581-64.4134251558098
787171.87224.22057638604-52.4205763860436
797251.27186.1604797306365.0395202693708
807258.87260.35066924254-1.55066924253515
817231.57308.36302270647-76.8630227064668
827261.77261.280272182230.419727817768944
837252.87293.28449349194-40.4844934919411
847194.27297.85694284386-103.65694284386
857211.97196.1946403987915.7053596012101
867177.87172.417339254465.38266074554031
877145.97166.56112272076-20.6611227207559
887170.67110.9452178031559.6547821968479
897189.67160.6704651360928.9295348639062
9071617212.65675225307-51.6567522530722
917219.97171.3713719985248.5286280014752
927155.37187.21045612457-31.910456124574
937155.87157.02185213169-1.22185213169359
947232.17164.8001711469267.2998288530853
957254.97236.1070485671218.7929514328825
967278.87283.14670456789-4.34670456789445
977291.27316.10245768936-24.9024576893589
987298.67279.6871498678818.9128501321175
997256.37304.22154772469-47.9215477246935
1007187.77261.89398309868-74.1939830986794
1017126.37186.34376936502-60.0437693650183
1027034.67117.95445154483-83.3544515448311
1037018.67031.40250789756-12.8025078975606
1047024.46927.3071385256597.0928614743525
1057028.26981.3044858317746.8955141682345
1067042.27027.7674251070914.4325748929123
1077022.27021.230828873210.969171126787842
1086998.77019.35970998267-20.6597099826686
1096982.77001.34800357961-18.6480035796103
1106936.66946.51147875376-9.91147875376282
1116887.26895.44063169148-8.24063169148485
1126881.16849.5234081048731.5765918951292
1136890.96855.7876928612835.1123071387156
1146947.76875.2086076299972.4913923700078
1156887.56980.09609597971-92.5960959797076
1166937.16869.3710115541567.7289884458505

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6028.3 & 5776.81503739316 & 251.484962606835 \tabularnewline
14 & 6096.3 & 6091.95688046799 & 4.34311953200631 \tabularnewline
15 & 6184.8 & 6231.08934840812 & -46.2893484081196 \tabularnewline
16 & 6206.1 & 6252.54827841241 & -46.4482784124129 \tabularnewline
17 & 6324 & 6365.52891286459 & -41.5289128645927 \tabularnewline
18 & 6380.6 & 6418.17382888552 & -37.5738288855191 \tabularnewline
19 & 6504.6 & 6372.60843968874 & 131.991560311265 \tabularnewline
20 & 6591 & 6636.73999657115 & -45.7399965711475 \tabularnewline
21 & 6637.9 & 6690.9978930334 & -53.0978930333968 \tabularnewline
22 & 6653.8 & 6731.02021739867 & -77.2202173986698 \tabularnewline
23 & 6611.3 & 6758.1090268464 & -146.809026846398 \tabularnewline
24 & 6603.1 & 6659.69088632586 & -56.5908863258574 \tabularnewline
25 & 6562.8 & 6618.52591613792 & -55.7259161379152 \tabularnewline
26 & 6554.9 & 6529.45958450376 & 25.4404154962394 \tabularnewline
27 & 6529.8 & 6570.70460331602 & -40.9046033160212 \tabularnewline
28 & 6543.4 & 6493.31398185791 & 50.0860181420849 \tabularnewline
29 & 6481.5 & 6603.44407819539 & -121.944078195394 \tabularnewline
30 & 6489.6 & 6493.52149753266 & -3.92149753266312 \tabularnewline
31 & 6452.3 & 6417.78071856026 & 34.5192814397396 \tabularnewline
32 & 6444.5 & 6453.89356611407 & -9.39356611406583 \tabularnewline
33 & 6409.6 & 6429.84417331555 & -20.2441733155538 \tabularnewline
34 & 6427.5 & 6392.98490201881 & 34.5150979811942 \tabularnewline
35 & 6374.2 & 6422.64373721677 & -48.4437372167713 \tabularnewline
36 & 6400.5 & 6371.58140210067 & 28.9185978993337 \tabularnewline
37 & 6268.2 & 6369.15984112295 & -100.95984112295 \tabularnewline
38 & 6239.5 & 6220.64325213072 & 18.8567478692839 \tabularnewline
39 & 6220.1 & 6201.58698280407 & 18.5130171959327 \tabularnewline
40 & 6226.6 & 6162.31792880762 & 64.2820711923832 \tabularnewline
41 & 6207.1 & 6224.21643257502 & -17.1164325750169 \tabularnewline
42 & 6217.4 & 6221.70287616245 & -4.30287616244823 \tabularnewline
43 & 6196.9 & 6153.30100804225 & 43.5989919577505 \tabularnewline
44 & 6132.9 & 6189.59298448361 & -56.6929844836077 \tabularnewline
45 & 6151.2 & 6116.60930308465 & 34.5906969153548 \tabularnewline
46 & 6115.2 & 6138.22732996102 & -23.0273299610153 \tabularnewline
47 & 6122.6 & 6095.46118077099 & 27.1388192290078 \tabularnewline
48 & 6140.9 & 6128.1895216707 & 12.7104783293025 \tabularnewline
49 & 6146.5 & 6090.4564814818 & 56.0435185181977 \tabularnewline
50 & 6126 & 6131.88249003219 & -5.8824900321888 \tabularnewline
51 & 6131.9 & 6127.84561115882 & 4.05438884118212 \tabularnewline
52 & 6190.8 & 6117.82964826494 & 72.9703517350599 \tabularnewline
53 & 6209.2 & 6203.48366997277 & 5.71633002722865 \tabularnewline
54 & 6230.8 & 6260.50190267164 & -29.701902671638 \tabularnewline
55 & 6196.5 & 6214.50035678185 & -18.000356781854 \tabularnewline
56 & 6168.2 & 6199.85032243698 & -31.6503224369808 \tabularnewline
57 & 6213.4 & 6189.78353383974 & 23.6164661602625 \tabularnewline
58 & 6243 & 6212.72816690015 & 30.2718330998496 \tabularnewline
59 & 6298.1 & 6256.80841696352 & 41.2915830364818 \tabularnewline
60 & 6361.4 & 6335.33081524469 & 26.069184755308 \tabularnewline
61 & 6388.7 & 6357.64253520574 & 31.0574647942631 \tabularnewline
62 & 6416.3 & 6401.31996473586 & 14.9800352641423 \tabularnewline
63 & 6505.7 & 6455.53180406669 & 50.1681959333055 \tabularnewline
64 & 6538.7 & 6546.59894344874 & -7.89894344873846 \tabularnewline
65 & 6605.5 & 6585.70873339193 & 19.7912666080683 \tabularnewline
66 & 6668.9 & 6681.52101466553 & -12.6210146655303 \tabularnewline
67 & 6741.7 & 6690.28237722408 & 51.4176227759217 \tabularnewline
68 & 6813.2 & 6782.99781977666 & 30.2021802233348 \tabularnewline
69 & 6864.3 & 6902.68822066966 & -38.3882206696617 \tabularnewline
70 & 6870 & 6932.48976216834 & -62.4897621683413 \tabularnewline
71 & 6889.8 & 6938.30346428207 & -48.5034642820683 \tabularnewline
72 & 6938.8 & 6954.72586291371 & -15.9258629137094 \tabularnewline
73 & 7033.3 & 6947.36259678415 & 85.9374032158485 \tabularnewline
74 & 7104 & 7046.92052142396 & 57.0794785760418 \tabularnewline
75 & 7168.7 & 7167.06801493527 & 1.631985064726 \tabularnewline
76 & 7156 & 7221.63522638205 & -65.6352263820463 \tabularnewline
77 & 7156.6 & 7221.01342515581 & -64.4134251558098 \tabularnewline
78 & 7171.8 & 7224.22057638604 & -52.4205763860436 \tabularnewline
79 & 7251.2 & 7186.16047973063 & 65.0395202693708 \tabularnewline
80 & 7258.8 & 7260.35066924254 & -1.55066924253515 \tabularnewline
81 & 7231.5 & 7308.36302270647 & -76.8630227064668 \tabularnewline
82 & 7261.7 & 7261.28027218223 & 0.419727817768944 \tabularnewline
83 & 7252.8 & 7293.28449349194 & -40.4844934919411 \tabularnewline
84 & 7194.2 & 7297.85694284386 & -103.65694284386 \tabularnewline
85 & 7211.9 & 7196.19464039879 & 15.7053596012101 \tabularnewline
86 & 7177.8 & 7172.41733925446 & 5.38266074554031 \tabularnewline
87 & 7145.9 & 7166.56112272076 & -20.6611227207559 \tabularnewline
88 & 7170.6 & 7110.94521780315 & 59.6547821968479 \tabularnewline
89 & 7189.6 & 7160.67046513609 & 28.9295348639062 \tabularnewline
90 & 7161 & 7212.65675225307 & -51.6567522530722 \tabularnewline
91 & 7219.9 & 7171.37137199852 & 48.5286280014752 \tabularnewline
92 & 7155.3 & 7187.21045612457 & -31.910456124574 \tabularnewline
93 & 7155.8 & 7157.02185213169 & -1.22185213169359 \tabularnewline
94 & 7232.1 & 7164.80017114692 & 67.2998288530853 \tabularnewline
95 & 7254.9 & 7236.10704856712 & 18.7929514328825 \tabularnewline
96 & 7278.8 & 7283.14670456789 & -4.34670456789445 \tabularnewline
97 & 7291.2 & 7316.10245768936 & -24.9024576893589 \tabularnewline
98 & 7298.6 & 7279.68714986788 & 18.9128501321175 \tabularnewline
99 & 7256.3 & 7304.22154772469 & -47.9215477246935 \tabularnewline
100 & 7187.7 & 7261.89398309868 & -74.1939830986794 \tabularnewline
101 & 7126.3 & 7186.34376936502 & -60.0437693650183 \tabularnewline
102 & 7034.6 & 7117.95445154483 & -83.3544515448311 \tabularnewline
103 & 7018.6 & 7031.40250789756 & -12.8025078975606 \tabularnewline
104 & 7024.4 & 6927.30713852565 & 97.0928614743525 \tabularnewline
105 & 7028.2 & 6981.30448583177 & 46.8955141682345 \tabularnewline
106 & 7042.2 & 7027.76742510709 & 14.4325748929123 \tabularnewline
107 & 7022.2 & 7021.23082887321 & 0.969171126787842 \tabularnewline
108 & 6998.7 & 7019.35970998267 & -20.6597099826686 \tabularnewline
109 & 6982.7 & 7001.34800357961 & -18.6480035796103 \tabularnewline
110 & 6936.6 & 6946.51147875376 & -9.91147875376282 \tabularnewline
111 & 6887.2 & 6895.44063169148 & -8.24063169148485 \tabularnewline
112 & 6881.1 & 6849.52340810487 & 31.5765918951292 \tabularnewline
113 & 6890.9 & 6855.78769286128 & 35.1123071387156 \tabularnewline
114 & 6947.7 & 6875.20860762999 & 72.4913923700078 \tabularnewline
115 & 6887.5 & 6980.09609597971 & -92.5960959797076 \tabularnewline
116 & 6937.1 & 6869.37101155415 & 67.7289884458505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300473&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]6028.3[/C][C]5776.81503739316[/C][C]251.484962606835[/C][/ROW]
[ROW][C]14[/C][C]6096.3[/C][C]6091.95688046799[/C][C]4.34311953200631[/C][/ROW]
[ROW][C]15[/C][C]6184.8[/C][C]6231.08934840812[/C][C]-46.2893484081196[/C][/ROW]
[ROW][C]16[/C][C]6206.1[/C][C]6252.54827841241[/C][C]-46.4482784124129[/C][/ROW]
[ROW][C]17[/C][C]6324[/C][C]6365.52891286459[/C][C]-41.5289128645927[/C][/ROW]
[ROW][C]18[/C][C]6380.6[/C][C]6418.17382888552[/C][C]-37.5738288855191[/C][/ROW]
[ROW][C]19[/C][C]6504.6[/C][C]6372.60843968874[/C][C]131.991560311265[/C][/ROW]
[ROW][C]20[/C][C]6591[/C][C]6636.73999657115[/C][C]-45.7399965711475[/C][/ROW]
[ROW][C]21[/C][C]6637.9[/C][C]6690.9978930334[/C][C]-53.0978930333968[/C][/ROW]
[ROW][C]22[/C][C]6653.8[/C][C]6731.02021739867[/C][C]-77.2202173986698[/C][/ROW]
[ROW][C]23[/C][C]6611.3[/C][C]6758.1090268464[/C][C]-146.809026846398[/C][/ROW]
[ROW][C]24[/C][C]6603.1[/C][C]6659.69088632586[/C][C]-56.5908863258574[/C][/ROW]
[ROW][C]25[/C][C]6562.8[/C][C]6618.52591613792[/C][C]-55.7259161379152[/C][/ROW]
[ROW][C]26[/C][C]6554.9[/C][C]6529.45958450376[/C][C]25.4404154962394[/C][/ROW]
[ROW][C]27[/C][C]6529.8[/C][C]6570.70460331602[/C][C]-40.9046033160212[/C][/ROW]
[ROW][C]28[/C][C]6543.4[/C][C]6493.31398185791[/C][C]50.0860181420849[/C][/ROW]
[ROW][C]29[/C][C]6481.5[/C][C]6603.44407819539[/C][C]-121.944078195394[/C][/ROW]
[ROW][C]30[/C][C]6489.6[/C][C]6493.52149753266[/C][C]-3.92149753266312[/C][/ROW]
[ROW][C]31[/C][C]6452.3[/C][C]6417.78071856026[/C][C]34.5192814397396[/C][/ROW]
[ROW][C]32[/C][C]6444.5[/C][C]6453.89356611407[/C][C]-9.39356611406583[/C][/ROW]
[ROW][C]33[/C][C]6409.6[/C][C]6429.84417331555[/C][C]-20.2441733155538[/C][/ROW]
[ROW][C]34[/C][C]6427.5[/C][C]6392.98490201881[/C][C]34.5150979811942[/C][/ROW]
[ROW][C]35[/C][C]6374.2[/C][C]6422.64373721677[/C][C]-48.4437372167713[/C][/ROW]
[ROW][C]36[/C][C]6400.5[/C][C]6371.58140210067[/C][C]28.9185978993337[/C][/ROW]
[ROW][C]37[/C][C]6268.2[/C][C]6369.15984112295[/C][C]-100.95984112295[/C][/ROW]
[ROW][C]38[/C][C]6239.5[/C][C]6220.64325213072[/C][C]18.8567478692839[/C][/ROW]
[ROW][C]39[/C][C]6220.1[/C][C]6201.58698280407[/C][C]18.5130171959327[/C][/ROW]
[ROW][C]40[/C][C]6226.6[/C][C]6162.31792880762[/C][C]64.2820711923832[/C][/ROW]
[ROW][C]41[/C][C]6207.1[/C][C]6224.21643257502[/C][C]-17.1164325750169[/C][/ROW]
[ROW][C]42[/C][C]6217.4[/C][C]6221.70287616245[/C][C]-4.30287616244823[/C][/ROW]
[ROW][C]43[/C][C]6196.9[/C][C]6153.30100804225[/C][C]43.5989919577505[/C][/ROW]
[ROW][C]44[/C][C]6132.9[/C][C]6189.59298448361[/C][C]-56.6929844836077[/C][/ROW]
[ROW][C]45[/C][C]6151.2[/C][C]6116.60930308465[/C][C]34.5906969153548[/C][/ROW]
[ROW][C]46[/C][C]6115.2[/C][C]6138.22732996102[/C][C]-23.0273299610153[/C][/ROW]
[ROW][C]47[/C][C]6122.6[/C][C]6095.46118077099[/C][C]27.1388192290078[/C][/ROW]
[ROW][C]48[/C][C]6140.9[/C][C]6128.1895216707[/C][C]12.7104783293025[/C][/ROW]
[ROW][C]49[/C][C]6146.5[/C][C]6090.4564814818[/C][C]56.0435185181977[/C][/ROW]
[ROW][C]50[/C][C]6126[/C][C]6131.88249003219[/C][C]-5.8824900321888[/C][/ROW]
[ROW][C]51[/C][C]6131.9[/C][C]6127.84561115882[/C][C]4.05438884118212[/C][/ROW]
[ROW][C]52[/C][C]6190.8[/C][C]6117.82964826494[/C][C]72.9703517350599[/C][/ROW]
[ROW][C]53[/C][C]6209.2[/C][C]6203.48366997277[/C][C]5.71633002722865[/C][/ROW]
[ROW][C]54[/C][C]6230.8[/C][C]6260.50190267164[/C][C]-29.701902671638[/C][/ROW]
[ROW][C]55[/C][C]6196.5[/C][C]6214.50035678185[/C][C]-18.000356781854[/C][/ROW]
[ROW][C]56[/C][C]6168.2[/C][C]6199.85032243698[/C][C]-31.6503224369808[/C][/ROW]
[ROW][C]57[/C][C]6213.4[/C][C]6189.78353383974[/C][C]23.6164661602625[/C][/ROW]
[ROW][C]58[/C][C]6243[/C][C]6212.72816690015[/C][C]30.2718330998496[/C][/ROW]
[ROW][C]59[/C][C]6298.1[/C][C]6256.80841696352[/C][C]41.2915830364818[/C][/ROW]
[ROW][C]60[/C][C]6361.4[/C][C]6335.33081524469[/C][C]26.069184755308[/C][/ROW]
[ROW][C]61[/C][C]6388.7[/C][C]6357.64253520574[/C][C]31.0574647942631[/C][/ROW]
[ROW][C]62[/C][C]6416.3[/C][C]6401.31996473586[/C][C]14.9800352641423[/C][/ROW]
[ROW][C]63[/C][C]6505.7[/C][C]6455.53180406669[/C][C]50.1681959333055[/C][/ROW]
[ROW][C]64[/C][C]6538.7[/C][C]6546.59894344874[/C][C]-7.89894344873846[/C][/ROW]
[ROW][C]65[/C][C]6605.5[/C][C]6585.70873339193[/C][C]19.7912666080683[/C][/ROW]
[ROW][C]66[/C][C]6668.9[/C][C]6681.52101466553[/C][C]-12.6210146655303[/C][/ROW]
[ROW][C]67[/C][C]6741.7[/C][C]6690.28237722408[/C][C]51.4176227759217[/C][/ROW]
[ROW][C]68[/C][C]6813.2[/C][C]6782.99781977666[/C][C]30.2021802233348[/C][/ROW]
[ROW][C]69[/C][C]6864.3[/C][C]6902.68822066966[/C][C]-38.3882206696617[/C][/ROW]
[ROW][C]70[/C][C]6870[/C][C]6932.48976216834[/C][C]-62.4897621683413[/C][/ROW]
[ROW][C]71[/C][C]6889.8[/C][C]6938.30346428207[/C][C]-48.5034642820683[/C][/ROW]
[ROW][C]72[/C][C]6938.8[/C][C]6954.72586291371[/C][C]-15.9258629137094[/C][/ROW]
[ROW][C]73[/C][C]7033.3[/C][C]6947.36259678415[/C][C]85.9374032158485[/C][/ROW]
[ROW][C]74[/C][C]7104[/C][C]7046.92052142396[/C][C]57.0794785760418[/C][/ROW]
[ROW][C]75[/C][C]7168.7[/C][C]7167.06801493527[/C][C]1.631985064726[/C][/ROW]
[ROW][C]76[/C][C]7156[/C][C]7221.63522638205[/C][C]-65.6352263820463[/C][/ROW]
[ROW][C]77[/C][C]7156.6[/C][C]7221.01342515581[/C][C]-64.4134251558098[/C][/ROW]
[ROW][C]78[/C][C]7171.8[/C][C]7224.22057638604[/C][C]-52.4205763860436[/C][/ROW]
[ROW][C]79[/C][C]7251.2[/C][C]7186.16047973063[/C][C]65.0395202693708[/C][/ROW]
[ROW][C]80[/C][C]7258.8[/C][C]7260.35066924254[/C][C]-1.55066924253515[/C][/ROW]
[ROW][C]81[/C][C]7231.5[/C][C]7308.36302270647[/C][C]-76.8630227064668[/C][/ROW]
[ROW][C]82[/C][C]7261.7[/C][C]7261.28027218223[/C][C]0.419727817768944[/C][/ROW]
[ROW][C]83[/C][C]7252.8[/C][C]7293.28449349194[/C][C]-40.4844934919411[/C][/ROW]
[ROW][C]84[/C][C]7194.2[/C][C]7297.85694284386[/C][C]-103.65694284386[/C][/ROW]
[ROW][C]85[/C][C]7211.9[/C][C]7196.19464039879[/C][C]15.7053596012101[/C][/ROW]
[ROW][C]86[/C][C]7177.8[/C][C]7172.41733925446[/C][C]5.38266074554031[/C][/ROW]
[ROW][C]87[/C][C]7145.9[/C][C]7166.56112272076[/C][C]-20.6611227207559[/C][/ROW]
[ROW][C]88[/C][C]7170.6[/C][C]7110.94521780315[/C][C]59.6547821968479[/C][/ROW]
[ROW][C]89[/C][C]7189.6[/C][C]7160.67046513609[/C][C]28.9295348639062[/C][/ROW]
[ROW][C]90[/C][C]7161[/C][C]7212.65675225307[/C][C]-51.6567522530722[/C][/ROW]
[ROW][C]91[/C][C]7219.9[/C][C]7171.37137199852[/C][C]48.5286280014752[/C][/ROW]
[ROW][C]92[/C][C]7155.3[/C][C]7187.21045612457[/C][C]-31.910456124574[/C][/ROW]
[ROW][C]93[/C][C]7155.8[/C][C]7157.02185213169[/C][C]-1.22185213169359[/C][/ROW]
[ROW][C]94[/C][C]7232.1[/C][C]7164.80017114692[/C][C]67.2998288530853[/C][/ROW]
[ROW][C]95[/C][C]7254.9[/C][C]7236.10704856712[/C][C]18.7929514328825[/C][/ROW]
[ROW][C]96[/C][C]7278.8[/C][C]7283.14670456789[/C][C]-4.34670456789445[/C][/ROW]
[ROW][C]97[/C][C]7291.2[/C][C]7316.10245768936[/C][C]-24.9024576893589[/C][/ROW]
[ROW][C]98[/C][C]7298.6[/C][C]7279.68714986788[/C][C]18.9128501321175[/C][/ROW]
[ROW][C]99[/C][C]7256.3[/C][C]7304.22154772469[/C][C]-47.9215477246935[/C][/ROW]
[ROW][C]100[/C][C]7187.7[/C][C]7261.89398309868[/C][C]-74.1939830986794[/C][/ROW]
[ROW][C]101[/C][C]7126.3[/C][C]7186.34376936502[/C][C]-60.0437693650183[/C][/ROW]
[ROW][C]102[/C][C]7034.6[/C][C]7117.95445154483[/C][C]-83.3544515448311[/C][/ROW]
[ROW][C]103[/C][C]7018.6[/C][C]7031.40250789756[/C][C]-12.8025078975606[/C][/ROW]
[ROW][C]104[/C][C]7024.4[/C][C]6927.30713852565[/C][C]97.0928614743525[/C][/ROW]
[ROW][C]105[/C][C]7028.2[/C][C]6981.30448583177[/C][C]46.8955141682345[/C][/ROW]
[ROW][C]106[/C][C]7042.2[/C][C]7027.76742510709[/C][C]14.4325748929123[/C][/ROW]
[ROW][C]107[/C][C]7022.2[/C][C]7021.23082887321[/C][C]0.969171126787842[/C][/ROW]
[ROW][C]108[/C][C]6998.7[/C][C]7019.35970998267[/C][C]-20.6597099826686[/C][/ROW]
[ROW][C]109[/C][C]6982.7[/C][C]7001.34800357961[/C][C]-18.6480035796103[/C][/ROW]
[ROW][C]110[/C][C]6936.6[/C][C]6946.51147875376[/C][C]-9.91147875376282[/C][/ROW]
[ROW][C]111[/C][C]6887.2[/C][C]6895.44063169148[/C][C]-8.24063169148485[/C][/ROW]
[ROW][C]112[/C][C]6881.1[/C][C]6849.52340810487[/C][C]31.5765918951292[/C][/ROW]
[ROW][C]113[/C][C]6890.9[/C][C]6855.78769286128[/C][C]35.1123071387156[/C][/ROW]
[ROW][C]114[/C][C]6947.7[/C][C]6875.20860762999[/C][C]72.4913923700078[/C][/ROW]
[ROW][C]115[/C][C]6887.5[/C][C]6980.09609597971[/C][C]-92.5960959797076[/C][/ROW]
[ROW][C]116[/C][C]6937.1[/C][C]6869.37101155415[/C][C]67.7289884458505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300473&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300473&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
136028.35776.81503739316251.484962606835
146096.36091.956880467994.34311953200631
156184.86231.08934840812-46.2893484081196
166206.16252.54827841241-46.4482784124129
1763246365.52891286459-41.5289128645927
186380.66418.17382888552-37.5738288855191
196504.66372.60843968874131.991560311265
2065916636.73999657115-45.7399965711475
216637.96690.9978930334-53.0978930333968
226653.86731.02021739867-77.2202173986698
236611.36758.1090268464-146.809026846398
246603.16659.69088632586-56.5908863258574
256562.86618.52591613792-55.7259161379152
266554.96529.4595845037625.4404154962394
276529.86570.70460331602-40.9046033160212
286543.46493.3139818579150.0860181420849
296481.56603.44407819539-121.944078195394
306489.66493.52149753266-3.92149753266312
316452.36417.7807185602634.5192814397396
326444.56453.89356611407-9.39356611406583
336409.66429.84417331555-20.2441733155538
346427.56392.9849020188134.5150979811942
356374.26422.64373721677-48.4437372167713
366400.56371.5814021006728.9185978993337
376268.26369.15984112295-100.95984112295
386239.56220.6432521307218.8567478692839
396220.16201.5869828040718.5130171959327
406226.66162.3179288076264.2820711923832
416207.16224.21643257502-17.1164325750169
426217.46221.70287616245-4.30287616244823
436196.96153.3010080422543.5989919577505
446132.96189.59298448361-56.6929844836077
456151.26116.6093030846534.5906969153548
466115.26138.22732996102-23.0273299610153
476122.66095.4611807709927.1388192290078
486140.96128.189521670712.7104783293025
496146.56090.456481481856.0435185181977
5061266131.88249003219-5.8824900321888
516131.96127.845611158824.05438884118212
526190.86117.8296482649472.9703517350599
536209.26203.483669972775.71633002722865
546230.86260.50190267164-29.701902671638
556196.56214.50035678185-18.000356781854
566168.26199.85032243698-31.6503224369808
576213.46189.7835338397423.6164661602625
5862436212.7281669001530.2718330998496
596298.16256.8084169635241.2915830364818
606361.46335.3308152446926.069184755308
616388.76357.6425352057431.0574647942631
626416.36401.3199647358614.9800352641423
636505.76455.5318040666950.1681959333055
646538.76546.59894344874-7.89894344873846
656605.56585.7087333919319.7912666080683
666668.96681.52101466553-12.6210146655303
676741.76690.2823772240851.4176227759217
686813.26782.9978197766630.2021802233348
696864.36902.68822066966-38.3882206696617
7068706932.48976216834-62.4897621683413
716889.86938.30346428207-48.5034642820683
726938.86954.72586291371-15.9258629137094
737033.36947.3625967841585.9374032158485
7471047046.9205214239657.0794785760418
757168.77167.068014935271.631985064726
7671567221.63522638205-65.6352263820463
777156.67221.01342515581-64.4134251558098
787171.87224.22057638604-52.4205763860436
797251.27186.1604797306365.0395202693708
807258.87260.35066924254-1.55066924253515
817231.57308.36302270647-76.8630227064668
827261.77261.280272182230.419727817768944
837252.87293.28449349194-40.4844934919411
847194.27297.85694284386-103.65694284386
857211.97196.1946403987915.7053596012101
867177.87172.417339254465.38266074554031
877145.97166.56112272076-20.6611227207559
887170.67110.9452178031559.6547821968479
897189.67160.6704651360928.9295348639062
9071617212.65675225307-51.6567522530722
917219.97171.3713719985248.5286280014752
927155.37187.21045612457-31.910456124574
937155.87157.02185213169-1.22185213169359
947232.17164.8001711469267.2998288530853
957254.97236.1070485671218.7929514328825
967278.87283.14670456789-4.34670456789445
977291.27316.10245768936-24.9024576893589
987298.67279.6871498678818.9128501321175
997256.37304.22154772469-47.9215477246935
1007187.77261.89398309868-74.1939830986794
1017126.37186.34376936502-60.0437693650183
1027034.67117.95445154483-83.3544515448311
1037018.67031.40250789756-12.8025078975606
1047024.46927.3071385256597.0928614743525
1057028.26981.3044858317746.8955141682345
1067042.27027.7674251070914.4325748929123
1077022.27021.230828873210.969171126787842
1086998.77019.35970998267-20.6597099826686
1096982.77001.34800357961-18.6480035796103
1106936.66946.51147875376-9.91147875376282
1116887.26895.44063169148-8.24063169148485
1126881.16849.5234081048731.5765918951292
1136890.96855.7876928612835.1123071387156
1146947.76875.2086076299972.4913923700078
1156887.56980.09609597971-92.5960959797076
1166937.16869.3710115541567.7289884458505







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1176917.410523510216808.322086253797026.49896076664
1186936.692784850236780.233760445957093.1518092545
1196929.342294367226721.0652536487137.61933508644
1206935.483882870476671.131457928917199.83630781204

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 6917.41052351021 & 6808.32208625379 & 7026.49896076664 \tabularnewline
118 & 6936.69278485023 & 6780.23376044595 & 7093.1518092545 \tabularnewline
119 & 6929.34229436722 & 6721.065253648 & 7137.61933508644 \tabularnewline
120 & 6935.48388287047 & 6671.13145792891 & 7199.83630781204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300473&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]117[/C][C]6917.41052351021[/C][C]6808.32208625379[/C][C]7026.49896076664[/C][/ROW]
[ROW][C]118[/C][C]6936.69278485023[/C][C]6780.23376044595[/C][C]7093.1518092545[/C][/ROW]
[ROW][C]119[/C][C]6929.34229436722[/C][C]6721.065253648[/C][C]7137.61933508644[/C][/ROW]
[ROW][C]120[/C][C]6935.48388287047[/C][C]6671.13145792891[/C][C]7199.83630781204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300473&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300473&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
1176917.410523510216808.322086253797026.49896076664
1186936.692784850236780.233760445957093.1518092545
1196929.342294367226721.0652536487137.61933508644
1206935.483882870476671.131457928917199.83630781204



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 4 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
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')