Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 10 Aug 2012 07:46:07 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/10/t13445992503knjpyc082gu8xi.htm/, Retrieved Sun, 05 May 2024 11:35:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169182, Retrieved Sun, 05 May 2024 11:35:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKenneth Pijpen
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1] [2012-08-10 11:46:07] [bc260e3c602952c552b9bde15a0b19a6] [Current]
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Dataseries X:
36439
36368
36290
36147
37615
37543
36439
35705
35777
35777
35848
35998
35998
35335
35043
35335
36368
36218
34822
33640
33419
32977
33276
33640
33497
33198
32614
33198
33718
33568
31873
31139
30405
29814
29743
30184
29593
29372
29151
30405
30548
29814
27826
26943
25547
24955
25247
25689
25689
25326
25247
26430
27385
26943
25468
24735
23189
22234
22968
23702
23702
22747
22676
23922
24735
24442
22968
22013
19947
19142
19434
20688
20759
18921
19584
21201
21935
21493
19506
18109
16492
15238
15751
16855
16563
14946
15459
17076
17960
17447
15459
14576
13251
11854
12075
13179
13322
11997
12218
14063
14504
13764
11042
9646
7801
5963
6554
7359
7217
5813
6625
8613
9496
9055
7288
5892
4417
2721
3021
3534




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time13 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 13 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169182&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]13 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169182&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169182&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time13 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.40085143146767
beta0.0368982697380461
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.40085143146767 \tabularnewline
beta & 0.0368982697380461 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169182&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]0.40085143146767[/C][/ROW]
[ROW][C]beta[/C][C]0.0368982697380461[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169182&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169182&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
alpha0.40085143146767
beta0.0368982697380461
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133599836579.1669337607-581.166933760702
143533535689.5399635775-354.539963577539
153504335287.387835967-244.387835967027
163533535540.4006732982-205.400673298216
173636836555.9202125426-187.920212542616
183621836374.2506767935-156.250676793512
193482234828.9231924434-6.9231924434207
203364033989.3931115889-349.393111588877
213341933846.9990295776-427.999029577622
223297733585.5569038626-608.556903862591
233327633313.7368984264-37.7368984263594
243364033370.5477532212269.452246778805
253349733071.6925407073425.307459292715
263319832693.4246131307504.575386869321
273261432686.4836480023-72.483648002286
283319833019.14227018178.857729819967
293371834192.2278358069-474.227835806931
303356833903.593641738-335.593641738044
313187332362.0204146134-489.020414613391
323113931103.094836208835.9051637912489
333040531052.7945626117-647.794562611736
342981430576.5582222429-762.558222242933
352974330564.2268973078-821.226897307752
363018430458.652556883-274.652556882967
372959329994.6508340727-401.650834072701
382937229279.735695740792.2643042593227
392915128703.0237082769447.976291723066
403040529343.84680853921061.15319146076
413054830441.3028195309106.697180469142
422981430439.1843588224-625.184358822386
432782628655.9082205169-829.90822051691
442694327536.1090821431-593.109082143121
452554726775.9896551228-1228.98965512282
462495525941.3834710799-986.383471079946
472524725744.2332080414-497.233208041398
482568926040.8565226963-351.856522696336
492568925413.5198284105275.480171589523
502532625219.6806137986106.31938620139
512524724815.6532816919431.346718308116
522643025770.8748194888659.125180511175
532738526083.05045274831301.9495472517
542694326086.9575644459856.042435554136
552546824762.0944421909705.905557809088
562473524409.8432620724325.156737927584
572318923660.4438269228-471.443826922787
582223423309.6815303349-1075.68153033491
592296823403.3123192759-435.312319275869
602370223846.2774255057-144.277425505697
612370223715.5057187788-13.5057187788479
622274723337.6880702453-590.688070245349
632267622871.9091334838-195.909133483794
642392223725.795007671196.204992328985
652473524244.3363980487490.663601951259
662444223650.6549409278791.345059072184
672296822203.727737615764.272262385013
682201321641.4353603078371.564639692235
691994720428.7304535018-481.730453501808
701914219707.038388827-565.038388827044
711943420391.8120859964-957.812085996415
722068820794.7519806711-106.751980671092
732075920752.97553950026.02446049982245
741892120033.0589335078-1112.0589335078
751958419582.99784394611.00215605385165
762120120741.8418373994459.158162600579
772193521537.1934345677397.806565432253
782149321080.0501408644412.949859135577
791950619453.232488367952.7675116321079
801810918347.9289684238-238.928968423781
811649216347.7134138565144.286586143506
821523815804.7637134308-566.763713430839
831575116231.206862528-480.206862528041
841685517320.2619148857-465.261914885701
851656317181.7984514444-618.7984514444
861494615511.7333931378-565.733393137762
871545915925.8479587671-466.847958767119
881707617143.02855922-67.0285592200307
891796017654.2875311548305.712468845184
901744717131.5279284111315.472071588883
911545915210.6183189085248.381681091496
921457613972.6356571603603.364342839701
931325112515.7939280099735.206071990138
941185411768.566802311585.4331976884805
951207512502.8273168974-427.82731689739
961317913617.1306472554-438.13064725545
971332213393.2505044506-71.2505044506233
981199711978.262218176918.7377818230543
991221812698.3522493296-480.352249329551
1001406314161.9134101886-98.9134101885866
1011450414895.4895010298-391.489501029761
1021376414100.5617742354-336.561774235448
1031104211869.9011316117-827.901131611698
104964610389.0720938489-743.072093848938
10578018427.48318140025-626.483181400254
10659636680.95111794077-717.951117940773
10765546709.61257729945-155.612577299446
10873597854.84460351487-495.844603514868
10972177754.7760733583-537.776073358298
11058136126.92706908122-313.927069081217
11166256329.94885794486295.051142055141
11286138259.6489075273353.351092472696
11394968932.68744005986563.312559940139
11490558500.99368345765554.006316542349
11572886293.695737659994.304262341007
11658925581.83974998516310.160250014843
11744174115.58689235411301.41310764589
11827212703.2170416164317.7829583835737
11930213391.62147039326-370.621470393259
12035344271.53578539853-737.535785398533

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 35998 & 36579.1669337607 & -581.166933760702 \tabularnewline
14 & 35335 & 35689.5399635775 & -354.539963577539 \tabularnewline
15 & 35043 & 35287.387835967 & -244.387835967027 \tabularnewline
16 & 35335 & 35540.4006732982 & -205.400673298216 \tabularnewline
17 & 36368 & 36555.9202125426 & -187.920212542616 \tabularnewline
18 & 36218 & 36374.2506767935 & -156.250676793512 \tabularnewline
19 & 34822 & 34828.9231924434 & -6.9231924434207 \tabularnewline
20 & 33640 & 33989.3931115889 & -349.393111588877 \tabularnewline
21 & 33419 & 33846.9990295776 & -427.999029577622 \tabularnewline
22 & 32977 & 33585.5569038626 & -608.556903862591 \tabularnewline
23 & 33276 & 33313.7368984264 & -37.7368984263594 \tabularnewline
24 & 33640 & 33370.5477532212 & 269.452246778805 \tabularnewline
25 & 33497 & 33071.6925407073 & 425.307459292715 \tabularnewline
26 & 33198 & 32693.4246131307 & 504.575386869321 \tabularnewline
27 & 32614 & 32686.4836480023 & -72.483648002286 \tabularnewline
28 & 33198 & 33019.14227018 & 178.857729819967 \tabularnewline
29 & 33718 & 34192.2278358069 & -474.227835806931 \tabularnewline
30 & 33568 & 33903.593641738 & -335.593641738044 \tabularnewline
31 & 31873 & 32362.0204146134 & -489.020414613391 \tabularnewline
32 & 31139 & 31103.0948362088 & 35.9051637912489 \tabularnewline
33 & 30405 & 31052.7945626117 & -647.794562611736 \tabularnewline
34 & 29814 & 30576.5582222429 & -762.558222242933 \tabularnewline
35 & 29743 & 30564.2268973078 & -821.226897307752 \tabularnewline
36 & 30184 & 30458.652556883 & -274.652556882967 \tabularnewline
37 & 29593 & 29994.6508340727 & -401.650834072701 \tabularnewline
38 & 29372 & 29279.7356957407 & 92.2643042593227 \tabularnewline
39 & 29151 & 28703.0237082769 & 447.976291723066 \tabularnewline
40 & 30405 & 29343.8468085392 & 1061.15319146076 \tabularnewline
41 & 30548 & 30441.3028195309 & 106.697180469142 \tabularnewline
42 & 29814 & 30439.1843588224 & -625.184358822386 \tabularnewline
43 & 27826 & 28655.9082205169 & -829.90822051691 \tabularnewline
44 & 26943 & 27536.1090821431 & -593.109082143121 \tabularnewline
45 & 25547 & 26775.9896551228 & -1228.98965512282 \tabularnewline
46 & 24955 & 25941.3834710799 & -986.383471079946 \tabularnewline
47 & 25247 & 25744.2332080414 & -497.233208041398 \tabularnewline
48 & 25689 & 26040.8565226963 & -351.856522696336 \tabularnewline
49 & 25689 & 25413.5198284105 & 275.480171589523 \tabularnewline
50 & 25326 & 25219.6806137986 & 106.31938620139 \tabularnewline
51 & 25247 & 24815.6532816919 & 431.346718308116 \tabularnewline
52 & 26430 & 25770.8748194888 & 659.125180511175 \tabularnewline
53 & 27385 & 26083.0504527483 & 1301.9495472517 \tabularnewline
54 & 26943 & 26086.9575644459 & 856.042435554136 \tabularnewline
55 & 25468 & 24762.0944421909 & 705.905557809088 \tabularnewline
56 & 24735 & 24409.8432620724 & 325.156737927584 \tabularnewline
57 & 23189 & 23660.4438269228 & -471.443826922787 \tabularnewline
58 & 22234 & 23309.6815303349 & -1075.68153033491 \tabularnewline
59 & 22968 & 23403.3123192759 & -435.312319275869 \tabularnewline
60 & 23702 & 23846.2774255057 & -144.277425505697 \tabularnewline
61 & 23702 & 23715.5057187788 & -13.5057187788479 \tabularnewline
62 & 22747 & 23337.6880702453 & -590.688070245349 \tabularnewline
63 & 22676 & 22871.9091334838 & -195.909133483794 \tabularnewline
64 & 23922 & 23725.795007671 & 196.204992328985 \tabularnewline
65 & 24735 & 24244.3363980487 & 490.663601951259 \tabularnewline
66 & 24442 & 23650.6549409278 & 791.345059072184 \tabularnewline
67 & 22968 & 22203.727737615 & 764.272262385013 \tabularnewline
68 & 22013 & 21641.4353603078 & 371.564639692235 \tabularnewline
69 & 19947 & 20428.7304535018 & -481.730453501808 \tabularnewline
70 & 19142 & 19707.038388827 & -565.038388827044 \tabularnewline
71 & 19434 & 20391.8120859964 & -957.812085996415 \tabularnewline
72 & 20688 & 20794.7519806711 & -106.751980671092 \tabularnewline
73 & 20759 & 20752.9755395002 & 6.02446049982245 \tabularnewline
74 & 18921 & 20033.0589335078 & -1112.0589335078 \tabularnewline
75 & 19584 & 19582.9978439461 & 1.00215605385165 \tabularnewline
76 & 21201 & 20741.8418373994 & 459.158162600579 \tabularnewline
77 & 21935 & 21537.1934345677 & 397.806565432253 \tabularnewline
78 & 21493 & 21080.0501408644 & 412.949859135577 \tabularnewline
79 & 19506 & 19453.2324883679 & 52.7675116321079 \tabularnewline
80 & 18109 & 18347.9289684238 & -238.928968423781 \tabularnewline
81 & 16492 & 16347.7134138565 & 144.286586143506 \tabularnewline
82 & 15238 & 15804.7637134308 & -566.763713430839 \tabularnewline
83 & 15751 & 16231.206862528 & -480.206862528041 \tabularnewline
84 & 16855 & 17320.2619148857 & -465.261914885701 \tabularnewline
85 & 16563 & 17181.7984514444 & -618.7984514444 \tabularnewline
86 & 14946 & 15511.7333931378 & -565.733393137762 \tabularnewline
87 & 15459 & 15925.8479587671 & -466.847958767119 \tabularnewline
88 & 17076 & 17143.02855922 & -67.0285592200307 \tabularnewline
89 & 17960 & 17654.2875311548 & 305.712468845184 \tabularnewline
90 & 17447 & 17131.5279284111 & 315.472071588883 \tabularnewline
91 & 15459 & 15210.6183189085 & 248.381681091496 \tabularnewline
92 & 14576 & 13972.6356571603 & 603.364342839701 \tabularnewline
93 & 13251 & 12515.7939280099 & 735.206071990138 \tabularnewline
94 & 11854 & 11768.5668023115 & 85.4331976884805 \tabularnewline
95 & 12075 & 12502.8273168974 & -427.82731689739 \tabularnewline
96 & 13179 & 13617.1306472554 & -438.13064725545 \tabularnewline
97 & 13322 & 13393.2505044506 & -71.2505044506233 \tabularnewline
98 & 11997 & 11978.2622181769 & 18.7377818230543 \tabularnewline
99 & 12218 & 12698.3522493296 & -480.352249329551 \tabularnewline
100 & 14063 & 14161.9134101886 & -98.9134101885866 \tabularnewline
101 & 14504 & 14895.4895010298 & -391.489501029761 \tabularnewline
102 & 13764 & 14100.5617742354 & -336.561774235448 \tabularnewline
103 & 11042 & 11869.9011316117 & -827.901131611698 \tabularnewline
104 & 9646 & 10389.0720938489 & -743.072093848938 \tabularnewline
105 & 7801 & 8427.48318140025 & -626.483181400254 \tabularnewline
106 & 5963 & 6680.95111794077 & -717.951117940773 \tabularnewline
107 & 6554 & 6709.61257729945 & -155.612577299446 \tabularnewline
108 & 7359 & 7854.84460351487 & -495.844603514868 \tabularnewline
109 & 7217 & 7754.7760733583 & -537.776073358298 \tabularnewline
110 & 5813 & 6126.92706908122 & -313.927069081217 \tabularnewline
111 & 6625 & 6329.94885794486 & 295.051142055141 \tabularnewline
112 & 8613 & 8259.6489075273 & 353.351092472696 \tabularnewline
113 & 9496 & 8932.68744005986 & 563.312559940139 \tabularnewline
114 & 9055 & 8500.99368345765 & 554.006316542349 \tabularnewline
115 & 7288 & 6293.695737659 & 994.304262341007 \tabularnewline
116 & 5892 & 5581.83974998516 & 310.160250014843 \tabularnewline
117 & 4417 & 4115.58689235411 & 301.41310764589 \tabularnewline
118 & 2721 & 2703.21704161643 & 17.7829583835737 \tabularnewline
119 & 3021 & 3391.62147039326 & -370.621470393259 \tabularnewline
120 & 3534 & 4271.53578539853 & -737.535785398533 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169182&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]35998[/C][C]36579.1669337607[/C][C]-581.166933760702[/C][/ROW]
[ROW][C]14[/C][C]35335[/C][C]35689.5399635775[/C][C]-354.539963577539[/C][/ROW]
[ROW][C]15[/C][C]35043[/C][C]35287.387835967[/C][C]-244.387835967027[/C][/ROW]
[ROW][C]16[/C][C]35335[/C][C]35540.4006732982[/C][C]-205.400673298216[/C][/ROW]
[ROW][C]17[/C][C]36368[/C][C]36555.9202125426[/C][C]-187.920212542616[/C][/ROW]
[ROW][C]18[/C][C]36218[/C][C]36374.2506767935[/C][C]-156.250676793512[/C][/ROW]
[ROW][C]19[/C][C]34822[/C][C]34828.9231924434[/C][C]-6.9231924434207[/C][/ROW]
[ROW][C]20[/C][C]33640[/C][C]33989.3931115889[/C][C]-349.393111588877[/C][/ROW]
[ROW][C]21[/C][C]33419[/C][C]33846.9990295776[/C][C]-427.999029577622[/C][/ROW]
[ROW][C]22[/C][C]32977[/C][C]33585.5569038626[/C][C]-608.556903862591[/C][/ROW]
[ROW][C]23[/C][C]33276[/C][C]33313.7368984264[/C][C]-37.7368984263594[/C][/ROW]
[ROW][C]24[/C][C]33640[/C][C]33370.5477532212[/C][C]269.452246778805[/C][/ROW]
[ROW][C]25[/C][C]33497[/C][C]33071.6925407073[/C][C]425.307459292715[/C][/ROW]
[ROW][C]26[/C][C]33198[/C][C]32693.4246131307[/C][C]504.575386869321[/C][/ROW]
[ROW][C]27[/C][C]32614[/C][C]32686.4836480023[/C][C]-72.483648002286[/C][/ROW]
[ROW][C]28[/C][C]33198[/C][C]33019.14227018[/C][C]178.857729819967[/C][/ROW]
[ROW][C]29[/C][C]33718[/C][C]34192.2278358069[/C][C]-474.227835806931[/C][/ROW]
[ROW][C]30[/C][C]33568[/C][C]33903.593641738[/C][C]-335.593641738044[/C][/ROW]
[ROW][C]31[/C][C]31873[/C][C]32362.0204146134[/C][C]-489.020414613391[/C][/ROW]
[ROW][C]32[/C][C]31139[/C][C]31103.0948362088[/C][C]35.9051637912489[/C][/ROW]
[ROW][C]33[/C][C]30405[/C][C]31052.7945626117[/C][C]-647.794562611736[/C][/ROW]
[ROW][C]34[/C][C]29814[/C][C]30576.5582222429[/C][C]-762.558222242933[/C][/ROW]
[ROW][C]35[/C][C]29743[/C][C]30564.2268973078[/C][C]-821.226897307752[/C][/ROW]
[ROW][C]36[/C][C]30184[/C][C]30458.652556883[/C][C]-274.652556882967[/C][/ROW]
[ROW][C]37[/C][C]29593[/C][C]29994.6508340727[/C][C]-401.650834072701[/C][/ROW]
[ROW][C]38[/C][C]29372[/C][C]29279.7356957407[/C][C]92.2643042593227[/C][/ROW]
[ROW][C]39[/C][C]29151[/C][C]28703.0237082769[/C][C]447.976291723066[/C][/ROW]
[ROW][C]40[/C][C]30405[/C][C]29343.8468085392[/C][C]1061.15319146076[/C][/ROW]
[ROW][C]41[/C][C]30548[/C][C]30441.3028195309[/C][C]106.697180469142[/C][/ROW]
[ROW][C]42[/C][C]29814[/C][C]30439.1843588224[/C][C]-625.184358822386[/C][/ROW]
[ROW][C]43[/C][C]27826[/C][C]28655.9082205169[/C][C]-829.90822051691[/C][/ROW]
[ROW][C]44[/C][C]26943[/C][C]27536.1090821431[/C][C]-593.109082143121[/C][/ROW]
[ROW][C]45[/C][C]25547[/C][C]26775.9896551228[/C][C]-1228.98965512282[/C][/ROW]
[ROW][C]46[/C][C]24955[/C][C]25941.3834710799[/C][C]-986.383471079946[/C][/ROW]
[ROW][C]47[/C][C]25247[/C][C]25744.2332080414[/C][C]-497.233208041398[/C][/ROW]
[ROW][C]48[/C][C]25689[/C][C]26040.8565226963[/C][C]-351.856522696336[/C][/ROW]
[ROW][C]49[/C][C]25689[/C][C]25413.5198284105[/C][C]275.480171589523[/C][/ROW]
[ROW][C]50[/C][C]25326[/C][C]25219.6806137986[/C][C]106.31938620139[/C][/ROW]
[ROW][C]51[/C][C]25247[/C][C]24815.6532816919[/C][C]431.346718308116[/C][/ROW]
[ROW][C]52[/C][C]26430[/C][C]25770.8748194888[/C][C]659.125180511175[/C][/ROW]
[ROW][C]53[/C][C]27385[/C][C]26083.0504527483[/C][C]1301.9495472517[/C][/ROW]
[ROW][C]54[/C][C]26943[/C][C]26086.9575644459[/C][C]856.042435554136[/C][/ROW]
[ROW][C]55[/C][C]25468[/C][C]24762.0944421909[/C][C]705.905557809088[/C][/ROW]
[ROW][C]56[/C][C]24735[/C][C]24409.8432620724[/C][C]325.156737927584[/C][/ROW]
[ROW][C]57[/C][C]23189[/C][C]23660.4438269228[/C][C]-471.443826922787[/C][/ROW]
[ROW][C]58[/C][C]22234[/C][C]23309.6815303349[/C][C]-1075.68153033491[/C][/ROW]
[ROW][C]59[/C][C]22968[/C][C]23403.3123192759[/C][C]-435.312319275869[/C][/ROW]
[ROW][C]60[/C][C]23702[/C][C]23846.2774255057[/C][C]-144.277425505697[/C][/ROW]
[ROW][C]61[/C][C]23702[/C][C]23715.5057187788[/C][C]-13.5057187788479[/C][/ROW]
[ROW][C]62[/C][C]22747[/C][C]23337.6880702453[/C][C]-590.688070245349[/C][/ROW]
[ROW][C]63[/C][C]22676[/C][C]22871.9091334838[/C][C]-195.909133483794[/C][/ROW]
[ROW][C]64[/C][C]23922[/C][C]23725.795007671[/C][C]196.204992328985[/C][/ROW]
[ROW][C]65[/C][C]24735[/C][C]24244.3363980487[/C][C]490.663601951259[/C][/ROW]
[ROW][C]66[/C][C]24442[/C][C]23650.6549409278[/C][C]791.345059072184[/C][/ROW]
[ROW][C]67[/C][C]22968[/C][C]22203.727737615[/C][C]764.272262385013[/C][/ROW]
[ROW][C]68[/C][C]22013[/C][C]21641.4353603078[/C][C]371.564639692235[/C][/ROW]
[ROW][C]69[/C][C]19947[/C][C]20428.7304535018[/C][C]-481.730453501808[/C][/ROW]
[ROW][C]70[/C][C]19142[/C][C]19707.038388827[/C][C]-565.038388827044[/C][/ROW]
[ROW][C]71[/C][C]19434[/C][C]20391.8120859964[/C][C]-957.812085996415[/C][/ROW]
[ROW][C]72[/C][C]20688[/C][C]20794.7519806711[/C][C]-106.751980671092[/C][/ROW]
[ROW][C]73[/C][C]20759[/C][C]20752.9755395002[/C][C]6.02446049982245[/C][/ROW]
[ROW][C]74[/C][C]18921[/C][C]20033.0589335078[/C][C]-1112.0589335078[/C][/ROW]
[ROW][C]75[/C][C]19584[/C][C]19582.9978439461[/C][C]1.00215605385165[/C][/ROW]
[ROW][C]76[/C][C]21201[/C][C]20741.8418373994[/C][C]459.158162600579[/C][/ROW]
[ROW][C]77[/C][C]21935[/C][C]21537.1934345677[/C][C]397.806565432253[/C][/ROW]
[ROW][C]78[/C][C]21493[/C][C]21080.0501408644[/C][C]412.949859135577[/C][/ROW]
[ROW][C]79[/C][C]19506[/C][C]19453.2324883679[/C][C]52.7675116321079[/C][/ROW]
[ROW][C]80[/C][C]18109[/C][C]18347.9289684238[/C][C]-238.928968423781[/C][/ROW]
[ROW][C]81[/C][C]16492[/C][C]16347.7134138565[/C][C]144.286586143506[/C][/ROW]
[ROW][C]82[/C][C]15238[/C][C]15804.7637134308[/C][C]-566.763713430839[/C][/ROW]
[ROW][C]83[/C][C]15751[/C][C]16231.206862528[/C][C]-480.206862528041[/C][/ROW]
[ROW][C]84[/C][C]16855[/C][C]17320.2619148857[/C][C]-465.261914885701[/C][/ROW]
[ROW][C]85[/C][C]16563[/C][C]17181.7984514444[/C][C]-618.7984514444[/C][/ROW]
[ROW][C]86[/C][C]14946[/C][C]15511.7333931378[/C][C]-565.733393137762[/C][/ROW]
[ROW][C]87[/C][C]15459[/C][C]15925.8479587671[/C][C]-466.847958767119[/C][/ROW]
[ROW][C]88[/C][C]17076[/C][C]17143.02855922[/C][C]-67.0285592200307[/C][/ROW]
[ROW][C]89[/C][C]17960[/C][C]17654.2875311548[/C][C]305.712468845184[/C][/ROW]
[ROW][C]90[/C][C]17447[/C][C]17131.5279284111[/C][C]315.472071588883[/C][/ROW]
[ROW][C]91[/C][C]15459[/C][C]15210.6183189085[/C][C]248.381681091496[/C][/ROW]
[ROW][C]92[/C][C]14576[/C][C]13972.6356571603[/C][C]603.364342839701[/C][/ROW]
[ROW][C]93[/C][C]13251[/C][C]12515.7939280099[/C][C]735.206071990138[/C][/ROW]
[ROW][C]94[/C][C]11854[/C][C]11768.5668023115[/C][C]85.4331976884805[/C][/ROW]
[ROW][C]95[/C][C]12075[/C][C]12502.8273168974[/C][C]-427.82731689739[/C][/ROW]
[ROW][C]96[/C][C]13179[/C][C]13617.1306472554[/C][C]-438.13064725545[/C][/ROW]
[ROW][C]97[/C][C]13322[/C][C]13393.2505044506[/C][C]-71.2505044506233[/C][/ROW]
[ROW][C]98[/C][C]11997[/C][C]11978.2622181769[/C][C]18.7377818230543[/C][/ROW]
[ROW][C]99[/C][C]12218[/C][C]12698.3522493296[/C][C]-480.352249329551[/C][/ROW]
[ROW][C]100[/C][C]14063[/C][C]14161.9134101886[/C][C]-98.9134101885866[/C][/ROW]
[ROW][C]101[/C][C]14504[/C][C]14895.4895010298[/C][C]-391.489501029761[/C][/ROW]
[ROW][C]102[/C][C]13764[/C][C]14100.5617742354[/C][C]-336.561774235448[/C][/ROW]
[ROW][C]103[/C][C]11042[/C][C]11869.9011316117[/C][C]-827.901131611698[/C][/ROW]
[ROW][C]104[/C][C]9646[/C][C]10389.0720938489[/C][C]-743.072093848938[/C][/ROW]
[ROW][C]105[/C][C]7801[/C][C]8427.48318140025[/C][C]-626.483181400254[/C][/ROW]
[ROW][C]106[/C][C]5963[/C][C]6680.95111794077[/C][C]-717.951117940773[/C][/ROW]
[ROW][C]107[/C][C]6554[/C][C]6709.61257729945[/C][C]-155.612577299446[/C][/ROW]
[ROW][C]108[/C][C]7359[/C][C]7854.84460351487[/C][C]-495.844603514868[/C][/ROW]
[ROW][C]109[/C][C]7217[/C][C]7754.7760733583[/C][C]-537.776073358298[/C][/ROW]
[ROW][C]110[/C][C]5813[/C][C]6126.92706908122[/C][C]-313.927069081217[/C][/ROW]
[ROW][C]111[/C][C]6625[/C][C]6329.94885794486[/C][C]295.051142055141[/C][/ROW]
[ROW][C]112[/C][C]8613[/C][C]8259.6489075273[/C][C]353.351092472696[/C][/ROW]
[ROW][C]113[/C][C]9496[/C][C]8932.68744005986[/C][C]563.312559940139[/C][/ROW]
[ROW][C]114[/C][C]9055[/C][C]8500.99368345765[/C][C]554.006316542349[/C][/ROW]
[ROW][C]115[/C][C]7288[/C][C]6293.695737659[/C][C]994.304262341007[/C][/ROW]
[ROW][C]116[/C][C]5892[/C][C]5581.83974998516[/C][C]310.160250014843[/C][/ROW]
[ROW][C]117[/C][C]4417[/C][C]4115.58689235411[/C][C]301.41310764589[/C][/ROW]
[ROW][C]118[/C][C]2721[/C][C]2703.21704161643[/C][C]17.7829583835737[/C][/ROW]
[ROW][C]119[/C][C]3021[/C][C]3391.62147039326[/C][C]-370.621470393259[/C][/ROW]
[ROW][C]120[/C][C]3534[/C][C]4271.53578539853[/C][C]-737.535785398533[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169182&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169182&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
133599836579.1669337607-581.166933760702
143533535689.5399635775-354.539963577539
153504335287.387835967-244.387835967027
163533535540.4006732982-205.400673298216
173636836555.9202125426-187.920212542616
183621836374.2506767935-156.250676793512
193482234828.9231924434-6.9231924434207
203364033989.3931115889-349.393111588877
213341933846.9990295776-427.999029577622
223297733585.5569038626-608.556903862591
233327633313.7368984264-37.7368984263594
243364033370.5477532212269.452246778805
253349733071.6925407073425.307459292715
263319832693.4246131307504.575386869321
273261432686.4836480023-72.483648002286
283319833019.14227018178.857729819967
293371834192.2278358069-474.227835806931
303356833903.593641738-335.593641738044
313187332362.0204146134-489.020414613391
323113931103.094836208835.9051637912489
333040531052.7945626117-647.794562611736
342981430576.5582222429-762.558222242933
352974330564.2268973078-821.226897307752
363018430458.652556883-274.652556882967
372959329994.6508340727-401.650834072701
382937229279.735695740792.2643042593227
392915128703.0237082769447.976291723066
403040529343.84680853921061.15319146076
413054830441.3028195309106.697180469142
422981430439.1843588224-625.184358822386
432782628655.9082205169-829.90822051691
442694327536.1090821431-593.109082143121
452554726775.9896551228-1228.98965512282
462495525941.3834710799-986.383471079946
472524725744.2332080414-497.233208041398
482568926040.8565226963-351.856522696336
492568925413.5198284105275.480171589523
502532625219.6806137986106.31938620139
512524724815.6532816919431.346718308116
522643025770.8748194888659.125180511175
532738526083.05045274831301.9495472517
542694326086.9575644459856.042435554136
552546824762.0944421909705.905557809088
562473524409.8432620724325.156737927584
572318923660.4438269228-471.443826922787
582223423309.6815303349-1075.68153033491
592296823403.3123192759-435.312319275869
602370223846.2774255057-144.277425505697
612370223715.5057187788-13.5057187788479
622274723337.6880702453-590.688070245349
632267622871.9091334838-195.909133483794
642392223725.795007671196.204992328985
652473524244.3363980487490.663601951259
662444223650.6549409278791.345059072184
672296822203.727737615764.272262385013
682201321641.4353603078371.564639692235
691994720428.7304535018-481.730453501808
701914219707.038388827-565.038388827044
711943420391.8120859964-957.812085996415
722068820794.7519806711-106.751980671092
732075920752.97553950026.02446049982245
741892120033.0589335078-1112.0589335078
751958419582.99784394611.00215605385165
762120120741.8418373994459.158162600579
772193521537.1934345677397.806565432253
782149321080.0501408644412.949859135577
791950619453.232488367952.7675116321079
801810918347.9289684238-238.928968423781
811649216347.7134138565144.286586143506
821523815804.7637134308-566.763713430839
831575116231.206862528-480.206862528041
841685517320.2619148857-465.261914885701
851656317181.7984514444-618.7984514444
861494615511.7333931378-565.733393137762
871545915925.8479587671-466.847958767119
881707617143.02855922-67.0285592200307
891796017654.2875311548305.712468845184
901744717131.5279284111315.472071588883
911545915210.6183189085248.381681091496
921457613972.6356571603603.364342839701
931325112515.7939280099735.206071990138
941185411768.566802311585.4331976884805
951207512502.8273168974-427.82731689739
961317913617.1306472554-438.13064725545
971332213393.2505044506-71.2505044506233
981199711978.262218176918.7377818230543
991221812698.3522493296-480.352249329551
1001406314161.9134101886-98.9134101885866
1011450414895.4895010298-391.489501029761
1021376414100.5617742354-336.561774235448
1031104211869.9011316117-827.901131611698
104964610389.0720938489-743.072093848938
10578018427.48318140025-626.483181400254
10659636680.95111794077-717.951117940773
10765546709.61257729945-155.612577299446
10873597854.84460351487-495.844603514868
10972177754.7760733583-537.776073358298
11058136126.92706908122-313.927069081217
11166256329.94885794486295.051142055141
11286138259.6489075273353.351092472696
11394968932.68744005986563.312559940139
11490558500.99368345765554.006316542349
11572886293.695737659994.304262341007
11658925581.83974998516310.160250014843
11744174115.58689235411301.41310764589
11827212703.2170416164317.7829583835737
11930213391.62147039326-370.621470393259
12035344271.53578539853-737.535785398533







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1214070.6054740953059.440593921855081.77035426814
1222821.541341935631726.510746323883916.57193754739
1233549.010630820892370.653870645944727.36739099583
1245424.7462810474163.318630636976686.17393145704
1256106.092257915954761.635285832527450.54922999938
1265458.836855035694031.228187544766886.44552252662
1273300.893235652821789.882664576514811.90380672913
1281773.48324278282178.7195547832183368.24693078242
129165.992059723501-1512.956625322991844.94074476999
130-1553.2636901551-3316.89423560023210.366855290032
131-1121.0899916038-2969.95197064286727.771987435264
132-323.356404689468-2258.042372152341611.3295627734

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 4070.605474095 & 3059.44059392185 & 5081.77035426814 \tabularnewline
122 & 2821.54134193563 & 1726.51074632388 & 3916.57193754739 \tabularnewline
123 & 3549.01063082089 & 2370.65387064594 & 4727.36739099583 \tabularnewline
124 & 5424.746281047 & 4163.31863063697 & 6686.17393145704 \tabularnewline
125 & 6106.09225791595 & 4761.63528583252 & 7450.54922999938 \tabularnewline
126 & 5458.83685503569 & 4031.22818754476 & 6886.44552252662 \tabularnewline
127 & 3300.89323565282 & 1789.88266457651 & 4811.90380672913 \tabularnewline
128 & 1773.48324278282 & 178.719554783218 & 3368.24693078242 \tabularnewline
129 & 165.992059723501 & -1512.95662532299 & 1844.94074476999 \tabularnewline
130 & -1553.2636901551 & -3316.89423560023 & 210.366855290032 \tabularnewline
131 & -1121.0899916038 & -2969.95197064286 & 727.771987435264 \tabularnewline
132 & -323.356404689468 & -2258.04237215234 & 1611.3295627734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169182&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]121[/C][C]4070.605474095[/C][C]3059.44059392185[/C][C]5081.77035426814[/C][/ROW]
[ROW][C]122[/C][C]2821.54134193563[/C][C]1726.51074632388[/C][C]3916.57193754739[/C][/ROW]
[ROW][C]123[/C][C]3549.01063082089[/C][C]2370.65387064594[/C][C]4727.36739099583[/C][/ROW]
[ROW][C]124[/C][C]5424.746281047[/C][C]4163.31863063697[/C][C]6686.17393145704[/C][/ROW]
[ROW][C]125[/C][C]6106.09225791595[/C][C]4761.63528583252[/C][C]7450.54922999938[/C][/ROW]
[ROW][C]126[/C][C]5458.83685503569[/C][C]4031.22818754476[/C][C]6886.44552252662[/C][/ROW]
[ROW][C]127[/C][C]3300.89323565282[/C][C]1789.88266457651[/C][C]4811.90380672913[/C][/ROW]
[ROW][C]128[/C][C]1773.48324278282[/C][C]178.719554783218[/C][C]3368.24693078242[/C][/ROW]
[ROW][C]129[/C][C]165.992059723501[/C][C]-1512.95662532299[/C][C]1844.94074476999[/C][/ROW]
[ROW][C]130[/C][C]-1553.2636901551[/C][C]-3316.89423560023[/C][C]210.366855290032[/C][/ROW]
[ROW][C]131[/C][C]-1121.0899916038[/C][C]-2969.95197064286[/C][C]727.771987435264[/C][/ROW]
[ROW][C]132[/C][C]-323.356404689468[/C][C]-2258.04237215234[/C][C]1611.3295627734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169182&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169182&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
1214070.6054740953059.440593921855081.77035426814
1222821.541341935631726.510746323883916.57193754739
1233549.010630820892370.653870645944727.36739099583
1245424.7462810474163.318630636976686.17393145704
1256106.092257915954761.635285832527450.54922999938
1265458.836855035694031.228187544766886.44552252662
1273300.893235652821789.882664576514811.90380672913
1281773.48324278282178.7195547832183368.24693078242
129165.992059723501-1512.956625322991844.94074476999
130-1553.2636901551-3316.89423560023210.366855290032
131-1121.0899916038-2969.95197064286727.771987435264
132-323.356404689468-2258.042372152341611.3295627734



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')