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Author's title

Exponential Smoothing bij Time Series Analysis (new)-niet -werkende werkzoe...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Jan 2010 00:33:38 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/26/t1264491617zzzuylwdkjv3deh.htm/, Retrieved Thu, 02 May 2024 15:09:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72506, Retrieved Thu, 02 May 2024 15:09:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-01-26 07:33:38] [4cbcf6936bc3ba2d1882311a9e44fae8] [Current]
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Dataseries X:
492865
480961
461935
456608
441977
439148
488180
520564
501492
485025
464196
460170
467037
460070
447988
442867
436087
431328
484015
509673
512927
502831
470984
471067
476049
474605
470439
461251
454724
455626
516847
525192
522975
518585
509239
512238
519164
517009
509933
509127
500857
506971
569323
579714
577992
565464
547344
554788
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590
517945
506174
501866
516141




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72506&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72506&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72506&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.615821652041268
beta0.118765866706064
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.615821652041268 \tabularnewline
beta & 0.118765866706064 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72506&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]0.615821652041268[/C][/ROW]
[ROW][C]beta[/C][C]0.118765866706064[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72506&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72506&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
alpha0.615821652041268
beta0.118765866706064
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13467037472363.576121795-5326.57612179499
14460070461985.31991359-1915.31991359015
15447988447802.705336887185.294663113018
16442867440692.5385565882174.46144341241
17436087433501.0057979722585.99420202849
18431328429060.9147981152267.08520188474
19484015482872.9941510961142.00584890414
20509673517619.499978366-7946.49997836648
21512927494236.86964417318690.1303558273
22502831490931.70616355511899.2938364450
23470984479617.187785356-8633.18778535567
24471067471583.195119805-516.195119805343
25476049477284.838288029-1235.83828802919
26474605472103.7664615062501.23353849392
27470439463138.4809441057300.51905589522
28461251463385.124885385-2134.12488538492
29454724455594.156086407-870.156086407427
30455626450546.1797419955079.82025800546
31516847507506.8953677869340.10463221383
32525192546258.682432269-21066.6824322692
33522975526518.306281595-3543.30628159537
34518585506775.02648913711809.9735108633
35509239487373.44281269521865.5571873054
36512238503326.3207276318911.67927236884
37519164517333.6334502551830.36654974462
38517009518477.008632763-1468.00863276346
39509933511621.364240714-1688.36424071412
40509127504760.6438423474366.35615765263
41500857503986.608040813-3129.60804081318
42506971502196.0177857334774.98221426667
43569323562946.3745733756376.62542662525
44579714590315.471076116-10601.4710761162
45577992586641.224517669-8649.22451766883
46565464572167.891862108-6703.89186210837
47547344546390.01297408953.987025920069
48554788544120.85740877310667.1425912273
49562325556249.4911655666075.50883443374
50560854558811.1920211922042.80797880818
51555332554360.94431283971.055687170709
52543599551986.566648985-8387.56664898456
53536662540068.319813972-3406.31981397152
54542722540713.5764949842008.42350501625
55593530599742.680573712-6212.68057371234
56610763611282.766075753-519.766075753025
57612613613750.797599158-1137.79759915778
58611324604383.629149636940.37085037003
59594167590681.2062791583485.79372084187
60595454594618.981284408835.018715592101
61590865599125.871433409-8260.87143340858
62589379590458.197316543-1079.1973165432
63584428582593.8228132921834.17718670797
64573100576138.937168938-3038.93716893846
65567456568802.713766931-1346.71376693109
66569028572321.718686744-3293.71868674399
67620735624064.658499904-3329.65849990386
68628884638915.505962765-10031.5059627648
69628232633941.132577976-5709.13257797586
70612117623180.518266678-11063.5182666781
71595404594065.1816050231338.81839497702
72597141592506.8502855334634.14971446723
73593408592981.164534575426.83546542516
74590072590180.299805429-108.2998054286
75579799581861.778167286-2062.77816728572
76574205568678.5979399285526.40206007194
77572775565437.3482600517337.65173994948
78572942572361.675404226580.324595774175
79619567625565.16877017-5998.1687701703
80625809635091.455175316-9282.45517531584
81619916631187.180302219-11271.1803022191
82587625613485.75173597-25860.7517359707
83565742577481.872909657-11739.8729096568
84557274565638.04356287-8364.04356287047
85560576552043.4086749528532.59132504812
86548854550173.478856835-1319.47885683458
87531673536414.45706619-4741.45706618985
88525919520357.6106924295561.38930757134
89511038513696.632341192-2658.63234119164
90498662507000.780898371-8338.78089837148
91555362546663.8188198968698.18118010368
92564591559532.991900595058.00809940964
93541657560299.008870119-18642.0088701185
94527070528517.524193867-1447.52419386664
95509846510822.381644337-976.381644336914
96514258505540.6966714028717.30332859757
97516922508842.5848474758079.4151525253
98507561502761.6211412794799.37885872147
99492622491756.59297945865.407020549697
100490243483821.3020527296421.69794727088
101469357475305.68445808-5948.6844580801
102477580464934.44622227912645.5537777211
103528379526132.9770596912246.02294030902
104533590535226.047266048-1636.04726604815
105517945523870.844402354-5925.84440235398
106506174508562.197987808-2388.19798780815
107501866492436.1714923609429.82850763958
108516141500015.45606388716125.5439361132

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 467037 & 472363.576121795 & -5326.57612179499 \tabularnewline
14 & 460070 & 461985.31991359 & -1915.31991359015 \tabularnewline
15 & 447988 & 447802.705336887 & 185.294663113018 \tabularnewline
16 & 442867 & 440692.538556588 & 2174.46144341241 \tabularnewline
17 & 436087 & 433501.005797972 & 2585.99420202849 \tabularnewline
18 & 431328 & 429060.914798115 & 2267.08520188474 \tabularnewline
19 & 484015 & 482872.994151096 & 1142.00584890414 \tabularnewline
20 & 509673 & 517619.499978366 & -7946.49997836648 \tabularnewline
21 & 512927 & 494236.869644173 & 18690.1303558273 \tabularnewline
22 & 502831 & 490931.706163555 & 11899.2938364450 \tabularnewline
23 & 470984 & 479617.187785356 & -8633.18778535567 \tabularnewline
24 & 471067 & 471583.195119805 & -516.195119805343 \tabularnewline
25 & 476049 & 477284.838288029 & -1235.83828802919 \tabularnewline
26 & 474605 & 472103.766461506 & 2501.23353849392 \tabularnewline
27 & 470439 & 463138.480944105 & 7300.51905589522 \tabularnewline
28 & 461251 & 463385.124885385 & -2134.12488538492 \tabularnewline
29 & 454724 & 455594.156086407 & -870.156086407427 \tabularnewline
30 & 455626 & 450546.179741995 & 5079.82025800546 \tabularnewline
31 & 516847 & 507506.895367786 & 9340.10463221383 \tabularnewline
32 & 525192 & 546258.682432269 & -21066.6824322692 \tabularnewline
33 & 522975 & 526518.306281595 & -3543.30628159537 \tabularnewline
34 & 518585 & 506775.026489137 & 11809.9735108633 \tabularnewline
35 & 509239 & 487373.442812695 & 21865.5571873054 \tabularnewline
36 & 512238 & 503326.320727631 & 8911.67927236884 \tabularnewline
37 & 519164 & 517333.633450255 & 1830.36654974462 \tabularnewline
38 & 517009 & 518477.008632763 & -1468.00863276346 \tabularnewline
39 & 509933 & 511621.364240714 & -1688.36424071412 \tabularnewline
40 & 509127 & 504760.643842347 & 4366.35615765263 \tabularnewline
41 & 500857 & 503986.608040813 & -3129.60804081318 \tabularnewline
42 & 506971 & 502196.017785733 & 4774.98221426667 \tabularnewline
43 & 569323 & 562946.374573375 & 6376.62542662525 \tabularnewline
44 & 579714 & 590315.471076116 & -10601.4710761162 \tabularnewline
45 & 577992 & 586641.224517669 & -8649.22451766883 \tabularnewline
46 & 565464 & 572167.891862108 & -6703.89186210837 \tabularnewline
47 & 547344 & 546390.01297408 & 953.987025920069 \tabularnewline
48 & 554788 & 544120.857408773 & 10667.1425912273 \tabularnewline
49 & 562325 & 556249.491165566 & 6075.50883443374 \tabularnewline
50 & 560854 & 558811.192021192 & 2042.80797880818 \tabularnewline
51 & 555332 & 554360.94431283 & 971.055687170709 \tabularnewline
52 & 543599 & 551986.566648985 & -8387.56664898456 \tabularnewline
53 & 536662 & 540068.319813972 & -3406.31981397152 \tabularnewline
54 & 542722 & 540713.576494984 & 2008.42350501625 \tabularnewline
55 & 593530 & 599742.680573712 & -6212.68057371234 \tabularnewline
56 & 610763 & 611282.766075753 & -519.766075753025 \tabularnewline
57 & 612613 & 613750.797599158 & -1137.79759915778 \tabularnewline
58 & 611324 & 604383.62914963 & 6940.37085037003 \tabularnewline
59 & 594167 & 590681.206279158 & 3485.79372084187 \tabularnewline
60 & 595454 & 594618.981284408 & 835.018715592101 \tabularnewline
61 & 590865 & 599125.871433409 & -8260.87143340858 \tabularnewline
62 & 589379 & 590458.197316543 & -1079.1973165432 \tabularnewline
63 & 584428 & 582593.822813292 & 1834.17718670797 \tabularnewline
64 & 573100 & 576138.937168938 & -3038.93716893846 \tabularnewline
65 & 567456 & 568802.713766931 & -1346.71376693109 \tabularnewline
66 & 569028 & 572321.718686744 & -3293.71868674399 \tabularnewline
67 & 620735 & 624064.658499904 & -3329.65849990386 \tabularnewline
68 & 628884 & 638915.505962765 & -10031.5059627648 \tabularnewline
69 & 628232 & 633941.132577976 & -5709.13257797586 \tabularnewline
70 & 612117 & 623180.518266678 & -11063.5182666781 \tabularnewline
71 & 595404 & 594065.181605023 & 1338.81839497702 \tabularnewline
72 & 597141 & 592506.850285533 & 4634.14971446723 \tabularnewline
73 & 593408 & 592981.164534575 & 426.83546542516 \tabularnewline
74 & 590072 & 590180.299805429 & -108.2998054286 \tabularnewline
75 & 579799 & 581861.778167286 & -2062.77816728572 \tabularnewline
76 & 574205 & 568678.597939928 & 5526.40206007194 \tabularnewline
77 & 572775 & 565437.348260051 & 7337.65173994948 \tabularnewline
78 & 572942 & 572361.675404226 & 580.324595774175 \tabularnewline
79 & 619567 & 625565.16877017 & -5998.1687701703 \tabularnewline
80 & 625809 & 635091.455175316 & -9282.45517531584 \tabularnewline
81 & 619916 & 631187.180302219 & -11271.1803022191 \tabularnewline
82 & 587625 & 613485.75173597 & -25860.7517359707 \tabularnewline
83 & 565742 & 577481.872909657 & -11739.8729096568 \tabularnewline
84 & 557274 & 565638.04356287 & -8364.04356287047 \tabularnewline
85 & 560576 & 552043.408674952 & 8532.59132504812 \tabularnewline
86 & 548854 & 550173.478856835 & -1319.47885683458 \tabularnewline
87 & 531673 & 536414.45706619 & -4741.45706618985 \tabularnewline
88 & 525919 & 520357.610692429 & 5561.38930757134 \tabularnewline
89 & 511038 & 513696.632341192 & -2658.63234119164 \tabularnewline
90 & 498662 & 507000.780898371 & -8338.78089837148 \tabularnewline
91 & 555362 & 546663.818819896 & 8698.18118010368 \tabularnewline
92 & 564591 & 559532.99190059 & 5058.00809940964 \tabularnewline
93 & 541657 & 560299.008870119 & -18642.0088701185 \tabularnewline
94 & 527070 & 528517.524193867 & -1447.52419386664 \tabularnewline
95 & 509846 & 510822.381644337 & -976.381644336914 \tabularnewline
96 & 514258 & 505540.696671402 & 8717.30332859757 \tabularnewline
97 & 516922 & 508842.584847475 & 8079.4151525253 \tabularnewline
98 & 507561 & 502761.621141279 & 4799.37885872147 \tabularnewline
99 & 492622 & 491756.59297945 & 865.407020549697 \tabularnewline
100 & 490243 & 483821.302052729 & 6421.69794727088 \tabularnewline
101 & 469357 & 475305.68445808 & -5948.6844580801 \tabularnewline
102 & 477580 & 464934.446222279 & 12645.5537777211 \tabularnewline
103 & 528379 & 526132.977059691 & 2246.02294030902 \tabularnewline
104 & 533590 & 535226.047266048 & -1636.04726604815 \tabularnewline
105 & 517945 & 523870.844402354 & -5925.84440235398 \tabularnewline
106 & 506174 & 508562.197987808 & -2388.19798780815 \tabularnewline
107 & 501866 & 492436.171492360 & 9429.82850763958 \tabularnewline
108 & 516141 & 500015.456063887 & 16125.5439361132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72506&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]467037[/C][C]472363.576121795[/C][C]-5326.57612179499[/C][/ROW]
[ROW][C]14[/C][C]460070[/C][C]461985.31991359[/C][C]-1915.31991359015[/C][/ROW]
[ROW][C]15[/C][C]447988[/C][C]447802.705336887[/C][C]185.294663113018[/C][/ROW]
[ROW][C]16[/C][C]442867[/C][C]440692.538556588[/C][C]2174.46144341241[/C][/ROW]
[ROW][C]17[/C][C]436087[/C][C]433501.005797972[/C][C]2585.99420202849[/C][/ROW]
[ROW][C]18[/C][C]431328[/C][C]429060.914798115[/C][C]2267.08520188474[/C][/ROW]
[ROW][C]19[/C][C]484015[/C][C]482872.994151096[/C][C]1142.00584890414[/C][/ROW]
[ROW][C]20[/C][C]509673[/C][C]517619.499978366[/C][C]-7946.49997836648[/C][/ROW]
[ROW][C]21[/C][C]512927[/C][C]494236.869644173[/C][C]18690.1303558273[/C][/ROW]
[ROW][C]22[/C][C]502831[/C][C]490931.706163555[/C][C]11899.2938364450[/C][/ROW]
[ROW][C]23[/C][C]470984[/C][C]479617.187785356[/C][C]-8633.18778535567[/C][/ROW]
[ROW][C]24[/C][C]471067[/C][C]471583.195119805[/C][C]-516.195119805343[/C][/ROW]
[ROW][C]25[/C][C]476049[/C][C]477284.838288029[/C][C]-1235.83828802919[/C][/ROW]
[ROW][C]26[/C][C]474605[/C][C]472103.766461506[/C][C]2501.23353849392[/C][/ROW]
[ROW][C]27[/C][C]470439[/C][C]463138.480944105[/C][C]7300.51905589522[/C][/ROW]
[ROW][C]28[/C][C]461251[/C][C]463385.124885385[/C][C]-2134.12488538492[/C][/ROW]
[ROW][C]29[/C][C]454724[/C][C]455594.156086407[/C][C]-870.156086407427[/C][/ROW]
[ROW][C]30[/C][C]455626[/C][C]450546.179741995[/C][C]5079.82025800546[/C][/ROW]
[ROW][C]31[/C][C]516847[/C][C]507506.895367786[/C][C]9340.10463221383[/C][/ROW]
[ROW][C]32[/C][C]525192[/C][C]546258.682432269[/C][C]-21066.6824322692[/C][/ROW]
[ROW][C]33[/C][C]522975[/C][C]526518.306281595[/C][C]-3543.30628159537[/C][/ROW]
[ROW][C]34[/C][C]518585[/C][C]506775.026489137[/C][C]11809.9735108633[/C][/ROW]
[ROW][C]35[/C][C]509239[/C][C]487373.442812695[/C][C]21865.5571873054[/C][/ROW]
[ROW][C]36[/C][C]512238[/C][C]503326.320727631[/C][C]8911.67927236884[/C][/ROW]
[ROW][C]37[/C][C]519164[/C][C]517333.633450255[/C][C]1830.36654974462[/C][/ROW]
[ROW][C]38[/C][C]517009[/C][C]518477.008632763[/C][C]-1468.00863276346[/C][/ROW]
[ROW][C]39[/C][C]509933[/C][C]511621.364240714[/C][C]-1688.36424071412[/C][/ROW]
[ROW][C]40[/C][C]509127[/C][C]504760.643842347[/C][C]4366.35615765263[/C][/ROW]
[ROW][C]41[/C][C]500857[/C][C]503986.608040813[/C][C]-3129.60804081318[/C][/ROW]
[ROW][C]42[/C][C]506971[/C][C]502196.017785733[/C][C]4774.98221426667[/C][/ROW]
[ROW][C]43[/C][C]569323[/C][C]562946.374573375[/C][C]6376.62542662525[/C][/ROW]
[ROW][C]44[/C][C]579714[/C][C]590315.471076116[/C][C]-10601.4710761162[/C][/ROW]
[ROW][C]45[/C][C]577992[/C][C]586641.224517669[/C][C]-8649.22451766883[/C][/ROW]
[ROW][C]46[/C][C]565464[/C][C]572167.891862108[/C][C]-6703.89186210837[/C][/ROW]
[ROW][C]47[/C][C]547344[/C][C]546390.01297408[/C][C]953.987025920069[/C][/ROW]
[ROW][C]48[/C][C]554788[/C][C]544120.857408773[/C][C]10667.1425912273[/C][/ROW]
[ROW][C]49[/C][C]562325[/C][C]556249.491165566[/C][C]6075.50883443374[/C][/ROW]
[ROW][C]50[/C][C]560854[/C][C]558811.192021192[/C][C]2042.80797880818[/C][/ROW]
[ROW][C]51[/C][C]555332[/C][C]554360.94431283[/C][C]971.055687170709[/C][/ROW]
[ROW][C]52[/C][C]543599[/C][C]551986.566648985[/C][C]-8387.56664898456[/C][/ROW]
[ROW][C]53[/C][C]536662[/C][C]540068.319813972[/C][C]-3406.31981397152[/C][/ROW]
[ROW][C]54[/C][C]542722[/C][C]540713.576494984[/C][C]2008.42350501625[/C][/ROW]
[ROW][C]55[/C][C]593530[/C][C]599742.680573712[/C][C]-6212.68057371234[/C][/ROW]
[ROW][C]56[/C][C]610763[/C][C]611282.766075753[/C][C]-519.766075753025[/C][/ROW]
[ROW][C]57[/C][C]612613[/C][C]613750.797599158[/C][C]-1137.79759915778[/C][/ROW]
[ROW][C]58[/C][C]611324[/C][C]604383.62914963[/C][C]6940.37085037003[/C][/ROW]
[ROW][C]59[/C][C]594167[/C][C]590681.206279158[/C][C]3485.79372084187[/C][/ROW]
[ROW][C]60[/C][C]595454[/C][C]594618.981284408[/C][C]835.018715592101[/C][/ROW]
[ROW][C]61[/C][C]590865[/C][C]599125.871433409[/C][C]-8260.87143340858[/C][/ROW]
[ROW][C]62[/C][C]589379[/C][C]590458.197316543[/C][C]-1079.1973165432[/C][/ROW]
[ROW][C]63[/C][C]584428[/C][C]582593.822813292[/C][C]1834.17718670797[/C][/ROW]
[ROW][C]64[/C][C]573100[/C][C]576138.937168938[/C][C]-3038.93716893846[/C][/ROW]
[ROW][C]65[/C][C]567456[/C][C]568802.713766931[/C][C]-1346.71376693109[/C][/ROW]
[ROW][C]66[/C][C]569028[/C][C]572321.718686744[/C][C]-3293.71868674399[/C][/ROW]
[ROW][C]67[/C][C]620735[/C][C]624064.658499904[/C][C]-3329.65849990386[/C][/ROW]
[ROW][C]68[/C][C]628884[/C][C]638915.505962765[/C][C]-10031.5059627648[/C][/ROW]
[ROW][C]69[/C][C]628232[/C][C]633941.132577976[/C][C]-5709.13257797586[/C][/ROW]
[ROW][C]70[/C][C]612117[/C][C]623180.518266678[/C][C]-11063.5182666781[/C][/ROW]
[ROW][C]71[/C][C]595404[/C][C]594065.181605023[/C][C]1338.81839497702[/C][/ROW]
[ROW][C]72[/C][C]597141[/C][C]592506.850285533[/C][C]4634.14971446723[/C][/ROW]
[ROW][C]73[/C][C]593408[/C][C]592981.164534575[/C][C]426.83546542516[/C][/ROW]
[ROW][C]74[/C][C]590072[/C][C]590180.299805429[/C][C]-108.2998054286[/C][/ROW]
[ROW][C]75[/C][C]579799[/C][C]581861.778167286[/C][C]-2062.77816728572[/C][/ROW]
[ROW][C]76[/C][C]574205[/C][C]568678.597939928[/C][C]5526.40206007194[/C][/ROW]
[ROW][C]77[/C][C]572775[/C][C]565437.348260051[/C][C]7337.65173994948[/C][/ROW]
[ROW][C]78[/C][C]572942[/C][C]572361.675404226[/C][C]580.324595774175[/C][/ROW]
[ROW][C]79[/C][C]619567[/C][C]625565.16877017[/C][C]-5998.1687701703[/C][/ROW]
[ROW][C]80[/C][C]625809[/C][C]635091.455175316[/C][C]-9282.45517531584[/C][/ROW]
[ROW][C]81[/C][C]619916[/C][C]631187.180302219[/C][C]-11271.1803022191[/C][/ROW]
[ROW][C]82[/C][C]587625[/C][C]613485.75173597[/C][C]-25860.7517359707[/C][/ROW]
[ROW][C]83[/C][C]565742[/C][C]577481.872909657[/C][C]-11739.8729096568[/C][/ROW]
[ROW][C]84[/C][C]557274[/C][C]565638.04356287[/C][C]-8364.04356287047[/C][/ROW]
[ROW][C]85[/C][C]560576[/C][C]552043.408674952[/C][C]8532.59132504812[/C][/ROW]
[ROW][C]86[/C][C]548854[/C][C]550173.478856835[/C][C]-1319.47885683458[/C][/ROW]
[ROW][C]87[/C][C]531673[/C][C]536414.45706619[/C][C]-4741.45706618985[/C][/ROW]
[ROW][C]88[/C][C]525919[/C][C]520357.610692429[/C][C]5561.38930757134[/C][/ROW]
[ROW][C]89[/C][C]511038[/C][C]513696.632341192[/C][C]-2658.63234119164[/C][/ROW]
[ROW][C]90[/C][C]498662[/C][C]507000.780898371[/C][C]-8338.78089837148[/C][/ROW]
[ROW][C]91[/C][C]555362[/C][C]546663.818819896[/C][C]8698.18118010368[/C][/ROW]
[ROW][C]92[/C][C]564591[/C][C]559532.99190059[/C][C]5058.00809940964[/C][/ROW]
[ROW][C]93[/C][C]541657[/C][C]560299.008870119[/C][C]-18642.0088701185[/C][/ROW]
[ROW][C]94[/C][C]527070[/C][C]528517.524193867[/C][C]-1447.52419386664[/C][/ROW]
[ROW][C]95[/C][C]509846[/C][C]510822.381644337[/C][C]-976.381644336914[/C][/ROW]
[ROW][C]96[/C][C]514258[/C][C]505540.696671402[/C][C]8717.30332859757[/C][/ROW]
[ROW][C]97[/C][C]516922[/C][C]508842.584847475[/C][C]8079.4151525253[/C][/ROW]
[ROW][C]98[/C][C]507561[/C][C]502761.621141279[/C][C]4799.37885872147[/C][/ROW]
[ROW][C]99[/C][C]492622[/C][C]491756.59297945[/C][C]865.407020549697[/C][/ROW]
[ROW][C]100[/C][C]490243[/C][C]483821.302052729[/C][C]6421.69794727088[/C][/ROW]
[ROW][C]101[/C][C]469357[/C][C]475305.68445808[/C][C]-5948.6844580801[/C][/ROW]
[ROW][C]102[/C][C]477580[/C][C]464934.446222279[/C][C]12645.5537777211[/C][/ROW]
[ROW][C]103[/C][C]528379[/C][C]526132.977059691[/C][C]2246.02294030902[/C][/ROW]
[ROW][C]104[/C][C]533590[/C][C]535226.047266048[/C][C]-1636.04726604815[/C][/ROW]
[ROW][C]105[/C][C]517945[/C][C]523870.844402354[/C][C]-5925.84440235398[/C][/ROW]
[ROW][C]106[/C][C]506174[/C][C]508562.197987808[/C][C]-2388.19798780815[/C][/ROW]
[ROW][C]107[/C][C]501866[/C][C]492436.171492360[/C][C]9429.82850763958[/C][/ROW]
[ROW][C]108[/C][C]516141[/C][C]500015.456063887[/C][C]16125.5439361132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72506&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72506&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
13467037472363.576121795-5326.57612179499
14460070461985.31991359-1915.31991359015
15447988447802.705336887185.294663113018
16442867440692.5385565882174.46144341241
17436087433501.0057979722585.99420202849
18431328429060.9147981152267.08520188474
19484015482872.9941510961142.00584890414
20509673517619.499978366-7946.49997836648
21512927494236.86964417318690.1303558273
22502831490931.70616355511899.2938364450
23470984479617.187785356-8633.18778535567
24471067471583.195119805-516.195119805343
25476049477284.838288029-1235.83828802919
26474605472103.7664615062501.23353849392
27470439463138.4809441057300.51905589522
28461251463385.124885385-2134.12488538492
29454724455594.156086407-870.156086407427
30455626450546.1797419955079.82025800546
31516847507506.8953677869340.10463221383
32525192546258.682432269-21066.6824322692
33522975526518.306281595-3543.30628159537
34518585506775.02648913711809.9735108633
35509239487373.44281269521865.5571873054
36512238503326.3207276318911.67927236884
37519164517333.6334502551830.36654974462
38517009518477.008632763-1468.00863276346
39509933511621.364240714-1688.36424071412
40509127504760.6438423474366.35615765263
41500857503986.608040813-3129.60804081318
42506971502196.0177857334774.98221426667
43569323562946.3745733756376.62542662525
44579714590315.471076116-10601.4710761162
45577992586641.224517669-8649.22451766883
46565464572167.891862108-6703.89186210837
47547344546390.01297408953.987025920069
48554788544120.85740877310667.1425912273
49562325556249.4911655666075.50883443374
50560854558811.1920211922042.80797880818
51555332554360.94431283971.055687170709
52543599551986.566648985-8387.56664898456
53536662540068.319813972-3406.31981397152
54542722540713.5764949842008.42350501625
55593530599742.680573712-6212.68057371234
56610763611282.766075753-519.766075753025
57612613613750.797599158-1137.79759915778
58611324604383.629149636940.37085037003
59594167590681.2062791583485.79372084187
60595454594618.981284408835.018715592101
61590865599125.871433409-8260.87143340858
62589379590458.197316543-1079.1973165432
63584428582593.8228132921834.17718670797
64573100576138.937168938-3038.93716893846
65567456568802.713766931-1346.71376693109
66569028572321.718686744-3293.71868674399
67620735624064.658499904-3329.65849990386
68628884638915.505962765-10031.5059627648
69628232633941.132577976-5709.13257797586
70612117623180.518266678-11063.5182666781
71595404594065.1816050231338.81839497702
72597141592506.8502855334634.14971446723
73593408592981.164534575426.83546542516
74590072590180.299805429-108.2998054286
75579799581861.778167286-2062.77816728572
76574205568678.5979399285526.40206007194
77572775565437.3482600517337.65173994948
78572942572361.675404226580.324595774175
79619567625565.16877017-5998.1687701703
80625809635091.455175316-9282.45517531584
81619916631187.180302219-11271.1803022191
82587625613485.75173597-25860.7517359707
83565742577481.872909657-11739.8729096568
84557274565638.04356287-8364.04356287047
85560576552043.4086749528532.59132504812
86548854550173.478856835-1319.47885683458
87531673536414.45706619-4741.45706618985
88525919520357.6106924295561.38930757134
89511038513696.632341192-2658.63234119164
90498662507000.780898371-8338.78089837148
91555362546663.8188198968698.18118010368
92564591559532.991900595058.00809940964
93541657560299.008870119-18642.0088701185
94527070528517.524193867-1447.52419386664
95509846510822.381644337-976.381644336914
96514258505540.6966714028717.30332859757
97516922508842.5848474758079.4151525253
98507561502761.6211412794799.37885872147
99492622491756.59297945865.407020549697
100490243483821.3020527296421.69794727088
101469357475305.68445808-5948.6844580801
102477580464934.44622227912645.5537777211
103528379526132.9770596912246.02294030902
104533590535226.047266048-1636.04726604815
105517945523870.844402354-5925.84440235398
106506174508562.197987808-2388.19798780815
107501866492436.1714923609429.82850763958
108516141500015.45606388716125.5439361132







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109510904.760811597495665.719673594526143.8019496
110501267.606771325482761.949819087519773.263723563
111488124.057954161466276.029809854509972.086098469
112484055.530228084458770.280467361509340.779988807
113468628.277883591439801.790043209497454.765723973
114471294.369437229438818.401891705503770.336982752
115522015.839250204485780.572549717558251.105950692
116529375.700995004489271.223031825569480.178958183
117518640.970893084474558.131096588562723.81068958
118510035.089449248461865.992661955558204.186236541
119501789.080843939449427.367617441554150.794070437
120507313.021319746450654.018137292563972.024502201

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 510904.760811597 & 495665.719673594 & 526143.8019496 \tabularnewline
110 & 501267.606771325 & 482761.949819087 & 519773.263723563 \tabularnewline
111 & 488124.057954161 & 466276.029809854 & 509972.086098469 \tabularnewline
112 & 484055.530228084 & 458770.280467361 & 509340.779988807 \tabularnewline
113 & 468628.277883591 & 439801.790043209 & 497454.765723973 \tabularnewline
114 & 471294.369437229 & 438818.401891705 & 503770.336982752 \tabularnewline
115 & 522015.839250204 & 485780.572549717 & 558251.105950692 \tabularnewline
116 & 529375.700995004 & 489271.223031825 & 569480.178958183 \tabularnewline
117 & 518640.970893084 & 474558.131096588 & 562723.81068958 \tabularnewline
118 & 510035.089449248 & 461865.992661955 & 558204.186236541 \tabularnewline
119 & 501789.080843939 & 449427.367617441 & 554150.794070437 \tabularnewline
120 & 507313.021319746 & 450654.018137292 & 563972.024502201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72506&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]510904.760811597[/C][C]495665.719673594[/C][C]526143.8019496[/C][/ROW]
[ROW][C]110[/C][C]501267.606771325[/C][C]482761.949819087[/C][C]519773.263723563[/C][/ROW]
[ROW][C]111[/C][C]488124.057954161[/C][C]466276.029809854[/C][C]509972.086098469[/C][/ROW]
[ROW][C]112[/C][C]484055.530228084[/C][C]458770.280467361[/C][C]509340.779988807[/C][/ROW]
[ROW][C]113[/C][C]468628.277883591[/C][C]439801.790043209[/C][C]497454.765723973[/C][/ROW]
[ROW][C]114[/C][C]471294.369437229[/C][C]438818.401891705[/C][C]503770.336982752[/C][/ROW]
[ROW][C]115[/C][C]522015.839250204[/C][C]485780.572549717[/C][C]558251.105950692[/C][/ROW]
[ROW][C]116[/C][C]529375.700995004[/C][C]489271.223031825[/C][C]569480.178958183[/C][/ROW]
[ROW][C]117[/C][C]518640.970893084[/C][C]474558.131096588[/C][C]562723.81068958[/C][/ROW]
[ROW][C]118[/C][C]510035.089449248[/C][C]461865.992661955[/C][C]558204.186236541[/C][/ROW]
[ROW][C]119[/C][C]501789.080843939[/C][C]449427.367617441[/C][C]554150.794070437[/C][/ROW]
[ROW][C]120[/C][C]507313.021319746[/C][C]450654.018137292[/C][C]563972.024502201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72506&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72506&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
109510904.760811597495665.719673594526143.8019496
110501267.606771325482761.949819087519773.263723563
111488124.057954161466276.029809854509972.086098469
112484055.530228084458770.280467361509340.779988807
113468628.277883591439801.790043209497454.765723973
114471294.369437229438818.401891705503770.336982752
115522015.839250204485780.572549717558251.105950692
116529375.700995004489271.223031825569480.178958183
117518640.970893084474558.131096588562723.81068958
118510035.089449248461865.992661955558204.186236541
119501789.080843939449427.367617441554150.794070437
120507313.021319746450654.018137292563972.024502201



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')