Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Aug 2010 19:19:58 +0000
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/Aug/16/t128198675457kummbec7ish13.htm/, Retrieved Thu, 16 May 2024 11:36:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79040, Retrieved Thu, 16 May 2024 11:36:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmattias debbaut
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [classical decompo...] [2010-08-16 19:19:58] [59fa324537f53fb6459bc6951db20f7b] [Current]
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Dataseries X:
900
899
898
896
916
915
900
890
891
891
892
894
896
889
878
883
901
897
881
866
867
866
862
871
865
856
847
859
870
872
856
839
829
825
822
827
822
812
810
816
820
823
810
793
777
772
765
765
753
742
736
740
742
742
728
707
699
696
689
692
673
653
642
648
654
653
630
609
598
601
592
591
568
538
523
530
529
534
513
491
480
478
462
461
437
411
400
405
395
407
385
366
349
343
332
327
306
276
269
268
260
274
247
226
212
199
188
179
155
124
117
116
105
112
86
64
53
42
32
24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79040&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79040&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79040&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.474509737981929
beta0.109980424057153
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.474509737981929 \tabularnewline
beta & 0.109980424057153 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79040&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]0.474509737981929[/C][/ROW]
[ROW][C]beta[/C][C]0.109980424057153[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79040&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79040&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
alpha0.474509737981929
beta0.109980424057153
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13896903.770888491585-7.77088849158486
14889892.83650764698-3.83650764697927
15878879.78255457044-1.78255457043906
16883883.677270637965-0.67727063796508
17901901.309957990233-0.309957990232760
18897897.00751071256-0.00751071256001978
19881879.9808478864781.01915211352241
20866868.959308324936-2.95930832493616
21867867.292335495294-0.292335495294196
22866866.018077851283-0.0180778512832376
23862865.638398416371-3.63839841637139
24871864.5083038618166.49169613818378
25865864.7479704950670.252029504932693
26856859.49110324043-3.49110324042977
27847847.675768997403-0.675768997402656
28859852.183016587226.8169834127807
29870873.09086321796-3.09086321795951
30872867.7021826935354.29781730646539
31856853.9299246018142.07007539818596
32839841.943201446102-2.94320144610219
33829841.875940892999-12.8759408929988
34825834.360315607434-9.36031560743447
35822826.784407948278-4.78440794827816
36827829.129726468095-2.12972646809533
37822820.82228929731.17771070270044
38812812.980619331017-0.98061933101701
39810802.982719714997.01728028501054
40816813.7445455213682.25545447863203
41820825.489205821766-5.48920582176584
42823821.5502354602971.44976453970332
43810804.812899675235.18710032477054
44793791.3343954758851.66560452411511
45777787.418860610278-10.4188606102782
46772781.961988489794-9.96198848979361
47765775.565519365578-10.5655193655775
48765774.860936287358-9.8609362873583
49753763.250970817308-10.2509708173083
50742747.229430873978-5.22943087397778
51736737.245218203866-1.24521820386576
52740738.0771593873581.92284061264218
53742741.847279925470.152720074530293
54742741.1388202161920.861179783808097
55728724.7425280877083.25747191229209
56707707.43442221544-0.434422215440236
57699694.3515142890714.64848571092864
58696694.0295097921661.97049020783356
59689691.465648497205-2.46564849720528
60692693.16948672136-1.16948672135993
61673685.220962762477-12.2209627624771
62653670.655439264295-17.6554392642953
63642655.642040473916-13.6420404739156
64648649.334880788702-1.33488078870209
65654647.6148260812176.38517391878338
66653647.818782676935.18121732306997
67630634.439669594048-4.43966959404827
68609611.689698128818-2.68969812881812
69598598.880552017984-0.880552017983973
70601592.0761177764838.92388222351747
71592588.6800004423683.31999955763217
72591590.9185397143580.0814602856419242
73568577.322600841805-9.3226008418053
74538560.646388107491-22.6463881074912
75523543.286387955832-20.2863879558323
76530535.807350992743-5.80735099274261
77529531.738635342179-2.73863534217855
78534523.3453726630110.6546273369898
79513507.6111869168385.38881308316201
80491490.8555126286050.144487371395201
81480479.1638990907390.83610090926146
82478475.3288742643892.67112573561121
83462464.709057863621-2.70905786362118
84461458.7227478915832.27725210841652
85437441.589932636353-4.5899326363529
86411420.786323599084-9.78632359908397
87400408.6521977364-8.65219773639961
88405409.14032888495-4.14032888494961
89395404.366251105912-9.36625110591217
90407396.22254422560110.7774557743990
91385380.1870051958874.81299480411258
92366362.6491256849183.35087431508248
93349352.563721873452-3.56372187345175
94343344.895839178019-1.89583917801906
95332329.5568471730162.44315282698352
96327325.5123861460911.48761385390941
97306307.07581436036-1.0758143603598
98276288.009108495393-12.0091084953934
99269273.570104211447-4.57010421144713
100268271.955898722831-3.95589872283085
101260261.930948891483-1.93094889148279
102274261.06124060616912.9387593938314
103247247.179743554591-0.179743554591198
104226229.589440102179-3.58944010217937
105212213.634612075621-1.63461207562054
106199204.857537420710-5.85753742071049
107188189.584014525368-1.58401452536751
108179179.806136301810-0.80613630181034
109155162.297327857733-7.29732785773254
110124139.9346030249-15.9346030249000
111117122.761255042656-5.76125504265616
112116112.2284388462793.77156115372080
113105102.7322101767032.26778982329726
11411297.809218749405814.1907812505942
1158685.95493565760720.0450643423927772
1166470.8606110124776-6.86061101247756
1175354.5112363119745-1.51123631197454
1184241.45977952976620.540220470233834
1193229.37697362302442.62302637697558
1202418.46655428853285.53344571146723

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 896 & 903.770888491585 & -7.77088849158486 \tabularnewline
14 & 889 & 892.83650764698 & -3.83650764697927 \tabularnewline
15 & 878 & 879.78255457044 & -1.78255457043906 \tabularnewline
16 & 883 & 883.677270637965 & -0.67727063796508 \tabularnewline
17 & 901 & 901.309957990233 & -0.309957990232760 \tabularnewline
18 & 897 & 897.00751071256 & -0.00751071256001978 \tabularnewline
19 & 881 & 879.980847886478 & 1.01915211352241 \tabularnewline
20 & 866 & 868.959308324936 & -2.95930832493616 \tabularnewline
21 & 867 & 867.292335495294 & -0.292335495294196 \tabularnewline
22 & 866 & 866.018077851283 & -0.0180778512832376 \tabularnewline
23 & 862 & 865.638398416371 & -3.63839841637139 \tabularnewline
24 & 871 & 864.508303861816 & 6.49169613818378 \tabularnewline
25 & 865 & 864.747970495067 & 0.252029504932693 \tabularnewline
26 & 856 & 859.49110324043 & -3.49110324042977 \tabularnewline
27 & 847 & 847.675768997403 & -0.675768997402656 \tabularnewline
28 & 859 & 852.18301658722 & 6.8169834127807 \tabularnewline
29 & 870 & 873.09086321796 & -3.09086321795951 \tabularnewline
30 & 872 & 867.702182693535 & 4.29781730646539 \tabularnewline
31 & 856 & 853.929924601814 & 2.07007539818596 \tabularnewline
32 & 839 & 841.943201446102 & -2.94320144610219 \tabularnewline
33 & 829 & 841.875940892999 & -12.8759408929988 \tabularnewline
34 & 825 & 834.360315607434 & -9.36031560743447 \tabularnewline
35 & 822 & 826.784407948278 & -4.78440794827816 \tabularnewline
36 & 827 & 829.129726468095 & -2.12972646809533 \tabularnewline
37 & 822 & 820.8222892973 & 1.17771070270044 \tabularnewline
38 & 812 & 812.980619331017 & -0.98061933101701 \tabularnewline
39 & 810 & 802.98271971499 & 7.01728028501054 \tabularnewline
40 & 816 & 813.744545521368 & 2.25545447863203 \tabularnewline
41 & 820 & 825.489205821766 & -5.48920582176584 \tabularnewline
42 & 823 & 821.550235460297 & 1.44976453970332 \tabularnewline
43 & 810 & 804.81289967523 & 5.18710032477054 \tabularnewline
44 & 793 & 791.334395475885 & 1.66560452411511 \tabularnewline
45 & 777 & 787.418860610278 & -10.4188606102782 \tabularnewline
46 & 772 & 781.961988489794 & -9.96198848979361 \tabularnewline
47 & 765 & 775.565519365578 & -10.5655193655775 \tabularnewline
48 & 765 & 774.860936287358 & -9.8609362873583 \tabularnewline
49 & 753 & 763.250970817308 & -10.2509708173083 \tabularnewline
50 & 742 & 747.229430873978 & -5.22943087397778 \tabularnewline
51 & 736 & 737.245218203866 & -1.24521820386576 \tabularnewline
52 & 740 & 738.077159387358 & 1.92284061264218 \tabularnewline
53 & 742 & 741.84727992547 & 0.152720074530293 \tabularnewline
54 & 742 & 741.138820216192 & 0.861179783808097 \tabularnewline
55 & 728 & 724.742528087708 & 3.25747191229209 \tabularnewline
56 & 707 & 707.43442221544 & -0.434422215440236 \tabularnewline
57 & 699 & 694.351514289071 & 4.64848571092864 \tabularnewline
58 & 696 & 694.029509792166 & 1.97049020783356 \tabularnewline
59 & 689 & 691.465648497205 & -2.46564849720528 \tabularnewline
60 & 692 & 693.16948672136 & -1.16948672135993 \tabularnewline
61 & 673 & 685.220962762477 & -12.2209627624771 \tabularnewline
62 & 653 & 670.655439264295 & -17.6554392642953 \tabularnewline
63 & 642 & 655.642040473916 & -13.6420404739156 \tabularnewline
64 & 648 & 649.334880788702 & -1.33488078870209 \tabularnewline
65 & 654 & 647.614826081217 & 6.38517391878338 \tabularnewline
66 & 653 & 647.81878267693 & 5.18121732306997 \tabularnewline
67 & 630 & 634.439669594048 & -4.43966959404827 \tabularnewline
68 & 609 & 611.689698128818 & -2.68969812881812 \tabularnewline
69 & 598 & 598.880552017984 & -0.880552017983973 \tabularnewline
70 & 601 & 592.076117776483 & 8.92388222351747 \tabularnewline
71 & 592 & 588.680000442368 & 3.31999955763217 \tabularnewline
72 & 591 & 590.918539714358 & 0.0814602856419242 \tabularnewline
73 & 568 & 577.322600841805 & -9.3226008418053 \tabularnewline
74 & 538 & 560.646388107491 & -22.6463881074912 \tabularnewline
75 & 523 & 543.286387955832 & -20.2863879558323 \tabularnewline
76 & 530 & 535.807350992743 & -5.80735099274261 \tabularnewline
77 & 529 & 531.738635342179 & -2.73863534217855 \tabularnewline
78 & 534 & 523.34537266301 & 10.6546273369898 \tabularnewline
79 & 513 & 507.611186916838 & 5.38881308316201 \tabularnewline
80 & 491 & 490.855512628605 & 0.144487371395201 \tabularnewline
81 & 480 & 479.163899090739 & 0.83610090926146 \tabularnewline
82 & 478 & 475.328874264389 & 2.67112573561121 \tabularnewline
83 & 462 & 464.709057863621 & -2.70905786362118 \tabularnewline
84 & 461 & 458.722747891583 & 2.27725210841652 \tabularnewline
85 & 437 & 441.589932636353 & -4.5899326363529 \tabularnewline
86 & 411 & 420.786323599084 & -9.78632359908397 \tabularnewline
87 & 400 & 408.6521977364 & -8.65219773639961 \tabularnewline
88 & 405 & 409.14032888495 & -4.14032888494961 \tabularnewline
89 & 395 & 404.366251105912 & -9.36625110591217 \tabularnewline
90 & 407 & 396.222544225601 & 10.7774557743990 \tabularnewline
91 & 385 & 380.187005195887 & 4.81299480411258 \tabularnewline
92 & 366 & 362.649125684918 & 3.35087431508248 \tabularnewline
93 & 349 & 352.563721873452 & -3.56372187345175 \tabularnewline
94 & 343 & 344.895839178019 & -1.89583917801906 \tabularnewline
95 & 332 & 329.556847173016 & 2.44315282698352 \tabularnewline
96 & 327 & 325.512386146091 & 1.48761385390941 \tabularnewline
97 & 306 & 307.07581436036 & -1.0758143603598 \tabularnewline
98 & 276 & 288.009108495393 & -12.0091084953934 \tabularnewline
99 & 269 & 273.570104211447 & -4.57010421144713 \tabularnewline
100 & 268 & 271.955898722831 & -3.95589872283085 \tabularnewline
101 & 260 & 261.930948891483 & -1.93094889148279 \tabularnewline
102 & 274 & 261.061240606169 & 12.9387593938314 \tabularnewline
103 & 247 & 247.179743554591 & -0.179743554591198 \tabularnewline
104 & 226 & 229.589440102179 & -3.58944010217937 \tabularnewline
105 & 212 & 213.634612075621 & -1.63461207562054 \tabularnewline
106 & 199 & 204.857537420710 & -5.85753742071049 \tabularnewline
107 & 188 & 189.584014525368 & -1.58401452536751 \tabularnewline
108 & 179 & 179.806136301810 & -0.80613630181034 \tabularnewline
109 & 155 & 162.297327857733 & -7.29732785773254 \tabularnewline
110 & 124 & 139.9346030249 & -15.9346030249000 \tabularnewline
111 & 117 & 122.761255042656 & -5.76125504265616 \tabularnewline
112 & 116 & 112.228438846279 & 3.77156115372080 \tabularnewline
113 & 105 & 102.732210176703 & 2.26778982329726 \tabularnewline
114 & 112 & 97.8092187494058 & 14.1907812505942 \tabularnewline
115 & 86 & 85.9549356576072 & 0.0450643423927772 \tabularnewline
116 & 64 & 70.8606110124776 & -6.86061101247756 \tabularnewline
117 & 53 & 54.5112363119745 & -1.51123631197454 \tabularnewline
118 & 42 & 41.4597795297662 & 0.540220470233834 \tabularnewline
119 & 32 & 29.3769736230244 & 2.62302637697558 \tabularnewline
120 & 24 & 18.4665542885328 & 5.53344571146723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79040&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]896[/C][C]903.770888491585[/C][C]-7.77088849158486[/C][/ROW]
[ROW][C]14[/C][C]889[/C][C]892.83650764698[/C][C]-3.83650764697927[/C][/ROW]
[ROW][C]15[/C][C]878[/C][C]879.78255457044[/C][C]-1.78255457043906[/C][/ROW]
[ROW][C]16[/C][C]883[/C][C]883.677270637965[/C][C]-0.67727063796508[/C][/ROW]
[ROW][C]17[/C][C]901[/C][C]901.309957990233[/C][C]-0.309957990232760[/C][/ROW]
[ROW][C]18[/C][C]897[/C][C]897.00751071256[/C][C]-0.00751071256001978[/C][/ROW]
[ROW][C]19[/C][C]881[/C][C]879.980847886478[/C][C]1.01915211352241[/C][/ROW]
[ROW][C]20[/C][C]866[/C][C]868.959308324936[/C][C]-2.95930832493616[/C][/ROW]
[ROW][C]21[/C][C]867[/C][C]867.292335495294[/C][C]-0.292335495294196[/C][/ROW]
[ROW][C]22[/C][C]866[/C][C]866.018077851283[/C][C]-0.0180778512832376[/C][/ROW]
[ROW][C]23[/C][C]862[/C][C]865.638398416371[/C][C]-3.63839841637139[/C][/ROW]
[ROW][C]24[/C][C]871[/C][C]864.508303861816[/C][C]6.49169613818378[/C][/ROW]
[ROW][C]25[/C][C]865[/C][C]864.747970495067[/C][C]0.252029504932693[/C][/ROW]
[ROW][C]26[/C][C]856[/C][C]859.49110324043[/C][C]-3.49110324042977[/C][/ROW]
[ROW][C]27[/C][C]847[/C][C]847.675768997403[/C][C]-0.675768997402656[/C][/ROW]
[ROW][C]28[/C][C]859[/C][C]852.18301658722[/C][C]6.8169834127807[/C][/ROW]
[ROW][C]29[/C][C]870[/C][C]873.09086321796[/C][C]-3.09086321795951[/C][/ROW]
[ROW][C]30[/C][C]872[/C][C]867.702182693535[/C][C]4.29781730646539[/C][/ROW]
[ROW][C]31[/C][C]856[/C][C]853.929924601814[/C][C]2.07007539818596[/C][/ROW]
[ROW][C]32[/C][C]839[/C][C]841.943201446102[/C][C]-2.94320144610219[/C][/ROW]
[ROW][C]33[/C][C]829[/C][C]841.875940892999[/C][C]-12.8759408929988[/C][/ROW]
[ROW][C]34[/C][C]825[/C][C]834.360315607434[/C][C]-9.36031560743447[/C][/ROW]
[ROW][C]35[/C][C]822[/C][C]826.784407948278[/C][C]-4.78440794827816[/C][/ROW]
[ROW][C]36[/C][C]827[/C][C]829.129726468095[/C][C]-2.12972646809533[/C][/ROW]
[ROW][C]37[/C][C]822[/C][C]820.8222892973[/C][C]1.17771070270044[/C][/ROW]
[ROW][C]38[/C][C]812[/C][C]812.980619331017[/C][C]-0.98061933101701[/C][/ROW]
[ROW][C]39[/C][C]810[/C][C]802.98271971499[/C][C]7.01728028501054[/C][/ROW]
[ROW][C]40[/C][C]816[/C][C]813.744545521368[/C][C]2.25545447863203[/C][/ROW]
[ROW][C]41[/C][C]820[/C][C]825.489205821766[/C][C]-5.48920582176584[/C][/ROW]
[ROW][C]42[/C][C]823[/C][C]821.550235460297[/C][C]1.44976453970332[/C][/ROW]
[ROW][C]43[/C][C]810[/C][C]804.81289967523[/C][C]5.18710032477054[/C][/ROW]
[ROW][C]44[/C][C]793[/C][C]791.334395475885[/C][C]1.66560452411511[/C][/ROW]
[ROW][C]45[/C][C]777[/C][C]787.418860610278[/C][C]-10.4188606102782[/C][/ROW]
[ROW][C]46[/C][C]772[/C][C]781.961988489794[/C][C]-9.96198848979361[/C][/ROW]
[ROW][C]47[/C][C]765[/C][C]775.565519365578[/C][C]-10.5655193655775[/C][/ROW]
[ROW][C]48[/C][C]765[/C][C]774.860936287358[/C][C]-9.8609362873583[/C][/ROW]
[ROW][C]49[/C][C]753[/C][C]763.250970817308[/C][C]-10.2509708173083[/C][/ROW]
[ROW][C]50[/C][C]742[/C][C]747.229430873978[/C][C]-5.22943087397778[/C][/ROW]
[ROW][C]51[/C][C]736[/C][C]737.245218203866[/C][C]-1.24521820386576[/C][/ROW]
[ROW][C]52[/C][C]740[/C][C]738.077159387358[/C][C]1.92284061264218[/C][/ROW]
[ROW][C]53[/C][C]742[/C][C]741.84727992547[/C][C]0.152720074530293[/C][/ROW]
[ROW][C]54[/C][C]742[/C][C]741.138820216192[/C][C]0.861179783808097[/C][/ROW]
[ROW][C]55[/C][C]728[/C][C]724.742528087708[/C][C]3.25747191229209[/C][/ROW]
[ROW][C]56[/C][C]707[/C][C]707.43442221544[/C][C]-0.434422215440236[/C][/ROW]
[ROW][C]57[/C][C]699[/C][C]694.351514289071[/C][C]4.64848571092864[/C][/ROW]
[ROW][C]58[/C][C]696[/C][C]694.029509792166[/C][C]1.97049020783356[/C][/ROW]
[ROW][C]59[/C][C]689[/C][C]691.465648497205[/C][C]-2.46564849720528[/C][/ROW]
[ROW][C]60[/C][C]692[/C][C]693.16948672136[/C][C]-1.16948672135993[/C][/ROW]
[ROW][C]61[/C][C]673[/C][C]685.220962762477[/C][C]-12.2209627624771[/C][/ROW]
[ROW][C]62[/C][C]653[/C][C]670.655439264295[/C][C]-17.6554392642953[/C][/ROW]
[ROW][C]63[/C][C]642[/C][C]655.642040473916[/C][C]-13.6420404739156[/C][/ROW]
[ROW][C]64[/C][C]648[/C][C]649.334880788702[/C][C]-1.33488078870209[/C][/ROW]
[ROW][C]65[/C][C]654[/C][C]647.614826081217[/C][C]6.38517391878338[/C][/ROW]
[ROW][C]66[/C][C]653[/C][C]647.81878267693[/C][C]5.18121732306997[/C][/ROW]
[ROW][C]67[/C][C]630[/C][C]634.439669594048[/C][C]-4.43966959404827[/C][/ROW]
[ROW][C]68[/C][C]609[/C][C]611.689698128818[/C][C]-2.68969812881812[/C][/ROW]
[ROW][C]69[/C][C]598[/C][C]598.880552017984[/C][C]-0.880552017983973[/C][/ROW]
[ROW][C]70[/C][C]601[/C][C]592.076117776483[/C][C]8.92388222351747[/C][/ROW]
[ROW][C]71[/C][C]592[/C][C]588.680000442368[/C][C]3.31999955763217[/C][/ROW]
[ROW][C]72[/C][C]591[/C][C]590.918539714358[/C][C]0.0814602856419242[/C][/ROW]
[ROW][C]73[/C][C]568[/C][C]577.322600841805[/C][C]-9.3226008418053[/C][/ROW]
[ROW][C]74[/C][C]538[/C][C]560.646388107491[/C][C]-22.6463881074912[/C][/ROW]
[ROW][C]75[/C][C]523[/C][C]543.286387955832[/C][C]-20.2863879558323[/C][/ROW]
[ROW][C]76[/C][C]530[/C][C]535.807350992743[/C][C]-5.80735099274261[/C][/ROW]
[ROW][C]77[/C][C]529[/C][C]531.738635342179[/C][C]-2.73863534217855[/C][/ROW]
[ROW][C]78[/C][C]534[/C][C]523.34537266301[/C][C]10.6546273369898[/C][/ROW]
[ROW][C]79[/C][C]513[/C][C]507.611186916838[/C][C]5.38881308316201[/C][/ROW]
[ROW][C]80[/C][C]491[/C][C]490.855512628605[/C][C]0.144487371395201[/C][/ROW]
[ROW][C]81[/C][C]480[/C][C]479.163899090739[/C][C]0.83610090926146[/C][/ROW]
[ROW][C]82[/C][C]478[/C][C]475.328874264389[/C][C]2.67112573561121[/C][/ROW]
[ROW][C]83[/C][C]462[/C][C]464.709057863621[/C][C]-2.70905786362118[/C][/ROW]
[ROW][C]84[/C][C]461[/C][C]458.722747891583[/C][C]2.27725210841652[/C][/ROW]
[ROW][C]85[/C][C]437[/C][C]441.589932636353[/C][C]-4.5899326363529[/C][/ROW]
[ROW][C]86[/C][C]411[/C][C]420.786323599084[/C][C]-9.78632359908397[/C][/ROW]
[ROW][C]87[/C][C]400[/C][C]408.6521977364[/C][C]-8.65219773639961[/C][/ROW]
[ROW][C]88[/C][C]405[/C][C]409.14032888495[/C][C]-4.14032888494961[/C][/ROW]
[ROW][C]89[/C][C]395[/C][C]404.366251105912[/C][C]-9.36625110591217[/C][/ROW]
[ROW][C]90[/C][C]407[/C][C]396.222544225601[/C][C]10.7774557743990[/C][/ROW]
[ROW][C]91[/C][C]385[/C][C]380.187005195887[/C][C]4.81299480411258[/C][/ROW]
[ROW][C]92[/C][C]366[/C][C]362.649125684918[/C][C]3.35087431508248[/C][/ROW]
[ROW][C]93[/C][C]349[/C][C]352.563721873452[/C][C]-3.56372187345175[/C][/ROW]
[ROW][C]94[/C][C]343[/C][C]344.895839178019[/C][C]-1.89583917801906[/C][/ROW]
[ROW][C]95[/C][C]332[/C][C]329.556847173016[/C][C]2.44315282698352[/C][/ROW]
[ROW][C]96[/C][C]327[/C][C]325.512386146091[/C][C]1.48761385390941[/C][/ROW]
[ROW][C]97[/C][C]306[/C][C]307.07581436036[/C][C]-1.0758143603598[/C][/ROW]
[ROW][C]98[/C][C]276[/C][C]288.009108495393[/C][C]-12.0091084953934[/C][/ROW]
[ROW][C]99[/C][C]269[/C][C]273.570104211447[/C][C]-4.57010421144713[/C][/ROW]
[ROW][C]100[/C][C]268[/C][C]271.955898722831[/C][C]-3.95589872283085[/C][/ROW]
[ROW][C]101[/C][C]260[/C][C]261.930948891483[/C][C]-1.93094889148279[/C][/ROW]
[ROW][C]102[/C][C]274[/C][C]261.061240606169[/C][C]12.9387593938314[/C][/ROW]
[ROW][C]103[/C][C]247[/C][C]247.179743554591[/C][C]-0.179743554591198[/C][/ROW]
[ROW][C]104[/C][C]226[/C][C]229.589440102179[/C][C]-3.58944010217937[/C][/ROW]
[ROW][C]105[/C][C]212[/C][C]213.634612075621[/C][C]-1.63461207562054[/C][/ROW]
[ROW][C]106[/C][C]199[/C][C]204.857537420710[/C][C]-5.85753742071049[/C][/ROW]
[ROW][C]107[/C][C]188[/C][C]189.584014525368[/C][C]-1.58401452536751[/C][/ROW]
[ROW][C]108[/C][C]179[/C][C]179.806136301810[/C][C]-0.80613630181034[/C][/ROW]
[ROW][C]109[/C][C]155[/C][C]162.297327857733[/C][C]-7.29732785773254[/C][/ROW]
[ROW][C]110[/C][C]124[/C][C]139.9346030249[/C][C]-15.9346030249000[/C][/ROW]
[ROW][C]111[/C][C]117[/C][C]122.761255042656[/C][C]-5.76125504265616[/C][/ROW]
[ROW][C]112[/C][C]116[/C][C]112.228438846279[/C][C]3.77156115372080[/C][/ROW]
[ROW][C]113[/C][C]105[/C][C]102.732210176703[/C][C]2.26778982329726[/C][/ROW]
[ROW][C]114[/C][C]112[/C][C]97.8092187494058[/C][C]14.1907812505942[/C][/ROW]
[ROW][C]115[/C][C]86[/C][C]85.9549356576072[/C][C]0.0450643423927772[/C][/ROW]
[ROW][C]116[/C][C]64[/C][C]70.8606110124776[/C][C]-6.86061101247756[/C][/ROW]
[ROW][C]117[/C][C]53[/C][C]54.5112363119745[/C][C]-1.51123631197454[/C][/ROW]
[ROW][C]118[/C][C]42[/C][C]41.4597795297662[/C][C]0.540220470233834[/C][/ROW]
[ROW][C]119[/C][C]32[/C][C]29.3769736230244[/C][C]2.62302637697558[/C][/ROW]
[ROW][C]120[/C][C]24[/C][C]18.4665542885328[/C][C]5.53344571146723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79040&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79040&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
13896903.770888491585-7.77088849158486
14889892.83650764698-3.83650764697927
15878879.78255457044-1.78255457043906
16883883.677270637965-0.67727063796508
17901901.309957990233-0.309957990232760
18897897.00751071256-0.00751071256001978
19881879.9808478864781.01915211352241
20866868.959308324936-2.95930832493616
21867867.292335495294-0.292335495294196
22866866.018077851283-0.0180778512832376
23862865.638398416371-3.63839841637139
24871864.5083038618166.49169613818378
25865864.7479704950670.252029504932693
26856859.49110324043-3.49110324042977
27847847.675768997403-0.675768997402656
28859852.183016587226.8169834127807
29870873.09086321796-3.09086321795951
30872867.7021826935354.29781730646539
31856853.9299246018142.07007539818596
32839841.943201446102-2.94320144610219
33829841.875940892999-12.8759408929988
34825834.360315607434-9.36031560743447
35822826.784407948278-4.78440794827816
36827829.129726468095-2.12972646809533
37822820.82228929731.17771070270044
38812812.980619331017-0.98061933101701
39810802.982719714997.01728028501054
40816813.7445455213682.25545447863203
41820825.489205821766-5.48920582176584
42823821.5502354602971.44976453970332
43810804.812899675235.18710032477054
44793791.3343954758851.66560452411511
45777787.418860610278-10.4188606102782
46772781.961988489794-9.96198848979361
47765775.565519365578-10.5655193655775
48765774.860936287358-9.8609362873583
49753763.250970817308-10.2509708173083
50742747.229430873978-5.22943087397778
51736737.245218203866-1.24521820386576
52740738.0771593873581.92284061264218
53742741.847279925470.152720074530293
54742741.1388202161920.861179783808097
55728724.7425280877083.25747191229209
56707707.43442221544-0.434422215440236
57699694.3515142890714.64848571092864
58696694.0295097921661.97049020783356
59689691.465648497205-2.46564849720528
60692693.16948672136-1.16948672135993
61673685.220962762477-12.2209627624771
62653670.655439264295-17.6554392642953
63642655.642040473916-13.6420404739156
64648649.334880788702-1.33488078870209
65654647.6148260812176.38517391878338
66653647.818782676935.18121732306997
67630634.439669594048-4.43966959404827
68609611.689698128818-2.68969812881812
69598598.880552017984-0.880552017983973
70601592.0761177764838.92388222351747
71592588.6800004423683.31999955763217
72591590.9185397143580.0814602856419242
73568577.322600841805-9.3226008418053
74538560.646388107491-22.6463881074912
75523543.286387955832-20.2863879558323
76530535.807350992743-5.80735099274261
77529531.738635342179-2.73863534217855
78534523.3453726630110.6546273369898
79513507.6111869168385.38881308316201
80491490.8555126286050.144487371395201
81480479.1638990907390.83610090926146
82478475.3288742643892.67112573561121
83462464.709057863621-2.70905786362118
84461458.7227478915832.27725210841652
85437441.589932636353-4.5899326363529
86411420.786323599084-9.78632359908397
87400408.6521977364-8.65219773639961
88405409.14032888495-4.14032888494961
89395404.366251105912-9.36625110591217
90407396.22254422560110.7774557743990
91385380.1870051958874.81299480411258
92366362.6491256849183.35087431508248
93349352.563721873452-3.56372187345175
94343344.895839178019-1.89583917801906
95332329.5568471730162.44315282698352
96327325.5123861460911.48761385390941
97306307.07581436036-1.0758143603598
98276288.009108495393-12.0091084953934
99269273.570104211447-4.57010421144713
100268271.955898722831-3.95589872283085
101260261.930948891483-1.93094889148279
102274261.06124060616912.9387593938314
103247247.179743554591-0.179743554591198
104226229.589440102179-3.58944010217937
105212213.634612075621-1.63461207562054
106199204.857537420710-5.85753742071049
107188189.584014525368-1.58401452536751
108179179.806136301810-0.80613630181034
109155162.297327857733-7.29732785773254
110124139.9346030249-15.9346030249000
111117122.761255042656-5.76125504265616
112116112.2284388462793.77156115372080
113105102.7322101767032.26778982329726
11411297.809218749405814.1907812505942
1158685.95493565760720.0450643423927772
1166470.8606110124776-6.86061101247756
1175354.5112363119745-1.51123631197454
1184241.45977952976620.540220470233834
1193229.37697362302442.62302637697558
1202418.46655428853285.53344571146723







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1218.25680434010511-4.3887295257542720.9023382059645
122-3.16451383997611-17.198054711519410.8690270315672
123-14.7319763741312-30.86820555401821.40425280575568
124-28.4686487311091-47.3327159661397-9.60458149607852
125-41.3210877826505-62.3723405562992-20.2698350090018
126-61.510553324487-87.0604936165888-35.9606130323852
127-66.7573082191459-92.0681891928197-41.4464272454722
128-72.5503927618333-98.293345006633-46.8074405170336
129-86.623910827988-115.29354711593-57.9542745400462
130-101.048454177377-132.755180217567-69.3417281371869
131-118.243073530658-153.736302072643-82.749844988674
132-144.966165330087-184.780290439648-105.152040220525

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 8.25680434010511 & -4.38872952575427 & 20.9023382059645 \tabularnewline
122 & -3.16451383997611 & -17.1980547115194 & 10.8690270315672 \tabularnewline
123 & -14.7319763741312 & -30.8682055540182 & 1.40425280575568 \tabularnewline
124 & -28.4686487311091 & -47.3327159661397 & -9.60458149607852 \tabularnewline
125 & -41.3210877826505 & -62.3723405562992 & -20.2698350090018 \tabularnewline
126 & -61.510553324487 & -87.0604936165888 & -35.9606130323852 \tabularnewline
127 & -66.7573082191459 & -92.0681891928197 & -41.4464272454722 \tabularnewline
128 & -72.5503927618333 & -98.293345006633 & -46.8074405170336 \tabularnewline
129 & -86.623910827988 & -115.29354711593 & -57.9542745400462 \tabularnewline
130 & -101.048454177377 & -132.755180217567 & -69.3417281371869 \tabularnewline
131 & -118.243073530658 & -153.736302072643 & -82.749844988674 \tabularnewline
132 & -144.966165330087 & -184.780290439648 & -105.152040220525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79040&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]8.25680434010511[/C][C]-4.38872952575427[/C][C]20.9023382059645[/C][/ROW]
[ROW][C]122[/C][C]-3.16451383997611[/C][C]-17.1980547115194[/C][C]10.8690270315672[/C][/ROW]
[ROW][C]123[/C][C]-14.7319763741312[/C][C]-30.8682055540182[/C][C]1.40425280575568[/C][/ROW]
[ROW][C]124[/C][C]-28.4686487311091[/C][C]-47.3327159661397[/C][C]-9.60458149607852[/C][/ROW]
[ROW][C]125[/C][C]-41.3210877826505[/C][C]-62.3723405562992[/C][C]-20.2698350090018[/C][/ROW]
[ROW][C]126[/C][C]-61.510553324487[/C][C]-87.0604936165888[/C][C]-35.9606130323852[/C][/ROW]
[ROW][C]127[/C][C]-66.7573082191459[/C][C]-92.0681891928197[/C][C]-41.4464272454722[/C][/ROW]
[ROW][C]128[/C][C]-72.5503927618333[/C][C]-98.293345006633[/C][C]-46.8074405170336[/C][/ROW]
[ROW][C]129[/C][C]-86.623910827988[/C][C]-115.29354711593[/C][C]-57.9542745400462[/C][/ROW]
[ROW][C]130[/C][C]-101.048454177377[/C][C]-132.755180217567[/C][C]-69.3417281371869[/C][/ROW]
[ROW][C]131[/C][C]-118.243073530658[/C][C]-153.736302072643[/C][C]-82.749844988674[/C][/ROW]
[ROW][C]132[/C][C]-144.966165330087[/C][C]-184.780290439648[/C][C]-105.152040220525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79040&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79040&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
1218.25680434010511-4.3887295257542720.9023382059645
122-3.16451383997611-17.198054711519410.8690270315672
123-14.7319763741312-30.86820555401821.40425280575568
124-28.4686487311091-47.3327159661397-9.60458149607852
125-41.3210877826505-62.3723405562992-20.2698350090018
126-61.510553324487-87.0604936165888-35.9606130323852
127-66.7573082191459-92.0681891928197-41.4464272454722
128-72.5503927618333-98.293345006633-46.8074405170336
129-86.623910827988-115.29354711593-57.9542745400462
130-101.048454177377-132.755180217567-69.3417281371869
131-118.243073530658-153.736302072643-82.749844988674
132-144.966165330087-184.780290439648-105.152040220525



Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')