Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 04 Aug 2014 19:12:10 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Aug/04/t1407175974i97332zxsvhkv97.htm/, Retrieved Thu, 16 May 2024 01:20:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235397, Retrieved Thu, 16 May 2024 01:20:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsInes Van Dessel
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2013-11-21 12:15:19] [53fdf1af79096e48ffa0efd17209e500]
- RMPD    [Exponential Smoothing] [Tijdreeks 1 - Sta...] [2014-08-04 18:12:10] [188bf81caccb86647293be436f272d1b] [Current]
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Dataseries X:
19064
18993
18921
18772
20246
20168
19064
18330
18401
18401
18480
18622
18843
18843
18701
18330
20246
20538
20097
19064
19506
18843
19142
19285
19434
19064
19142
18622
20246
20759
20318
19506
20389
19434
20318
20246
20467
19655
20538
20467
21792
21493
20318
19726
20538
19434
20246
20389
20688
20026
20389
20610
21422
20759
19876
18921
19805
17375
18551
19213
19876
18921
18921
18921
19434
18701
17739
16934
17518
15238
16635
17447
17596
16784
16855
16635
17375
16855
15830
15089
16342
13621
15388
16193
16193
15238
14355
14284
15089
14355
12959
11997
13030
10601
12809
13984
14355
13543
12517
13251
13543
13322
11113
10088
10821
8613
10893
11705
12367
11263
10230
10821
11113
10529
8321
7359
8242
5813
8463
10088




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235397&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235397&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235397&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.659004759562522
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.659004759562522 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235397&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]0.659004759562522[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235397&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235397&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
alpha0.659004759562522
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31892118922-1
41877218850.3409952404-78.34099524044
52024618727.71390650811518.28609349188
62016819657.2716684969510.728331503142
71906419922.8440698009-858.844069800856
81833019285.86174008-955.861740080043
91840118584.9443038836-183.944303883582
101840118392.72413212998.27586787011387
111848018327.1779684458152.822031554198
121862218356.888414606265.111585393966
131884318460.5982111958382.401788804178
141884318641.602810083201.397189917003
151870118703.3245168008-2.32451680082158
161833018630.7926491654-300.7926491654
172024618361.5688617241884.43113827602
182053819532.41795091571005.5820490843
192009720124.1013073929-27.1013073928843
201906420035.2414168306-971.241416830606
211950619324.188700455181.81129954501
221884319373.0032121974-530.0032121974
231914218952.7285727759189.27142722411
241928519006.4593441658278.540655834229
251943419119.0189620922314.981037907804
261906419255.5929652454-191.592965245381
271914219058.3322892583.6677107500218
281862219042.4697088559-420.469708855941
292024618694.3781694681551.62183053199
302075919645.90434082971113.0956591703
312031820308.43967807139.56032192868588
321950620243.7399757253-737.739975725268
332038919686.5658204028702.434179597225
341943420078.4732880367-644.473288036741
352031819582.7623238096735.23767619038
362024619996.2874518288249.712548171232
372046720089.8492095961377.150790403903
381965520267.393375545-612.393375545038
392053819792.8232263363745.176773663701
402046720212.8982668961254.101733103878
412179220309.35251842471482.64748157534
422149321215.4242655362277.575734463804
432031821327.3479956869-1009.34799568691
441972620591.1828624743-865.182862474343
452053819950.0232382118587.976761788173
461943420266.5027227424-832.502722742393
472024619646.8794661064599.120533893602
482038919970.7027494939418.297250506079
492068820175.3626284893512.637371510657
502002620442.1930962445-416.193096244486
512038920096.9198649223292.080135077693
522061020218.4020641122391.597935887828
532142220405.46696769711016.53303230289
542075921004.3670742372-245.367074237238
551987620771.669004475-895.669004474967
561892120110.4188675333-1189.41886753334
571980519255.5861727154549.413827284596
581737519546.6524998654-2171.65249986541
591855118044.5231663383506.476833661742
601921318307.2938103295905.706189670498
611987618833.15850008761042.8414999124
621892119449.3960119992-528.39601199919
631892119030.1805251579-109.18052515787
641892118887.230039427333.769960572703
651943418838.4846041749595.515395825052
661870119159.9320844164-458.932084416418
671773918786.4936564701-1047.49365647005
681693418025.1903512447-1091.19035124474
691751817235.0907161858282.909283814246
701523817350.5292807438-2112.52928074377
711663515887.3624300184747.637569981569
721744716309.0591470641137.94085293596
731759616987.9675852495608.032414750523
741678417317.6638405384-533.663840538364
751685516894.9768296172-39.9768296171678
761663516797.6319086272-162.631908627234
771737516619.4567067851755.543293214851
781685517046.3633330693-191.363333069279
791583016849.2539857709-1019.25398577088
801508916106.5607579448-1017.5607579448
811634215364.9833753151977.016624684871
821362115937.8419811542-2316.84198115417
831538814340.03208841931047.96791158069
841619314959.64793001981233.35206998022
851619315701.432814353491.567185646967
861523815954.3779293391-716.377929339138
871435515411.2814642591-1056.2814642591
881428414644.1869518747-360.186951874683
891508914335.822036257753.17796374305
901435514761.1698991612-406.169899161228
911295914422.5020024229-1463.50200242295
921199713387.0472171969-1390.04721719694
931303012399.9994850475630.00051495248
941060112744.172822928-2143.17282292805
951280911260.81173205341548.18826794658
961398412210.07516932911773.92483067093
971435513308.10007584741046.89992415264
981354313927.0121086496-384.012108649593
991251713602.9463013199-1085.94630131987
1001325112816.3025201208434.697479879242
1011354313031.770228331511.229771668986
1021332213297.673081090924.3269189090624
1031111313242.7046364375-2129.7046364375
1041008811768.2191445628-1680.21914456282
1051082110589.9467311879231.053268812149
106861310671.2119350475-2058.21193504754
107108939243.840473662821649.15952633718
1081170510259.64445079691445.3555492031
1091236711141.14063698181225.85936301815
1101126311877.9877917651-614.98779176509
1111023011401.7079099191-1171.70790991905
1121082110558.5468204653262.453179534659
1131111310660.504714941452.495285059002
1141052910887.7012614745-358.701261474482
115832110580.3154229017-2259.31542290172
11673599020.41580585647-1661.41580585647
11782427854.53488218465387.465117815347
11858138038.87623898942-2225.87623898942
11984636501.013203298271961.98679670173
120100887722.971840523542365.02815947646

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 18921 & 18922 & -1 \tabularnewline
4 & 18772 & 18850.3409952404 & -78.34099524044 \tabularnewline
5 & 20246 & 18727.7139065081 & 1518.28609349188 \tabularnewline
6 & 20168 & 19657.2716684969 & 510.728331503142 \tabularnewline
7 & 19064 & 19922.8440698009 & -858.844069800856 \tabularnewline
8 & 18330 & 19285.86174008 & -955.861740080043 \tabularnewline
9 & 18401 & 18584.9443038836 & -183.944303883582 \tabularnewline
10 & 18401 & 18392.7241321299 & 8.27586787011387 \tabularnewline
11 & 18480 & 18327.1779684458 & 152.822031554198 \tabularnewline
12 & 18622 & 18356.888414606 & 265.111585393966 \tabularnewline
13 & 18843 & 18460.5982111958 & 382.401788804178 \tabularnewline
14 & 18843 & 18641.602810083 & 201.397189917003 \tabularnewline
15 & 18701 & 18703.3245168008 & -2.32451680082158 \tabularnewline
16 & 18330 & 18630.7926491654 & -300.7926491654 \tabularnewline
17 & 20246 & 18361.568861724 & 1884.43113827602 \tabularnewline
18 & 20538 & 19532.4179509157 & 1005.5820490843 \tabularnewline
19 & 20097 & 20124.1013073929 & -27.1013073928843 \tabularnewline
20 & 19064 & 20035.2414168306 & -971.241416830606 \tabularnewline
21 & 19506 & 19324.188700455 & 181.81129954501 \tabularnewline
22 & 18843 & 19373.0032121974 & -530.0032121974 \tabularnewline
23 & 19142 & 18952.7285727759 & 189.27142722411 \tabularnewline
24 & 19285 & 19006.4593441658 & 278.540655834229 \tabularnewline
25 & 19434 & 19119.0189620922 & 314.981037907804 \tabularnewline
26 & 19064 & 19255.5929652454 & -191.592965245381 \tabularnewline
27 & 19142 & 19058.33228925 & 83.6677107500218 \tabularnewline
28 & 18622 & 19042.4697088559 & -420.469708855941 \tabularnewline
29 & 20246 & 18694.378169468 & 1551.62183053199 \tabularnewline
30 & 20759 & 19645.9043408297 & 1113.0956591703 \tabularnewline
31 & 20318 & 20308.4396780713 & 9.56032192868588 \tabularnewline
32 & 19506 & 20243.7399757253 & -737.739975725268 \tabularnewline
33 & 20389 & 19686.5658204028 & 702.434179597225 \tabularnewline
34 & 19434 & 20078.4732880367 & -644.473288036741 \tabularnewline
35 & 20318 & 19582.7623238096 & 735.23767619038 \tabularnewline
36 & 20246 & 19996.2874518288 & 249.712548171232 \tabularnewline
37 & 20467 & 20089.8492095961 & 377.150790403903 \tabularnewline
38 & 19655 & 20267.393375545 & -612.393375545038 \tabularnewline
39 & 20538 & 19792.8232263363 & 745.176773663701 \tabularnewline
40 & 20467 & 20212.8982668961 & 254.101733103878 \tabularnewline
41 & 21792 & 20309.3525184247 & 1482.64748157534 \tabularnewline
42 & 21493 & 21215.4242655362 & 277.575734463804 \tabularnewline
43 & 20318 & 21327.3479956869 & -1009.34799568691 \tabularnewline
44 & 19726 & 20591.1828624743 & -865.182862474343 \tabularnewline
45 & 20538 & 19950.0232382118 & 587.976761788173 \tabularnewline
46 & 19434 & 20266.5027227424 & -832.502722742393 \tabularnewline
47 & 20246 & 19646.8794661064 & 599.120533893602 \tabularnewline
48 & 20389 & 19970.7027494939 & 418.297250506079 \tabularnewline
49 & 20688 & 20175.3626284893 & 512.637371510657 \tabularnewline
50 & 20026 & 20442.1930962445 & -416.193096244486 \tabularnewline
51 & 20389 & 20096.9198649223 & 292.080135077693 \tabularnewline
52 & 20610 & 20218.4020641122 & 391.597935887828 \tabularnewline
53 & 21422 & 20405.4669676971 & 1016.53303230289 \tabularnewline
54 & 20759 & 21004.3670742372 & -245.367074237238 \tabularnewline
55 & 19876 & 20771.669004475 & -895.669004474967 \tabularnewline
56 & 18921 & 20110.4188675333 & -1189.41886753334 \tabularnewline
57 & 19805 & 19255.5861727154 & 549.413827284596 \tabularnewline
58 & 17375 & 19546.6524998654 & -2171.65249986541 \tabularnewline
59 & 18551 & 18044.5231663383 & 506.476833661742 \tabularnewline
60 & 19213 & 18307.2938103295 & 905.706189670498 \tabularnewline
61 & 19876 & 18833.1585000876 & 1042.8414999124 \tabularnewline
62 & 18921 & 19449.3960119992 & -528.39601199919 \tabularnewline
63 & 18921 & 19030.1805251579 & -109.18052515787 \tabularnewline
64 & 18921 & 18887.2300394273 & 33.769960572703 \tabularnewline
65 & 19434 & 18838.4846041749 & 595.515395825052 \tabularnewline
66 & 18701 & 19159.9320844164 & -458.932084416418 \tabularnewline
67 & 17739 & 18786.4936564701 & -1047.49365647005 \tabularnewline
68 & 16934 & 18025.1903512447 & -1091.19035124474 \tabularnewline
69 & 17518 & 17235.0907161858 & 282.909283814246 \tabularnewline
70 & 15238 & 17350.5292807438 & -2112.52928074377 \tabularnewline
71 & 16635 & 15887.3624300184 & 747.637569981569 \tabularnewline
72 & 17447 & 16309.059147064 & 1137.94085293596 \tabularnewline
73 & 17596 & 16987.9675852495 & 608.032414750523 \tabularnewline
74 & 16784 & 17317.6638405384 & -533.663840538364 \tabularnewline
75 & 16855 & 16894.9768296172 & -39.9768296171678 \tabularnewline
76 & 16635 & 16797.6319086272 & -162.631908627234 \tabularnewline
77 & 17375 & 16619.4567067851 & 755.543293214851 \tabularnewline
78 & 16855 & 17046.3633330693 & -191.363333069279 \tabularnewline
79 & 15830 & 16849.2539857709 & -1019.25398577088 \tabularnewline
80 & 15089 & 16106.5607579448 & -1017.5607579448 \tabularnewline
81 & 16342 & 15364.9833753151 & 977.016624684871 \tabularnewline
82 & 13621 & 15937.8419811542 & -2316.84198115417 \tabularnewline
83 & 15388 & 14340.0320884193 & 1047.96791158069 \tabularnewline
84 & 16193 & 14959.6479300198 & 1233.35206998022 \tabularnewline
85 & 16193 & 15701.432814353 & 491.567185646967 \tabularnewline
86 & 15238 & 15954.3779293391 & -716.377929339138 \tabularnewline
87 & 14355 & 15411.2814642591 & -1056.2814642591 \tabularnewline
88 & 14284 & 14644.1869518747 & -360.186951874683 \tabularnewline
89 & 15089 & 14335.822036257 & 753.17796374305 \tabularnewline
90 & 14355 & 14761.1698991612 & -406.169899161228 \tabularnewline
91 & 12959 & 14422.5020024229 & -1463.50200242295 \tabularnewline
92 & 11997 & 13387.0472171969 & -1390.04721719694 \tabularnewline
93 & 13030 & 12399.9994850475 & 630.00051495248 \tabularnewline
94 & 10601 & 12744.172822928 & -2143.17282292805 \tabularnewline
95 & 12809 & 11260.8117320534 & 1548.18826794658 \tabularnewline
96 & 13984 & 12210.0751693291 & 1773.92483067093 \tabularnewline
97 & 14355 & 13308.1000758474 & 1046.89992415264 \tabularnewline
98 & 13543 & 13927.0121086496 & -384.012108649593 \tabularnewline
99 & 12517 & 13602.9463013199 & -1085.94630131987 \tabularnewline
100 & 13251 & 12816.3025201208 & 434.697479879242 \tabularnewline
101 & 13543 & 13031.770228331 & 511.229771668986 \tabularnewline
102 & 13322 & 13297.6730810909 & 24.3269189090624 \tabularnewline
103 & 11113 & 13242.7046364375 & -2129.7046364375 \tabularnewline
104 & 10088 & 11768.2191445628 & -1680.21914456282 \tabularnewline
105 & 10821 & 10589.9467311879 & 231.053268812149 \tabularnewline
106 & 8613 & 10671.2119350475 & -2058.21193504754 \tabularnewline
107 & 10893 & 9243.84047366282 & 1649.15952633718 \tabularnewline
108 & 11705 & 10259.6444507969 & 1445.3555492031 \tabularnewline
109 & 12367 & 11141.1406369818 & 1225.85936301815 \tabularnewline
110 & 11263 & 11877.9877917651 & -614.98779176509 \tabularnewline
111 & 10230 & 11401.7079099191 & -1171.70790991905 \tabularnewline
112 & 10821 & 10558.5468204653 & 262.453179534659 \tabularnewline
113 & 11113 & 10660.504714941 & 452.495285059002 \tabularnewline
114 & 10529 & 10887.7012614745 & -358.701261474482 \tabularnewline
115 & 8321 & 10580.3154229017 & -2259.31542290172 \tabularnewline
116 & 7359 & 9020.41580585647 & -1661.41580585647 \tabularnewline
117 & 8242 & 7854.53488218465 & 387.465117815347 \tabularnewline
118 & 5813 & 8038.87623898942 & -2225.87623898942 \tabularnewline
119 & 8463 & 6501.01320329827 & 1961.98679670173 \tabularnewline
120 & 10088 & 7722.97184052354 & 2365.02815947646 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235397&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]3[/C][C]18921[/C][C]18922[/C][C]-1[/C][/ROW]
[ROW][C]4[/C][C]18772[/C][C]18850.3409952404[/C][C]-78.34099524044[/C][/ROW]
[ROW][C]5[/C][C]20246[/C][C]18727.7139065081[/C][C]1518.28609349188[/C][/ROW]
[ROW][C]6[/C][C]20168[/C][C]19657.2716684969[/C][C]510.728331503142[/C][/ROW]
[ROW][C]7[/C][C]19064[/C][C]19922.8440698009[/C][C]-858.844069800856[/C][/ROW]
[ROW][C]8[/C][C]18330[/C][C]19285.86174008[/C][C]-955.861740080043[/C][/ROW]
[ROW][C]9[/C][C]18401[/C][C]18584.9443038836[/C][C]-183.944303883582[/C][/ROW]
[ROW][C]10[/C][C]18401[/C][C]18392.7241321299[/C][C]8.27586787011387[/C][/ROW]
[ROW][C]11[/C][C]18480[/C][C]18327.1779684458[/C][C]152.822031554198[/C][/ROW]
[ROW][C]12[/C][C]18622[/C][C]18356.888414606[/C][C]265.111585393966[/C][/ROW]
[ROW][C]13[/C][C]18843[/C][C]18460.5982111958[/C][C]382.401788804178[/C][/ROW]
[ROW][C]14[/C][C]18843[/C][C]18641.602810083[/C][C]201.397189917003[/C][/ROW]
[ROW][C]15[/C][C]18701[/C][C]18703.3245168008[/C][C]-2.32451680082158[/C][/ROW]
[ROW][C]16[/C][C]18330[/C][C]18630.7926491654[/C][C]-300.7926491654[/C][/ROW]
[ROW][C]17[/C][C]20246[/C][C]18361.568861724[/C][C]1884.43113827602[/C][/ROW]
[ROW][C]18[/C][C]20538[/C][C]19532.4179509157[/C][C]1005.5820490843[/C][/ROW]
[ROW][C]19[/C][C]20097[/C][C]20124.1013073929[/C][C]-27.1013073928843[/C][/ROW]
[ROW][C]20[/C][C]19064[/C][C]20035.2414168306[/C][C]-971.241416830606[/C][/ROW]
[ROW][C]21[/C][C]19506[/C][C]19324.188700455[/C][C]181.81129954501[/C][/ROW]
[ROW][C]22[/C][C]18843[/C][C]19373.0032121974[/C][C]-530.0032121974[/C][/ROW]
[ROW][C]23[/C][C]19142[/C][C]18952.7285727759[/C][C]189.27142722411[/C][/ROW]
[ROW][C]24[/C][C]19285[/C][C]19006.4593441658[/C][C]278.540655834229[/C][/ROW]
[ROW][C]25[/C][C]19434[/C][C]19119.0189620922[/C][C]314.981037907804[/C][/ROW]
[ROW][C]26[/C][C]19064[/C][C]19255.5929652454[/C][C]-191.592965245381[/C][/ROW]
[ROW][C]27[/C][C]19142[/C][C]19058.33228925[/C][C]83.6677107500218[/C][/ROW]
[ROW][C]28[/C][C]18622[/C][C]19042.4697088559[/C][C]-420.469708855941[/C][/ROW]
[ROW][C]29[/C][C]20246[/C][C]18694.378169468[/C][C]1551.62183053199[/C][/ROW]
[ROW][C]30[/C][C]20759[/C][C]19645.9043408297[/C][C]1113.0956591703[/C][/ROW]
[ROW][C]31[/C][C]20318[/C][C]20308.4396780713[/C][C]9.56032192868588[/C][/ROW]
[ROW][C]32[/C][C]19506[/C][C]20243.7399757253[/C][C]-737.739975725268[/C][/ROW]
[ROW][C]33[/C][C]20389[/C][C]19686.5658204028[/C][C]702.434179597225[/C][/ROW]
[ROW][C]34[/C][C]19434[/C][C]20078.4732880367[/C][C]-644.473288036741[/C][/ROW]
[ROW][C]35[/C][C]20318[/C][C]19582.7623238096[/C][C]735.23767619038[/C][/ROW]
[ROW][C]36[/C][C]20246[/C][C]19996.2874518288[/C][C]249.712548171232[/C][/ROW]
[ROW][C]37[/C][C]20467[/C][C]20089.8492095961[/C][C]377.150790403903[/C][/ROW]
[ROW][C]38[/C][C]19655[/C][C]20267.393375545[/C][C]-612.393375545038[/C][/ROW]
[ROW][C]39[/C][C]20538[/C][C]19792.8232263363[/C][C]745.176773663701[/C][/ROW]
[ROW][C]40[/C][C]20467[/C][C]20212.8982668961[/C][C]254.101733103878[/C][/ROW]
[ROW][C]41[/C][C]21792[/C][C]20309.3525184247[/C][C]1482.64748157534[/C][/ROW]
[ROW][C]42[/C][C]21493[/C][C]21215.4242655362[/C][C]277.575734463804[/C][/ROW]
[ROW][C]43[/C][C]20318[/C][C]21327.3479956869[/C][C]-1009.34799568691[/C][/ROW]
[ROW][C]44[/C][C]19726[/C][C]20591.1828624743[/C][C]-865.182862474343[/C][/ROW]
[ROW][C]45[/C][C]20538[/C][C]19950.0232382118[/C][C]587.976761788173[/C][/ROW]
[ROW][C]46[/C][C]19434[/C][C]20266.5027227424[/C][C]-832.502722742393[/C][/ROW]
[ROW][C]47[/C][C]20246[/C][C]19646.8794661064[/C][C]599.120533893602[/C][/ROW]
[ROW][C]48[/C][C]20389[/C][C]19970.7027494939[/C][C]418.297250506079[/C][/ROW]
[ROW][C]49[/C][C]20688[/C][C]20175.3626284893[/C][C]512.637371510657[/C][/ROW]
[ROW][C]50[/C][C]20026[/C][C]20442.1930962445[/C][C]-416.193096244486[/C][/ROW]
[ROW][C]51[/C][C]20389[/C][C]20096.9198649223[/C][C]292.080135077693[/C][/ROW]
[ROW][C]52[/C][C]20610[/C][C]20218.4020641122[/C][C]391.597935887828[/C][/ROW]
[ROW][C]53[/C][C]21422[/C][C]20405.4669676971[/C][C]1016.53303230289[/C][/ROW]
[ROW][C]54[/C][C]20759[/C][C]21004.3670742372[/C][C]-245.367074237238[/C][/ROW]
[ROW][C]55[/C][C]19876[/C][C]20771.669004475[/C][C]-895.669004474967[/C][/ROW]
[ROW][C]56[/C][C]18921[/C][C]20110.4188675333[/C][C]-1189.41886753334[/C][/ROW]
[ROW][C]57[/C][C]19805[/C][C]19255.5861727154[/C][C]549.413827284596[/C][/ROW]
[ROW][C]58[/C][C]17375[/C][C]19546.6524998654[/C][C]-2171.65249986541[/C][/ROW]
[ROW][C]59[/C][C]18551[/C][C]18044.5231663383[/C][C]506.476833661742[/C][/ROW]
[ROW][C]60[/C][C]19213[/C][C]18307.2938103295[/C][C]905.706189670498[/C][/ROW]
[ROW][C]61[/C][C]19876[/C][C]18833.1585000876[/C][C]1042.8414999124[/C][/ROW]
[ROW][C]62[/C][C]18921[/C][C]19449.3960119992[/C][C]-528.39601199919[/C][/ROW]
[ROW][C]63[/C][C]18921[/C][C]19030.1805251579[/C][C]-109.18052515787[/C][/ROW]
[ROW][C]64[/C][C]18921[/C][C]18887.2300394273[/C][C]33.769960572703[/C][/ROW]
[ROW][C]65[/C][C]19434[/C][C]18838.4846041749[/C][C]595.515395825052[/C][/ROW]
[ROW][C]66[/C][C]18701[/C][C]19159.9320844164[/C][C]-458.932084416418[/C][/ROW]
[ROW][C]67[/C][C]17739[/C][C]18786.4936564701[/C][C]-1047.49365647005[/C][/ROW]
[ROW][C]68[/C][C]16934[/C][C]18025.1903512447[/C][C]-1091.19035124474[/C][/ROW]
[ROW][C]69[/C][C]17518[/C][C]17235.0907161858[/C][C]282.909283814246[/C][/ROW]
[ROW][C]70[/C][C]15238[/C][C]17350.5292807438[/C][C]-2112.52928074377[/C][/ROW]
[ROW][C]71[/C][C]16635[/C][C]15887.3624300184[/C][C]747.637569981569[/C][/ROW]
[ROW][C]72[/C][C]17447[/C][C]16309.059147064[/C][C]1137.94085293596[/C][/ROW]
[ROW][C]73[/C][C]17596[/C][C]16987.9675852495[/C][C]608.032414750523[/C][/ROW]
[ROW][C]74[/C][C]16784[/C][C]17317.6638405384[/C][C]-533.663840538364[/C][/ROW]
[ROW][C]75[/C][C]16855[/C][C]16894.9768296172[/C][C]-39.9768296171678[/C][/ROW]
[ROW][C]76[/C][C]16635[/C][C]16797.6319086272[/C][C]-162.631908627234[/C][/ROW]
[ROW][C]77[/C][C]17375[/C][C]16619.4567067851[/C][C]755.543293214851[/C][/ROW]
[ROW][C]78[/C][C]16855[/C][C]17046.3633330693[/C][C]-191.363333069279[/C][/ROW]
[ROW][C]79[/C][C]15830[/C][C]16849.2539857709[/C][C]-1019.25398577088[/C][/ROW]
[ROW][C]80[/C][C]15089[/C][C]16106.5607579448[/C][C]-1017.5607579448[/C][/ROW]
[ROW][C]81[/C][C]16342[/C][C]15364.9833753151[/C][C]977.016624684871[/C][/ROW]
[ROW][C]82[/C][C]13621[/C][C]15937.8419811542[/C][C]-2316.84198115417[/C][/ROW]
[ROW][C]83[/C][C]15388[/C][C]14340.0320884193[/C][C]1047.96791158069[/C][/ROW]
[ROW][C]84[/C][C]16193[/C][C]14959.6479300198[/C][C]1233.35206998022[/C][/ROW]
[ROW][C]85[/C][C]16193[/C][C]15701.432814353[/C][C]491.567185646967[/C][/ROW]
[ROW][C]86[/C][C]15238[/C][C]15954.3779293391[/C][C]-716.377929339138[/C][/ROW]
[ROW][C]87[/C][C]14355[/C][C]15411.2814642591[/C][C]-1056.2814642591[/C][/ROW]
[ROW][C]88[/C][C]14284[/C][C]14644.1869518747[/C][C]-360.186951874683[/C][/ROW]
[ROW][C]89[/C][C]15089[/C][C]14335.822036257[/C][C]753.17796374305[/C][/ROW]
[ROW][C]90[/C][C]14355[/C][C]14761.1698991612[/C][C]-406.169899161228[/C][/ROW]
[ROW][C]91[/C][C]12959[/C][C]14422.5020024229[/C][C]-1463.50200242295[/C][/ROW]
[ROW][C]92[/C][C]11997[/C][C]13387.0472171969[/C][C]-1390.04721719694[/C][/ROW]
[ROW][C]93[/C][C]13030[/C][C]12399.9994850475[/C][C]630.00051495248[/C][/ROW]
[ROW][C]94[/C][C]10601[/C][C]12744.172822928[/C][C]-2143.17282292805[/C][/ROW]
[ROW][C]95[/C][C]12809[/C][C]11260.8117320534[/C][C]1548.18826794658[/C][/ROW]
[ROW][C]96[/C][C]13984[/C][C]12210.0751693291[/C][C]1773.92483067093[/C][/ROW]
[ROW][C]97[/C][C]14355[/C][C]13308.1000758474[/C][C]1046.89992415264[/C][/ROW]
[ROW][C]98[/C][C]13543[/C][C]13927.0121086496[/C][C]-384.012108649593[/C][/ROW]
[ROW][C]99[/C][C]12517[/C][C]13602.9463013199[/C][C]-1085.94630131987[/C][/ROW]
[ROW][C]100[/C][C]13251[/C][C]12816.3025201208[/C][C]434.697479879242[/C][/ROW]
[ROW][C]101[/C][C]13543[/C][C]13031.770228331[/C][C]511.229771668986[/C][/ROW]
[ROW][C]102[/C][C]13322[/C][C]13297.6730810909[/C][C]24.3269189090624[/C][/ROW]
[ROW][C]103[/C][C]11113[/C][C]13242.7046364375[/C][C]-2129.7046364375[/C][/ROW]
[ROW][C]104[/C][C]10088[/C][C]11768.2191445628[/C][C]-1680.21914456282[/C][/ROW]
[ROW][C]105[/C][C]10821[/C][C]10589.9467311879[/C][C]231.053268812149[/C][/ROW]
[ROW][C]106[/C][C]8613[/C][C]10671.2119350475[/C][C]-2058.21193504754[/C][/ROW]
[ROW][C]107[/C][C]10893[/C][C]9243.84047366282[/C][C]1649.15952633718[/C][/ROW]
[ROW][C]108[/C][C]11705[/C][C]10259.6444507969[/C][C]1445.3555492031[/C][/ROW]
[ROW][C]109[/C][C]12367[/C][C]11141.1406369818[/C][C]1225.85936301815[/C][/ROW]
[ROW][C]110[/C][C]11263[/C][C]11877.9877917651[/C][C]-614.98779176509[/C][/ROW]
[ROW][C]111[/C][C]10230[/C][C]11401.7079099191[/C][C]-1171.70790991905[/C][/ROW]
[ROW][C]112[/C][C]10821[/C][C]10558.5468204653[/C][C]262.453179534659[/C][/ROW]
[ROW][C]113[/C][C]11113[/C][C]10660.504714941[/C][C]452.495285059002[/C][/ROW]
[ROW][C]114[/C][C]10529[/C][C]10887.7012614745[/C][C]-358.701261474482[/C][/ROW]
[ROW][C]115[/C][C]8321[/C][C]10580.3154229017[/C][C]-2259.31542290172[/C][/ROW]
[ROW][C]116[/C][C]7359[/C][C]9020.41580585647[/C][C]-1661.41580585647[/C][/ROW]
[ROW][C]117[/C][C]8242[/C][C]7854.53488218465[/C][C]387.465117815347[/C][/ROW]
[ROW][C]118[/C][C]5813[/C][C]8038.87623898942[/C][C]-2225.87623898942[/C][/ROW]
[ROW][C]119[/C][C]8463[/C][C]6501.01320329827[/C][C]1961.98679670173[/C][/ROW]
[ROW][C]120[/C][C]10088[/C][C]7722.97184052354[/C][C]2365.02815947646[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235397&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235397&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
31892118922-1
41877218850.3409952404-78.34099524044
52024618727.71390650811518.28609349188
62016819657.2716684969510.728331503142
71906419922.8440698009-858.844069800856
81833019285.86174008-955.861740080043
91840118584.9443038836-183.944303883582
101840118392.72413212998.27586787011387
111848018327.1779684458152.822031554198
121862218356.888414606265.111585393966
131884318460.5982111958382.401788804178
141884318641.602810083201.397189917003
151870118703.3245168008-2.32451680082158
161833018630.7926491654-300.7926491654
172024618361.5688617241884.43113827602
182053819532.41795091571005.5820490843
192009720124.1013073929-27.1013073928843
201906420035.2414168306-971.241416830606
211950619324.188700455181.81129954501
221884319373.0032121974-530.0032121974
231914218952.7285727759189.27142722411
241928519006.4593441658278.540655834229
251943419119.0189620922314.981037907804
261906419255.5929652454-191.592965245381
271914219058.3322892583.6677107500218
281862219042.4697088559-420.469708855941
292024618694.3781694681551.62183053199
302075919645.90434082971113.0956591703
312031820308.43967807139.56032192868588
321950620243.7399757253-737.739975725268
332038919686.5658204028702.434179597225
341943420078.4732880367-644.473288036741
352031819582.7623238096735.23767619038
362024619996.2874518288249.712548171232
372046720089.8492095961377.150790403903
381965520267.393375545-612.393375545038
392053819792.8232263363745.176773663701
402046720212.8982668961254.101733103878
412179220309.35251842471482.64748157534
422149321215.4242655362277.575734463804
432031821327.3479956869-1009.34799568691
441972620591.1828624743-865.182862474343
452053819950.0232382118587.976761788173
461943420266.5027227424-832.502722742393
472024619646.8794661064599.120533893602
482038919970.7027494939418.297250506079
492068820175.3626284893512.637371510657
502002620442.1930962445-416.193096244486
512038920096.9198649223292.080135077693
522061020218.4020641122391.597935887828
532142220405.46696769711016.53303230289
542075921004.3670742372-245.367074237238
551987620771.669004475-895.669004474967
561892120110.4188675333-1189.41886753334
571980519255.5861727154549.413827284596
581737519546.6524998654-2171.65249986541
591855118044.5231663383506.476833661742
601921318307.2938103295905.706189670498
611987618833.15850008761042.8414999124
621892119449.3960119992-528.39601199919
631892119030.1805251579-109.18052515787
641892118887.230039427333.769960572703
651943418838.4846041749595.515395825052
661870119159.9320844164-458.932084416418
671773918786.4936564701-1047.49365647005
681693418025.1903512447-1091.19035124474
691751817235.0907161858282.909283814246
701523817350.5292807438-2112.52928074377
711663515887.3624300184747.637569981569
721744716309.0591470641137.94085293596
731759616987.9675852495608.032414750523
741678417317.6638405384-533.663840538364
751685516894.9768296172-39.9768296171678
761663516797.6319086272-162.631908627234
771737516619.4567067851755.543293214851
781685517046.3633330693-191.363333069279
791583016849.2539857709-1019.25398577088
801508916106.5607579448-1017.5607579448
811634215364.9833753151977.016624684871
821362115937.8419811542-2316.84198115417
831538814340.03208841931047.96791158069
841619314959.64793001981233.35206998022
851619315701.432814353491.567185646967
861523815954.3779293391-716.377929339138
871435515411.2814642591-1056.2814642591
881428414644.1869518747-360.186951874683
891508914335.822036257753.17796374305
901435514761.1698991612-406.169899161228
911295914422.5020024229-1463.50200242295
921199713387.0472171969-1390.04721719694
931303012399.9994850475630.00051495248
941060112744.172822928-2143.17282292805
951280911260.81173205341548.18826794658
961398412210.07516932911773.92483067093
971435513308.10007584741046.89992415264
981354313927.0121086496-384.012108649593
991251713602.9463013199-1085.94630131987
1001325112816.3025201208434.697479879242
1011354313031.770228331511.229771668986
1021332213297.673081090924.3269189090624
1031111313242.7046364375-2129.7046364375
1041008811768.2191445628-1680.21914456282
1051082110589.9467311879231.053268812149
106861310671.2119350475-2058.21193504754
107108939243.840473662821649.15952633718
1081170510259.64445079691445.3555492031
1091236711141.14063698181225.85936301815
1101126311877.9877917651-614.98779176509
1111023011401.7079099191-1171.70790991905
1121082110558.5468204653262.453179534659
1131111310660.504714941452.495285059002
1141052910887.7012614745-358.701261474482
115832110580.3154229017-2259.31542290172
11673599020.41580585647-1661.41580585647
11782427854.53488218465387.465117815347
11858138038.87623898942-2225.87623898942
11984636501.013203298271961.98679670173
120100887722.971840523542365.02815947646







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1219210.536654117927233.4169890112111187.6563192246
1229139.536654117926771.7038763925511507.3694318433
1239068.536654117926365.8968415661911771.1764666696
1248997.536654117925997.2213624346211997.8519458012
1258926.536654117925655.5243119480412197.5489962878
1268855.536654117925334.5777455609612376.4955626749
1278784.536654117925030.2349175941112538.8383906417
1288713.536654117924739.5699428853412687.5033653505
1298642.536654117924460.4269813446612824.6463268912
1308571.536654117924191.1632444389412951.9100637969
1318500.536654117923930.4927701555713070.5805380803
1328429.536654117923677.3865097663513181.6867984695

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 9210.53665411792 & 7233.41698901121 & 11187.6563192246 \tabularnewline
122 & 9139.53665411792 & 6771.70387639255 & 11507.3694318433 \tabularnewline
123 & 9068.53665411792 & 6365.89684156619 & 11771.1764666696 \tabularnewline
124 & 8997.53665411792 & 5997.22136243462 & 11997.8519458012 \tabularnewline
125 & 8926.53665411792 & 5655.52431194804 & 12197.5489962878 \tabularnewline
126 & 8855.53665411792 & 5334.57774556096 & 12376.4955626749 \tabularnewline
127 & 8784.53665411792 & 5030.23491759411 & 12538.8383906417 \tabularnewline
128 & 8713.53665411792 & 4739.56994288534 & 12687.5033653505 \tabularnewline
129 & 8642.53665411792 & 4460.42698134466 & 12824.6463268912 \tabularnewline
130 & 8571.53665411792 & 4191.16324443894 & 12951.9100637969 \tabularnewline
131 & 8500.53665411792 & 3930.49277015557 & 13070.5805380803 \tabularnewline
132 & 8429.53665411792 & 3677.38650976635 & 13181.6867984695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235397&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]9210.53665411792[/C][C]7233.41698901121[/C][C]11187.6563192246[/C][/ROW]
[ROW][C]122[/C][C]9139.53665411792[/C][C]6771.70387639255[/C][C]11507.3694318433[/C][/ROW]
[ROW][C]123[/C][C]9068.53665411792[/C][C]6365.89684156619[/C][C]11771.1764666696[/C][/ROW]
[ROW][C]124[/C][C]8997.53665411792[/C][C]5997.22136243462[/C][C]11997.8519458012[/C][/ROW]
[ROW][C]125[/C][C]8926.53665411792[/C][C]5655.52431194804[/C][C]12197.5489962878[/C][/ROW]
[ROW][C]126[/C][C]8855.53665411792[/C][C]5334.57774556096[/C][C]12376.4955626749[/C][/ROW]
[ROW][C]127[/C][C]8784.53665411792[/C][C]5030.23491759411[/C][C]12538.8383906417[/C][/ROW]
[ROW][C]128[/C][C]8713.53665411792[/C][C]4739.56994288534[/C][C]12687.5033653505[/C][/ROW]
[ROW][C]129[/C][C]8642.53665411792[/C][C]4460.42698134466[/C][C]12824.6463268912[/C][/ROW]
[ROW][C]130[/C][C]8571.53665411792[/C][C]4191.16324443894[/C][C]12951.9100637969[/C][/ROW]
[ROW][C]131[/C][C]8500.53665411792[/C][C]3930.49277015557[/C][C]13070.5805380803[/C][/ROW]
[ROW][C]132[/C][C]8429.53665411792[/C][C]3677.38650976635[/C][C]13181.6867984695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235397&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235397&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
1219210.536654117927233.4169890112111187.6563192246
1229139.536654117926771.7038763925511507.3694318433
1239068.536654117926365.8968415661911771.1764666696
1248997.536654117925997.2213624346211997.8519458012
1258926.536654117925655.5243119480412197.5489962878
1268855.536654117925334.5777455609612376.4955626749
1278784.536654117925030.2349175941112538.8383906417
1288713.536654117924739.5699428853412687.5033653505
1298642.536654117924460.4269813446612824.6463268912
1308571.536654117924191.1632444389412951.9100637969
1318500.536654117923930.4927701555713070.5805380803
1328429.536654117923677.3865097663513181.6867984695



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')