Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 27 Dec 2010 15:21:52 +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/Dec/27/t1293463383r6e83sp0ohveq2g.htm/, Retrieved Mon, 06 May 2024 21:20:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116024, Retrieved Mon, 06 May 2024 21:20:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-12-27 15:21:52] [63a115f47699ab31b1a302b9539c58a2] [Current]
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Dataseries X:
20503
22885
26217
26583
27751
28158
27373
28367
26851
26733
26849
26733
27951
29781
32914
33488
35652
36488
35387
35676
34844
32447
31068
29010
29812
30951
32974
32936
34012
32946
31948
30599
27691
25073
23406
22248
22896
25317
26558
26471
27543
26198
24725
25005
23462
20780
19815
19761
21454
23899
24939
23580
24562
24696
23785
23812
21917
19713
19282
18788
21453
24482
27474
27264
27349
30632
29429
30084
26290
24379
23335
21346
21106
24514
28353
30805
31348
34556
33855
34787
32529
29998
29257
28155
30466
35704
39327
39351
42234
43630
43722
43121
37985
37135
34646
33026
35087
38846
42013
43908
42868
44423
44167
43636
44382
42142
43452
36912
42413
45344
44873
47510
49554
47369
45998
48140
48441
44928
40454
38661
37246
36843
36424
37594
38144
38737
34560
36080
33508
35462
33374
32110
35533
35532
37903
36763
40399
44164
44496
43110
43880
43930
44327




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116024&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116024&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116024&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.955476297029324
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.955476297029324 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116024&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]0.955476297029324[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116024&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116024&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
alpha0.955476297029324
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132795123606.75852272734344.24147727272
142978128949.1199494997831.880050500306
153291432239.3782863910674.621713609042
163348832886.8383432057601.161656794298
173565235211.3590569555440.640943044462
183648836197.7143668685290.285633131498
193538733596.78374202711790.21625797287
203567635703.6262764101-27.6262764100757
213484433594.85502412511249.14497587493
223244734103.6334401268-1656.63344012683
233106832019.8427885528-951.842788552829
242901030318.0878989256-1308.08789892564
252981229798.662634238313.3373657617267
263095130846.5645008638104.435499136187
273297433434.7650880421-460.765088042121
283293632994.1192541694-58.1192541694181
293401234681.5657078299-669.565707829883
303294634600.4505028695-1654.45050286947
313194830208.15306171981739.84693828016
323059932185.9318239906-1586.93182399058
332769128644.1276651643-953.127665164306
342507326919.3107579642-1846.31075796425
352340624685.6678147397-1279.66781473968
362224822654.8225315389-406.822531538946
372289623055.3697087059-159.369708705879
382531723942.31008557991374.68991442011
392655827719.0438346965-1161.04383469645
402647126627.2255405919-156.225540591859
412754328193.7099027009-650.709902700863
422619828086.7602545280-1888.76025452795
432472523621.71209056971103.28790943032
442500524843.1532796539161.846720346100
452346223000.4848768039461.515123196074
462078022587.5578039234-1807.55780392343
471981520416.1714318193-601.17143181929
481976119072.4756642477688.524335752296
492145420530.6183261198923.38167388018
502389922520.40399962991378.59600037009
512493926187.9696650275-1248.96966502745
522358025056.8785554112-1476.87855541118
532456225339.4939903978-777.49399039782
542469625056.2825654625-360.282565462487
552378522184.87566767051600.12433232954
562381223839.1158344686-27.1158344685791
572191721829.240536425387.7594635747373
581971320958.1712608702-1245.17126087015
591928219377.8446889211-95.844688921119
601878818574.3986777217213.601322278340
612145319589.22037566901863.77962433104
622448222497.80182807041984.19817192957
632747426627.0170606004846.982939399564
642726427488.4116364712-224.411636471235
652734928998.8687159533-1649.86871595327
663063227900.69971618202731.30028381796
672942928070.51152559881358.48847440118
683008429421.4235997856662.576400214424
692629028075.6475578758-1785.64755787580
702437925355.2352669807-976.235266980722
712333524083.0429375168-748.042937516828
722134622670.2146411082-1324.21464110823
732110622289.1616854156-1183.16168541560
742451422291.82441756012222.17558243989
752835326597.78839183421755.21160816575
763080528279.27147913322525.72852086683
773134832353.9556648559-1005.95566485592
783455632066.09618996622489.90381003381
793385531944.13672525861910.86327474136
803478733791.8452457619995.154754238058
813252932654.8359417111-125.835941711081
822999831556.3723400160-1558.37234001595
832925729738.1218031421-481.121803142105
842815528554.6770260139-399.677026013924
853046629063.27804715831402.72195284168
863570431688.30952756264015.69047243741
873932737687.14350230991639.85649769007
883935139292.713781963158.2862180368757
894223440852.57167537301381.42832462696
904363043001.4496232287628.55037677128
914372241075.23004384332646.76995615667
924312143585.3092210899-464.309221089861
933798541003.9060254657-3018.90602546565
943713537077.400708005657.599291994411
953464636851.1359451182-2205.13594511821
963302634024.0627426539-998.062742653878
973508734041.16987183711045.83012816290
983884636441.53870739552404.46129260454
994201340795.10046553121217.89953446879
1004390841927.08350310151980.91649689853
1014286845382.8802420564-2514.88024205639
1024442343775.4067944103647.59320558967
1034416741957.24079567152209.75920432855
1044363643911.2497927933-275.249792793271
1054438241396.74829030852985.25170969150
1064214243344.0507813587-1202.05078135866
1074345241813.47487923271638.52512076731
1083691242712.6720877668-5800.67208776683
1094241338232.00150288724180.99849711277
1104534443688.44069258561655.55930741443
1114487347273.6142317984-2400.61423179836
1124751044982.16547582292527.83452417714
1134955448760.3599076388793.640092361231
1144736950454.9042462039-3085.90424620392
1154599845139.0233421756858.97665782438
1164814045691.74983120452448.25016879552
1174844145924.65758741022516.34241258985
1184492847237.4941472631-2309.49414726311
1194045444775.255316445-4321.25531644498
1203866139648.8029748707-987.802974870654
1213724640211.1356843402-2965.13568434021
1223684338727.1711439165-1884.17114391654
1233642438749.6202731522-2325.62027315225
1243759436749.2592556008844.740744399249
1253814438842.0847173858-698.08471738582
1263873738938.5896787552-201.589678755248
1273456036554.2436827262-1994.24368272619
1283608034451.54610789871628.45389210132
1293350833904.1896721675-396.189672167457
1303546232219.30674712153242.69325287851
1313337434972.4803170590-1598.48031705896
1323211032595.9925914652-485.992591465169
1333553333549.75505365121983.24494634876
1343553236841.9794586496-1309.97945864956
1353790337393.4001832024509.599816797563
1363676338243.1809707146-1480.18097071461
1374039938045.90653866352353.09346133649
1384416441079.84572544163084.15427455839
1394449641755.13460050922740.86539949083
1404311044338.0174283625-1228.01742836252
1414388040971.22572410702908.77427589295
1424393042606.17405646911323.82594353094
1434432743310.36842112311016.63157887689

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 27951 & 23606.7585227273 & 4344.24147727272 \tabularnewline
14 & 29781 & 28949.1199494997 & 831.880050500306 \tabularnewline
15 & 32914 & 32239.3782863910 & 674.621713609042 \tabularnewline
16 & 33488 & 32886.8383432057 & 601.161656794298 \tabularnewline
17 & 35652 & 35211.3590569555 & 440.640943044462 \tabularnewline
18 & 36488 & 36197.7143668685 & 290.285633131498 \tabularnewline
19 & 35387 & 33596.7837420271 & 1790.21625797287 \tabularnewline
20 & 35676 & 35703.6262764101 & -27.6262764100757 \tabularnewline
21 & 34844 & 33594.8550241251 & 1249.14497587493 \tabularnewline
22 & 32447 & 34103.6334401268 & -1656.63344012683 \tabularnewline
23 & 31068 & 32019.8427885528 & -951.842788552829 \tabularnewline
24 & 29010 & 30318.0878989256 & -1308.08789892564 \tabularnewline
25 & 29812 & 29798.6626342383 & 13.3373657617267 \tabularnewline
26 & 30951 & 30846.5645008638 & 104.435499136187 \tabularnewline
27 & 32974 & 33434.7650880421 & -460.765088042121 \tabularnewline
28 & 32936 & 32994.1192541694 & -58.1192541694181 \tabularnewline
29 & 34012 & 34681.5657078299 & -669.565707829883 \tabularnewline
30 & 32946 & 34600.4505028695 & -1654.45050286947 \tabularnewline
31 & 31948 & 30208.1530617198 & 1739.84693828016 \tabularnewline
32 & 30599 & 32185.9318239906 & -1586.93182399058 \tabularnewline
33 & 27691 & 28644.1276651643 & -953.127665164306 \tabularnewline
34 & 25073 & 26919.3107579642 & -1846.31075796425 \tabularnewline
35 & 23406 & 24685.6678147397 & -1279.66781473968 \tabularnewline
36 & 22248 & 22654.8225315389 & -406.822531538946 \tabularnewline
37 & 22896 & 23055.3697087059 & -159.369708705879 \tabularnewline
38 & 25317 & 23942.3100855799 & 1374.68991442011 \tabularnewline
39 & 26558 & 27719.0438346965 & -1161.04383469645 \tabularnewline
40 & 26471 & 26627.2255405919 & -156.225540591859 \tabularnewline
41 & 27543 & 28193.7099027009 & -650.709902700863 \tabularnewline
42 & 26198 & 28086.7602545280 & -1888.76025452795 \tabularnewline
43 & 24725 & 23621.7120905697 & 1103.28790943032 \tabularnewline
44 & 25005 & 24843.1532796539 & 161.846720346100 \tabularnewline
45 & 23462 & 23000.4848768039 & 461.515123196074 \tabularnewline
46 & 20780 & 22587.5578039234 & -1807.55780392343 \tabularnewline
47 & 19815 & 20416.1714318193 & -601.17143181929 \tabularnewline
48 & 19761 & 19072.4756642477 & 688.524335752296 \tabularnewline
49 & 21454 & 20530.6183261198 & 923.38167388018 \tabularnewline
50 & 23899 & 22520.4039996299 & 1378.59600037009 \tabularnewline
51 & 24939 & 26187.9696650275 & -1248.96966502745 \tabularnewline
52 & 23580 & 25056.8785554112 & -1476.87855541118 \tabularnewline
53 & 24562 & 25339.4939903978 & -777.49399039782 \tabularnewline
54 & 24696 & 25056.2825654625 & -360.282565462487 \tabularnewline
55 & 23785 & 22184.8756676705 & 1600.12433232954 \tabularnewline
56 & 23812 & 23839.1158344686 & -27.1158344685791 \tabularnewline
57 & 21917 & 21829.2405364253 & 87.7594635747373 \tabularnewline
58 & 19713 & 20958.1712608702 & -1245.17126087015 \tabularnewline
59 & 19282 & 19377.8446889211 & -95.844688921119 \tabularnewline
60 & 18788 & 18574.3986777217 & 213.601322278340 \tabularnewline
61 & 21453 & 19589.2203756690 & 1863.77962433104 \tabularnewline
62 & 24482 & 22497.8018280704 & 1984.19817192957 \tabularnewline
63 & 27474 & 26627.0170606004 & 846.982939399564 \tabularnewline
64 & 27264 & 27488.4116364712 & -224.411636471235 \tabularnewline
65 & 27349 & 28998.8687159533 & -1649.86871595327 \tabularnewline
66 & 30632 & 27900.6997161820 & 2731.30028381796 \tabularnewline
67 & 29429 & 28070.5115255988 & 1358.48847440118 \tabularnewline
68 & 30084 & 29421.4235997856 & 662.576400214424 \tabularnewline
69 & 26290 & 28075.6475578758 & -1785.64755787580 \tabularnewline
70 & 24379 & 25355.2352669807 & -976.235266980722 \tabularnewline
71 & 23335 & 24083.0429375168 & -748.042937516828 \tabularnewline
72 & 21346 & 22670.2146411082 & -1324.21464110823 \tabularnewline
73 & 21106 & 22289.1616854156 & -1183.16168541560 \tabularnewline
74 & 24514 & 22291.8244175601 & 2222.17558243989 \tabularnewline
75 & 28353 & 26597.7883918342 & 1755.21160816575 \tabularnewline
76 & 30805 & 28279.2714791332 & 2525.72852086683 \tabularnewline
77 & 31348 & 32353.9556648559 & -1005.95566485592 \tabularnewline
78 & 34556 & 32066.0961899662 & 2489.90381003381 \tabularnewline
79 & 33855 & 31944.1367252586 & 1910.86327474136 \tabularnewline
80 & 34787 & 33791.8452457619 & 995.154754238058 \tabularnewline
81 & 32529 & 32654.8359417111 & -125.835941711081 \tabularnewline
82 & 29998 & 31556.3723400160 & -1558.37234001595 \tabularnewline
83 & 29257 & 29738.1218031421 & -481.121803142105 \tabularnewline
84 & 28155 & 28554.6770260139 & -399.677026013924 \tabularnewline
85 & 30466 & 29063.2780471583 & 1402.72195284168 \tabularnewline
86 & 35704 & 31688.3095275626 & 4015.69047243741 \tabularnewline
87 & 39327 & 37687.1435023099 & 1639.85649769007 \tabularnewline
88 & 39351 & 39292.7137819631 & 58.2862180368757 \tabularnewline
89 & 42234 & 40852.5716753730 & 1381.42832462696 \tabularnewline
90 & 43630 & 43001.4496232287 & 628.55037677128 \tabularnewline
91 & 43722 & 41075.2300438433 & 2646.76995615667 \tabularnewline
92 & 43121 & 43585.3092210899 & -464.309221089861 \tabularnewline
93 & 37985 & 41003.9060254657 & -3018.90602546565 \tabularnewline
94 & 37135 & 37077.4007080056 & 57.599291994411 \tabularnewline
95 & 34646 & 36851.1359451182 & -2205.13594511821 \tabularnewline
96 & 33026 & 34024.0627426539 & -998.062742653878 \tabularnewline
97 & 35087 & 34041.1698718371 & 1045.83012816290 \tabularnewline
98 & 38846 & 36441.5387073955 & 2404.46129260454 \tabularnewline
99 & 42013 & 40795.1004655312 & 1217.89953446879 \tabularnewline
100 & 43908 & 41927.0835031015 & 1980.91649689853 \tabularnewline
101 & 42868 & 45382.8802420564 & -2514.88024205639 \tabularnewline
102 & 44423 & 43775.4067944103 & 647.59320558967 \tabularnewline
103 & 44167 & 41957.2407956715 & 2209.75920432855 \tabularnewline
104 & 43636 & 43911.2497927933 & -275.249792793271 \tabularnewline
105 & 44382 & 41396.7482903085 & 2985.25170969150 \tabularnewline
106 & 42142 & 43344.0507813587 & -1202.05078135866 \tabularnewline
107 & 43452 & 41813.4748792327 & 1638.52512076731 \tabularnewline
108 & 36912 & 42712.6720877668 & -5800.67208776683 \tabularnewline
109 & 42413 & 38232.0015028872 & 4180.99849711277 \tabularnewline
110 & 45344 & 43688.4406925856 & 1655.55930741443 \tabularnewline
111 & 44873 & 47273.6142317984 & -2400.61423179836 \tabularnewline
112 & 47510 & 44982.1654758229 & 2527.83452417714 \tabularnewline
113 & 49554 & 48760.3599076388 & 793.640092361231 \tabularnewline
114 & 47369 & 50454.9042462039 & -3085.90424620392 \tabularnewline
115 & 45998 & 45139.0233421756 & 858.97665782438 \tabularnewline
116 & 48140 & 45691.7498312045 & 2448.25016879552 \tabularnewline
117 & 48441 & 45924.6575874102 & 2516.34241258985 \tabularnewline
118 & 44928 & 47237.4941472631 & -2309.49414726311 \tabularnewline
119 & 40454 & 44775.255316445 & -4321.25531644498 \tabularnewline
120 & 38661 & 39648.8029748707 & -987.802974870654 \tabularnewline
121 & 37246 & 40211.1356843402 & -2965.13568434021 \tabularnewline
122 & 36843 & 38727.1711439165 & -1884.17114391654 \tabularnewline
123 & 36424 & 38749.6202731522 & -2325.62027315225 \tabularnewline
124 & 37594 & 36749.2592556008 & 844.740744399249 \tabularnewline
125 & 38144 & 38842.0847173858 & -698.08471738582 \tabularnewline
126 & 38737 & 38938.5896787552 & -201.589678755248 \tabularnewline
127 & 34560 & 36554.2436827262 & -1994.24368272619 \tabularnewline
128 & 36080 & 34451.5461078987 & 1628.45389210132 \tabularnewline
129 & 33508 & 33904.1896721675 & -396.189672167457 \tabularnewline
130 & 35462 & 32219.3067471215 & 3242.69325287851 \tabularnewline
131 & 33374 & 34972.4803170590 & -1598.48031705896 \tabularnewline
132 & 32110 & 32595.9925914652 & -485.992591465169 \tabularnewline
133 & 35533 & 33549.7550536512 & 1983.24494634876 \tabularnewline
134 & 35532 & 36841.9794586496 & -1309.97945864956 \tabularnewline
135 & 37903 & 37393.4001832024 & 509.599816797563 \tabularnewline
136 & 36763 & 38243.1809707146 & -1480.18097071461 \tabularnewline
137 & 40399 & 38045.9065386635 & 2353.09346133649 \tabularnewline
138 & 44164 & 41079.8457254416 & 3084.15427455839 \tabularnewline
139 & 44496 & 41755.1346005092 & 2740.86539949083 \tabularnewline
140 & 43110 & 44338.0174283625 & -1228.01742836252 \tabularnewline
141 & 43880 & 40971.2257241070 & 2908.77427589295 \tabularnewline
142 & 43930 & 42606.1740564691 & 1323.82594353094 \tabularnewline
143 & 44327 & 43310.3684211231 & 1016.63157887689 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116024&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]27951[/C][C]23606.7585227273[/C][C]4344.24147727272[/C][/ROW]
[ROW][C]14[/C][C]29781[/C][C]28949.1199494997[/C][C]831.880050500306[/C][/ROW]
[ROW][C]15[/C][C]32914[/C][C]32239.3782863910[/C][C]674.621713609042[/C][/ROW]
[ROW][C]16[/C][C]33488[/C][C]32886.8383432057[/C][C]601.161656794298[/C][/ROW]
[ROW][C]17[/C][C]35652[/C][C]35211.3590569555[/C][C]440.640943044462[/C][/ROW]
[ROW][C]18[/C][C]36488[/C][C]36197.7143668685[/C][C]290.285633131498[/C][/ROW]
[ROW][C]19[/C][C]35387[/C][C]33596.7837420271[/C][C]1790.21625797287[/C][/ROW]
[ROW][C]20[/C][C]35676[/C][C]35703.6262764101[/C][C]-27.6262764100757[/C][/ROW]
[ROW][C]21[/C][C]34844[/C][C]33594.8550241251[/C][C]1249.14497587493[/C][/ROW]
[ROW][C]22[/C][C]32447[/C][C]34103.6334401268[/C][C]-1656.63344012683[/C][/ROW]
[ROW][C]23[/C][C]31068[/C][C]32019.8427885528[/C][C]-951.842788552829[/C][/ROW]
[ROW][C]24[/C][C]29010[/C][C]30318.0878989256[/C][C]-1308.08789892564[/C][/ROW]
[ROW][C]25[/C][C]29812[/C][C]29798.6626342383[/C][C]13.3373657617267[/C][/ROW]
[ROW][C]26[/C][C]30951[/C][C]30846.5645008638[/C][C]104.435499136187[/C][/ROW]
[ROW][C]27[/C][C]32974[/C][C]33434.7650880421[/C][C]-460.765088042121[/C][/ROW]
[ROW][C]28[/C][C]32936[/C][C]32994.1192541694[/C][C]-58.1192541694181[/C][/ROW]
[ROW][C]29[/C][C]34012[/C][C]34681.5657078299[/C][C]-669.565707829883[/C][/ROW]
[ROW][C]30[/C][C]32946[/C][C]34600.4505028695[/C][C]-1654.45050286947[/C][/ROW]
[ROW][C]31[/C][C]31948[/C][C]30208.1530617198[/C][C]1739.84693828016[/C][/ROW]
[ROW][C]32[/C][C]30599[/C][C]32185.9318239906[/C][C]-1586.93182399058[/C][/ROW]
[ROW][C]33[/C][C]27691[/C][C]28644.1276651643[/C][C]-953.127665164306[/C][/ROW]
[ROW][C]34[/C][C]25073[/C][C]26919.3107579642[/C][C]-1846.31075796425[/C][/ROW]
[ROW][C]35[/C][C]23406[/C][C]24685.6678147397[/C][C]-1279.66781473968[/C][/ROW]
[ROW][C]36[/C][C]22248[/C][C]22654.8225315389[/C][C]-406.822531538946[/C][/ROW]
[ROW][C]37[/C][C]22896[/C][C]23055.3697087059[/C][C]-159.369708705879[/C][/ROW]
[ROW][C]38[/C][C]25317[/C][C]23942.3100855799[/C][C]1374.68991442011[/C][/ROW]
[ROW][C]39[/C][C]26558[/C][C]27719.0438346965[/C][C]-1161.04383469645[/C][/ROW]
[ROW][C]40[/C][C]26471[/C][C]26627.2255405919[/C][C]-156.225540591859[/C][/ROW]
[ROW][C]41[/C][C]27543[/C][C]28193.7099027009[/C][C]-650.709902700863[/C][/ROW]
[ROW][C]42[/C][C]26198[/C][C]28086.7602545280[/C][C]-1888.76025452795[/C][/ROW]
[ROW][C]43[/C][C]24725[/C][C]23621.7120905697[/C][C]1103.28790943032[/C][/ROW]
[ROW][C]44[/C][C]25005[/C][C]24843.1532796539[/C][C]161.846720346100[/C][/ROW]
[ROW][C]45[/C][C]23462[/C][C]23000.4848768039[/C][C]461.515123196074[/C][/ROW]
[ROW][C]46[/C][C]20780[/C][C]22587.5578039234[/C][C]-1807.55780392343[/C][/ROW]
[ROW][C]47[/C][C]19815[/C][C]20416.1714318193[/C][C]-601.17143181929[/C][/ROW]
[ROW][C]48[/C][C]19761[/C][C]19072.4756642477[/C][C]688.524335752296[/C][/ROW]
[ROW][C]49[/C][C]21454[/C][C]20530.6183261198[/C][C]923.38167388018[/C][/ROW]
[ROW][C]50[/C][C]23899[/C][C]22520.4039996299[/C][C]1378.59600037009[/C][/ROW]
[ROW][C]51[/C][C]24939[/C][C]26187.9696650275[/C][C]-1248.96966502745[/C][/ROW]
[ROW][C]52[/C][C]23580[/C][C]25056.8785554112[/C][C]-1476.87855541118[/C][/ROW]
[ROW][C]53[/C][C]24562[/C][C]25339.4939903978[/C][C]-777.49399039782[/C][/ROW]
[ROW][C]54[/C][C]24696[/C][C]25056.2825654625[/C][C]-360.282565462487[/C][/ROW]
[ROW][C]55[/C][C]23785[/C][C]22184.8756676705[/C][C]1600.12433232954[/C][/ROW]
[ROW][C]56[/C][C]23812[/C][C]23839.1158344686[/C][C]-27.1158344685791[/C][/ROW]
[ROW][C]57[/C][C]21917[/C][C]21829.2405364253[/C][C]87.7594635747373[/C][/ROW]
[ROW][C]58[/C][C]19713[/C][C]20958.1712608702[/C][C]-1245.17126087015[/C][/ROW]
[ROW][C]59[/C][C]19282[/C][C]19377.8446889211[/C][C]-95.844688921119[/C][/ROW]
[ROW][C]60[/C][C]18788[/C][C]18574.3986777217[/C][C]213.601322278340[/C][/ROW]
[ROW][C]61[/C][C]21453[/C][C]19589.2203756690[/C][C]1863.77962433104[/C][/ROW]
[ROW][C]62[/C][C]24482[/C][C]22497.8018280704[/C][C]1984.19817192957[/C][/ROW]
[ROW][C]63[/C][C]27474[/C][C]26627.0170606004[/C][C]846.982939399564[/C][/ROW]
[ROW][C]64[/C][C]27264[/C][C]27488.4116364712[/C][C]-224.411636471235[/C][/ROW]
[ROW][C]65[/C][C]27349[/C][C]28998.8687159533[/C][C]-1649.86871595327[/C][/ROW]
[ROW][C]66[/C][C]30632[/C][C]27900.6997161820[/C][C]2731.30028381796[/C][/ROW]
[ROW][C]67[/C][C]29429[/C][C]28070.5115255988[/C][C]1358.48847440118[/C][/ROW]
[ROW][C]68[/C][C]30084[/C][C]29421.4235997856[/C][C]662.576400214424[/C][/ROW]
[ROW][C]69[/C][C]26290[/C][C]28075.6475578758[/C][C]-1785.64755787580[/C][/ROW]
[ROW][C]70[/C][C]24379[/C][C]25355.2352669807[/C][C]-976.235266980722[/C][/ROW]
[ROW][C]71[/C][C]23335[/C][C]24083.0429375168[/C][C]-748.042937516828[/C][/ROW]
[ROW][C]72[/C][C]21346[/C][C]22670.2146411082[/C][C]-1324.21464110823[/C][/ROW]
[ROW][C]73[/C][C]21106[/C][C]22289.1616854156[/C][C]-1183.16168541560[/C][/ROW]
[ROW][C]74[/C][C]24514[/C][C]22291.8244175601[/C][C]2222.17558243989[/C][/ROW]
[ROW][C]75[/C][C]28353[/C][C]26597.7883918342[/C][C]1755.21160816575[/C][/ROW]
[ROW][C]76[/C][C]30805[/C][C]28279.2714791332[/C][C]2525.72852086683[/C][/ROW]
[ROW][C]77[/C][C]31348[/C][C]32353.9556648559[/C][C]-1005.95566485592[/C][/ROW]
[ROW][C]78[/C][C]34556[/C][C]32066.0961899662[/C][C]2489.90381003381[/C][/ROW]
[ROW][C]79[/C][C]33855[/C][C]31944.1367252586[/C][C]1910.86327474136[/C][/ROW]
[ROW][C]80[/C][C]34787[/C][C]33791.8452457619[/C][C]995.154754238058[/C][/ROW]
[ROW][C]81[/C][C]32529[/C][C]32654.8359417111[/C][C]-125.835941711081[/C][/ROW]
[ROW][C]82[/C][C]29998[/C][C]31556.3723400160[/C][C]-1558.37234001595[/C][/ROW]
[ROW][C]83[/C][C]29257[/C][C]29738.1218031421[/C][C]-481.121803142105[/C][/ROW]
[ROW][C]84[/C][C]28155[/C][C]28554.6770260139[/C][C]-399.677026013924[/C][/ROW]
[ROW][C]85[/C][C]30466[/C][C]29063.2780471583[/C][C]1402.72195284168[/C][/ROW]
[ROW][C]86[/C][C]35704[/C][C]31688.3095275626[/C][C]4015.69047243741[/C][/ROW]
[ROW][C]87[/C][C]39327[/C][C]37687.1435023099[/C][C]1639.85649769007[/C][/ROW]
[ROW][C]88[/C][C]39351[/C][C]39292.7137819631[/C][C]58.2862180368757[/C][/ROW]
[ROW][C]89[/C][C]42234[/C][C]40852.5716753730[/C][C]1381.42832462696[/C][/ROW]
[ROW][C]90[/C][C]43630[/C][C]43001.4496232287[/C][C]628.55037677128[/C][/ROW]
[ROW][C]91[/C][C]43722[/C][C]41075.2300438433[/C][C]2646.76995615667[/C][/ROW]
[ROW][C]92[/C][C]43121[/C][C]43585.3092210899[/C][C]-464.309221089861[/C][/ROW]
[ROW][C]93[/C][C]37985[/C][C]41003.9060254657[/C][C]-3018.90602546565[/C][/ROW]
[ROW][C]94[/C][C]37135[/C][C]37077.4007080056[/C][C]57.599291994411[/C][/ROW]
[ROW][C]95[/C][C]34646[/C][C]36851.1359451182[/C][C]-2205.13594511821[/C][/ROW]
[ROW][C]96[/C][C]33026[/C][C]34024.0627426539[/C][C]-998.062742653878[/C][/ROW]
[ROW][C]97[/C][C]35087[/C][C]34041.1698718371[/C][C]1045.83012816290[/C][/ROW]
[ROW][C]98[/C][C]38846[/C][C]36441.5387073955[/C][C]2404.46129260454[/C][/ROW]
[ROW][C]99[/C][C]42013[/C][C]40795.1004655312[/C][C]1217.89953446879[/C][/ROW]
[ROW][C]100[/C][C]43908[/C][C]41927.0835031015[/C][C]1980.91649689853[/C][/ROW]
[ROW][C]101[/C][C]42868[/C][C]45382.8802420564[/C][C]-2514.88024205639[/C][/ROW]
[ROW][C]102[/C][C]44423[/C][C]43775.4067944103[/C][C]647.59320558967[/C][/ROW]
[ROW][C]103[/C][C]44167[/C][C]41957.2407956715[/C][C]2209.75920432855[/C][/ROW]
[ROW][C]104[/C][C]43636[/C][C]43911.2497927933[/C][C]-275.249792793271[/C][/ROW]
[ROW][C]105[/C][C]44382[/C][C]41396.7482903085[/C][C]2985.25170969150[/C][/ROW]
[ROW][C]106[/C][C]42142[/C][C]43344.0507813587[/C][C]-1202.05078135866[/C][/ROW]
[ROW][C]107[/C][C]43452[/C][C]41813.4748792327[/C][C]1638.52512076731[/C][/ROW]
[ROW][C]108[/C][C]36912[/C][C]42712.6720877668[/C][C]-5800.67208776683[/C][/ROW]
[ROW][C]109[/C][C]42413[/C][C]38232.0015028872[/C][C]4180.99849711277[/C][/ROW]
[ROW][C]110[/C][C]45344[/C][C]43688.4406925856[/C][C]1655.55930741443[/C][/ROW]
[ROW][C]111[/C][C]44873[/C][C]47273.6142317984[/C][C]-2400.61423179836[/C][/ROW]
[ROW][C]112[/C][C]47510[/C][C]44982.1654758229[/C][C]2527.83452417714[/C][/ROW]
[ROW][C]113[/C][C]49554[/C][C]48760.3599076388[/C][C]793.640092361231[/C][/ROW]
[ROW][C]114[/C][C]47369[/C][C]50454.9042462039[/C][C]-3085.90424620392[/C][/ROW]
[ROW][C]115[/C][C]45998[/C][C]45139.0233421756[/C][C]858.97665782438[/C][/ROW]
[ROW][C]116[/C][C]48140[/C][C]45691.7498312045[/C][C]2448.25016879552[/C][/ROW]
[ROW][C]117[/C][C]48441[/C][C]45924.6575874102[/C][C]2516.34241258985[/C][/ROW]
[ROW][C]118[/C][C]44928[/C][C]47237.4941472631[/C][C]-2309.49414726311[/C][/ROW]
[ROW][C]119[/C][C]40454[/C][C]44775.255316445[/C][C]-4321.25531644498[/C][/ROW]
[ROW][C]120[/C][C]38661[/C][C]39648.8029748707[/C][C]-987.802974870654[/C][/ROW]
[ROW][C]121[/C][C]37246[/C][C]40211.1356843402[/C][C]-2965.13568434021[/C][/ROW]
[ROW][C]122[/C][C]36843[/C][C]38727.1711439165[/C][C]-1884.17114391654[/C][/ROW]
[ROW][C]123[/C][C]36424[/C][C]38749.6202731522[/C][C]-2325.62027315225[/C][/ROW]
[ROW][C]124[/C][C]37594[/C][C]36749.2592556008[/C][C]844.740744399249[/C][/ROW]
[ROW][C]125[/C][C]38144[/C][C]38842.0847173858[/C][C]-698.08471738582[/C][/ROW]
[ROW][C]126[/C][C]38737[/C][C]38938.5896787552[/C][C]-201.589678755248[/C][/ROW]
[ROW][C]127[/C][C]34560[/C][C]36554.2436827262[/C][C]-1994.24368272619[/C][/ROW]
[ROW][C]128[/C][C]36080[/C][C]34451.5461078987[/C][C]1628.45389210132[/C][/ROW]
[ROW][C]129[/C][C]33508[/C][C]33904.1896721675[/C][C]-396.189672167457[/C][/ROW]
[ROW][C]130[/C][C]35462[/C][C]32219.3067471215[/C][C]3242.69325287851[/C][/ROW]
[ROW][C]131[/C][C]33374[/C][C]34972.4803170590[/C][C]-1598.48031705896[/C][/ROW]
[ROW][C]132[/C][C]32110[/C][C]32595.9925914652[/C][C]-485.992591465169[/C][/ROW]
[ROW][C]133[/C][C]35533[/C][C]33549.7550536512[/C][C]1983.24494634876[/C][/ROW]
[ROW][C]134[/C][C]35532[/C][C]36841.9794586496[/C][C]-1309.97945864956[/C][/ROW]
[ROW][C]135[/C][C]37903[/C][C]37393.4001832024[/C][C]509.599816797563[/C][/ROW]
[ROW][C]136[/C][C]36763[/C][C]38243.1809707146[/C][C]-1480.18097071461[/C][/ROW]
[ROW][C]137[/C][C]40399[/C][C]38045.9065386635[/C][C]2353.09346133649[/C][/ROW]
[ROW][C]138[/C][C]44164[/C][C]41079.8457254416[/C][C]3084.15427455839[/C][/ROW]
[ROW][C]139[/C][C]44496[/C][C]41755.1346005092[/C][C]2740.86539949083[/C][/ROW]
[ROW][C]140[/C][C]43110[/C][C]44338.0174283625[/C][C]-1228.01742836252[/C][/ROW]
[ROW][C]141[/C][C]43880[/C][C]40971.2257241070[/C][C]2908.77427589295[/C][/ROW]
[ROW][C]142[/C][C]43930[/C][C]42606.1740564691[/C][C]1323.82594353094[/C][/ROW]
[ROW][C]143[/C][C]44327[/C][C]43310.3684211231[/C][C]1016.63157887689[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116024&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116024&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
132795123606.75852272734344.24147727272
142978128949.1199494997831.880050500306
153291432239.3782863910674.621713609042
163348832886.8383432057601.161656794298
173565235211.3590569555440.640943044462
183648836197.7143668685290.285633131498
193538733596.78374202711790.21625797287
203567635703.6262764101-27.6262764100757
213484433594.85502412511249.14497587493
223244734103.6334401268-1656.63344012683
233106832019.8427885528-951.842788552829
242901030318.0878989256-1308.08789892564
252981229798.662634238313.3373657617267
263095130846.5645008638104.435499136187
273297433434.7650880421-460.765088042121
283293632994.1192541694-58.1192541694181
293401234681.5657078299-669.565707829883
303294634600.4505028695-1654.45050286947
313194830208.15306171981739.84693828016
323059932185.9318239906-1586.93182399058
332769128644.1276651643-953.127665164306
342507326919.3107579642-1846.31075796425
352340624685.6678147397-1279.66781473968
362224822654.8225315389-406.822531538946
372289623055.3697087059-159.369708705879
382531723942.31008557991374.68991442011
392655827719.0438346965-1161.04383469645
402647126627.2255405919-156.225540591859
412754328193.7099027009-650.709902700863
422619828086.7602545280-1888.76025452795
432472523621.71209056971103.28790943032
442500524843.1532796539161.846720346100
452346223000.4848768039461.515123196074
462078022587.5578039234-1807.55780392343
471981520416.1714318193-601.17143181929
481976119072.4756642477688.524335752296
492145420530.6183261198923.38167388018
502389922520.40399962991378.59600037009
512493926187.9696650275-1248.96966502745
522358025056.8785554112-1476.87855541118
532456225339.4939903978-777.49399039782
542469625056.2825654625-360.282565462487
552378522184.87566767051600.12433232954
562381223839.1158344686-27.1158344685791
572191721829.240536425387.7594635747373
581971320958.1712608702-1245.17126087015
591928219377.8446889211-95.844688921119
601878818574.3986777217213.601322278340
612145319589.22037566901863.77962433104
622448222497.80182807041984.19817192957
632747426627.0170606004846.982939399564
642726427488.4116364712-224.411636471235
652734928998.8687159533-1649.86871595327
663063227900.69971618202731.30028381796
672942928070.51152559881358.48847440118
683008429421.4235997856662.576400214424
692629028075.6475578758-1785.64755787580
702437925355.2352669807-976.235266980722
712333524083.0429375168-748.042937516828
722134622670.2146411082-1324.21464110823
732110622289.1616854156-1183.16168541560
742451422291.82441756012222.17558243989
752835326597.78839183421755.21160816575
763080528279.27147913322525.72852086683
773134832353.9556648559-1005.95566485592
783455632066.09618996622489.90381003381
793385531944.13672525861910.86327474136
803478733791.8452457619995.154754238058
813252932654.8359417111-125.835941711081
822999831556.3723400160-1558.37234001595
832925729738.1218031421-481.121803142105
842815528554.6770260139-399.677026013924
853046629063.27804715831402.72195284168
863570431688.30952756264015.69047243741
873932737687.14350230991639.85649769007
883935139292.713781963158.2862180368757
894223440852.57167537301381.42832462696
904363043001.4496232287628.55037677128
914372241075.23004384332646.76995615667
924312143585.3092210899-464.309221089861
933798541003.9060254657-3018.90602546565
943713537077.400708005657.599291994411
953464636851.1359451182-2205.13594511821
963302634024.0627426539-998.062742653878
973508734041.16987183711045.83012816290
983884636441.53870739552404.46129260454
994201340795.10046553121217.89953446879
1004390841927.08350310151980.91649689853
1014286845382.8802420564-2514.88024205639
1024442343775.4067944103647.59320558967
1034416741957.24079567152209.75920432855
1044363643911.2497927933-275.249792793271
1054438241396.74829030852985.25170969150
1064214243344.0507813587-1202.05078135866
1074345241813.47487923271638.52512076731
1083691242712.6720877668-5800.67208776683
1094241338232.00150288724180.99849711277
1104534443688.44069258561655.55930741443
1114487347273.6142317984-2400.61423179836
1124751044982.16547582292527.83452417714
1134955448760.3599076388793.640092361231
1144736950454.9042462039-3085.90424620392
1154599845139.0233421756858.97665782438
1164814045691.74983120452448.25016879552
1174844145924.65758741022516.34241258985
1184492847237.4941472631-2309.49414726311
1194045444775.255316445-4321.25531644498
1203866139648.8029748707-987.802974870654
1213724640211.1356843402-2965.13568434021
1223684338727.1711439165-1884.17114391654
1233642438749.6202731522-2325.62027315225
1243759436749.2592556008844.740744399249
1253814438842.0847173858-698.08471738582
1263873738938.5896787552-201.589678755248
1273456036554.2436827262-1994.24368272619
1283608034451.54610789871628.45389210132
1293350833904.1896721675-396.189672167457
1303546232219.30674712153242.69325287851
1313337434972.4803170590-1598.48031705896
1323211032595.9925914652-485.992591465169
1333553333549.75505365121983.24494634876
1343553236841.9794586496-1309.97945864956
1353790337393.4001832024509.599816797563
1363676338243.1809707146-1480.18097071461
1374039938045.90653866352353.09346133649
1384416441079.84572544163084.15427455839
1394449641755.13460050922740.86539949083
1404311044338.0174283625-1228.01742836252
1414388040971.22572410702908.77427589295
1424393042606.17405646911323.82594353094
1434432743310.36842112311016.63157887689







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
14443482.090199228340030.888323868146933.2920745885
14545010.146661788940236.827595332149783.4657282457
14646260.800984123840459.21883475252062.3831334957
14748144.890438203341471.650148687354818.1307277193
14848419.168271034940975.653208423155862.6833336468
14949806.843244033241665.608877363857948.0776107027
15050625.00693831141841.301709949359408.7121666727
15148338.175015749738955.890748874257720.4592826252
15248125.51656088938180.616431165858070.4166906122
15346116.251686864735638.903782176256593.5995915531
15444901.367376428433917.351733614155885.3830192426
1554432732858.679278669555795.3207213305

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
144 & 43482.0901992283 & 40030.8883238681 & 46933.2920745885 \tabularnewline
145 & 45010.1466617889 & 40236.8275953321 & 49783.4657282457 \tabularnewline
146 & 46260.8009841238 & 40459.218834752 & 52062.3831334957 \tabularnewline
147 & 48144.8904382033 & 41471.6501486873 & 54818.1307277193 \tabularnewline
148 & 48419.1682710349 & 40975.6532084231 & 55862.6833336468 \tabularnewline
149 & 49806.8432440332 & 41665.6088773638 & 57948.0776107027 \tabularnewline
150 & 50625.006938311 & 41841.3017099493 & 59408.7121666727 \tabularnewline
151 & 48338.1750157497 & 38955.8907488742 & 57720.4592826252 \tabularnewline
152 & 48125.516560889 & 38180.6164311658 & 58070.4166906122 \tabularnewline
153 & 46116.2516868647 & 35638.9037821762 & 56593.5995915531 \tabularnewline
154 & 44901.3673764284 & 33917.3517336141 & 55885.3830192426 \tabularnewline
155 & 44327 & 32858.6792786695 & 55795.3207213305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116024&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]144[/C][C]43482.0901992283[/C][C]40030.8883238681[/C][C]46933.2920745885[/C][/ROW]
[ROW][C]145[/C][C]45010.1466617889[/C][C]40236.8275953321[/C][C]49783.4657282457[/C][/ROW]
[ROW][C]146[/C][C]46260.8009841238[/C][C]40459.218834752[/C][C]52062.3831334957[/C][/ROW]
[ROW][C]147[/C][C]48144.8904382033[/C][C]41471.6501486873[/C][C]54818.1307277193[/C][/ROW]
[ROW][C]148[/C][C]48419.1682710349[/C][C]40975.6532084231[/C][C]55862.6833336468[/C][/ROW]
[ROW][C]149[/C][C]49806.8432440332[/C][C]41665.6088773638[/C][C]57948.0776107027[/C][/ROW]
[ROW][C]150[/C][C]50625.006938311[/C][C]41841.3017099493[/C][C]59408.7121666727[/C][/ROW]
[ROW][C]151[/C][C]48338.1750157497[/C][C]38955.8907488742[/C][C]57720.4592826252[/C][/ROW]
[ROW][C]152[/C][C]48125.516560889[/C][C]38180.6164311658[/C][C]58070.4166906122[/C][/ROW]
[ROW][C]153[/C][C]46116.2516868647[/C][C]35638.9037821762[/C][C]56593.5995915531[/C][/ROW]
[ROW][C]154[/C][C]44901.3673764284[/C][C]33917.3517336141[/C][C]55885.3830192426[/C][/ROW]
[ROW][C]155[/C][C]44327[/C][C]32858.6792786695[/C][C]55795.3207213305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116024&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116024&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
14443482.090199228340030.888323868146933.2920745885
14545010.146661788940236.827595332149783.4657282457
14646260.800984123840459.21883475252062.3831334957
14748144.890438203341471.650148687354818.1307277193
14848419.168271034940975.653208423155862.6833336468
14949806.843244033241665.608877363857948.0776107027
15050625.00693831141841.301709949359408.7121666727
15148338.175015749738955.890748874257720.4592826252
15248125.51656088938180.616431165858070.4166906122
15346116.251686864735638.903782176256593.5995915531
15444901.367376428433917.351733614155885.3830192426
1554432732858.679278669555795.3207213305



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')